diff options
Diffstat (limited to 'openssl-1.1.0h/crypto/ec')
42 files changed, 49348 insertions, 0 deletions
diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv4.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv4.pl new file mode 100755 index 0000000..2314b75 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv4.pl @@ -0,0 +1,1865 @@ +#! /usr/bin/env perl +# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +# ==================================================================== +# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL +# project. The module is, however, dual licensed under OpenSSL and +# CRYPTOGAMS licenses depending on where you obtain it. For further +# details see http://www.openssl.org/~appro/cryptogams/. +# ==================================================================== +# +# ECP_NISTZ256 module for ARMv4. +# +# October 2014. +# +# Original ECP_NISTZ256 submission targeting x86_64 is detailed in +# http://eprint.iacr.org/2013/816. In the process of adaptation +# original .c module was made 32-bit savvy in order to make this +# implementation possible. +# +# with/without -DECP_NISTZ256_ASM +# Cortex-A8 +53-170% +# Cortex-A9 +76-205% +# Cortex-A15 +100-316% +# Snapdragon S4 +66-187% +# +# Ranges denote minimum and maximum improvement coefficients depending +# on benchmark. Lower coefficients are for ECDSA sign, server-side +# operation. Keep in mind that +200% means 3x improvement. + +$flavour = shift; +if ($flavour=~/\w[\w\-]*\.\w+$/) { $output=$flavour; undef $flavour; } +else { while (($output=shift) && ($output!~/\w[\w\-]*\.\w+$/)) {} } + +if ($flavour && $flavour ne "void") { + $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; + ( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or + ( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or + die "can't locate arm-xlate.pl"; + + open STDOUT,"| \"$^X\" $xlate $flavour $output"; +} else { + open STDOUT,">$output"; +} + +$code.=<<___; +#include "arm_arch.h" + +.text +#if defined(__thumb2__) +.syntax unified +.thumb +#else +.code 32 +#endif +___ +######################################################################## +# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7 +# +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +open TABLE,"<ecp_nistz256_table.c" or +open TABLE,"<${dir}../ecp_nistz256_table.c" or +die "failed to open ecp_nistz256_table.c:",$!; + +use integer; + +foreach(<TABLE>) { + s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo; +} +close TABLE; + +# See ecp_nistz256_table.c for explanation for why it's 64*16*37. +# 64*16*37-1 is because $#arr returns last valid index or @arr, not +# amount of elements. +die "insane number of elements" if ($#arr != 64*16*37-1); + +$code.=<<___; +.globl ecp_nistz256_precomputed +.type ecp_nistz256_precomputed,%object +.align 12 +ecp_nistz256_precomputed: +___ +######################################################################## +# this conversion smashes P256_POINT_AFFINE by individual bytes with +# 64 byte interval, similar to +# 1111222233334444 +# 1234123412341234 +for(1..37) { + @tbl = splice(@arr,0,64*16); + for($i=0;$i<64;$i++) { + undef @line; + for($j=0;$j<64;$j++) { + push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff; + } + $code.=".byte\t"; + $code.=join(',',map { sprintf "0x%02x",$_} @line); + $code.="\n"; + } +} +$code.=<<___; +.size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed +.align 5 +.LRR: @ 2^512 mod P precomputed for NIST P256 polynomial +.long 0x00000003, 0x00000000, 0xffffffff, 0xfffffffb +.long 0xfffffffe, 0xffffffff, 0xfffffffd, 0x00000004 +.Lone: +.long 1,0,0,0,0,0,0,0 +.asciz "ECP_NISTZ256 for ARMv4, CRYPTOGAMS by <appro\@openssl.org>" +.align 6 +___ + +######################################################################## +# common register layout, note that $t2 is link register, so that if +# internal subroutine uses $t2, then it has to offload lr... + +($r_ptr,$a_ptr,$b_ptr,$ff,$a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7,$t1,$t2)= + map("r$_",(0..12,14)); +($t0,$t3)=($ff,$a_ptr); + +$code.=<<___; +@ void ecp_nistz256_to_mont(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_to_mont +.type ecp_nistz256_to_mont,%function +ecp_nistz256_to_mont: + adr $b_ptr,.LRR + b .Lecp_nistz256_mul_mont +.size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont + +@ void ecp_nistz256_from_mont(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_from_mont +.type ecp_nistz256_from_mont,%function +ecp_nistz256_from_mont: + adr $b_ptr,.Lone + b .Lecp_nistz256_mul_mont +.size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont + +@ void ecp_nistz256_mul_by_2(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_mul_by_2 +.type ecp_nistz256_mul_by_2,%function +.align 4 +ecp_nistz256_mul_by_2: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_mul_by_2 +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2 + +.type __ecp_nistz256_mul_by_2,%function +.align 4 +__ecp_nistz256_mul_by_2: + ldr $a0,[$a_ptr,#0] + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + adds $a0,$a0,$a0 @ a[0:7]+=a[0:7], i.e. add with itself + ldr $a3,[$a_ptr,#12] + adcs $a1,$a1,$a1 + ldr $a4,[$a_ptr,#16] + adcs $a2,$a2,$a2 + ldr $a5,[$a_ptr,#20] + adcs $a3,$a3,$a3 + ldr $a6,[$a_ptr,#24] + adcs $a4,$a4,$a4 + ldr $a7,[$a_ptr,#28] + adcs $a5,$a5,$a5 + adcs $a6,$a6,$a6 + mov $ff,#0 + adcs $a7,$a7,$a7 + adc $ff,$ff,#0 + + b .Lreduce_by_sub +.size __ecp_nistz256_mul_by_2,.-__ecp_nistz256_mul_by_2 + +@ void ecp_nistz256_add(BN_ULONG r0[8],const BN_ULONG r1[8], +@ const BN_ULONG r2[8]); +.globl ecp_nistz256_add +.type ecp_nistz256_add,%function +.align 4 +ecp_nistz256_add: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_add +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_add,.-ecp_nistz256_add + +.type __ecp_nistz256_add,%function +.align 4 +__ecp_nistz256_add: + str lr,[sp,#-4]! @ push lr + + ldr $a0,[$a_ptr,#0] + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + ldr $a3,[$a_ptr,#12] + ldr $a4,[$a_ptr,#16] + ldr $t0,[$b_ptr,#0] + ldr $a5,[$a_ptr,#20] + ldr $t1,[$b_ptr,#4] + ldr $a6,[$a_ptr,#24] + ldr $t2,[$b_ptr,#8] + ldr $a7,[$a_ptr,#28] + ldr $t3,[$b_ptr,#12] + adds $a0,$a0,$t0 + ldr $t0,[$b_ptr,#16] + adcs $a1,$a1,$t1 + ldr $t1,[$b_ptr,#20] + adcs $a2,$a2,$t2 + ldr $t2,[$b_ptr,#24] + adcs $a3,$a3,$t3 + ldr $t3,[$b_ptr,#28] + adcs $a4,$a4,$t0 + adcs $a5,$a5,$t1 + adcs $a6,$a6,$t2 + mov $ff,#0 + adcs $a7,$a7,$t3 + adc $ff,$ff,#0 + ldr lr,[sp],#4 @ pop lr + +.Lreduce_by_sub: + + @ if a+b >= modulus, subtract modulus. + @ + @ But since comparison implies subtraction, we subtract + @ modulus and then add it back if subraction borrowed. + + subs $a0,$a0,#-1 + sbcs $a1,$a1,#-1 + sbcs $a2,$a2,#-1 + sbcs $a3,$a3,#0 + sbcs $a4,$a4,#0 + sbcs $a5,$a5,#0 + sbcs $a6,$a6,#1 + sbcs $a7,$a7,#-1 + sbc $ff,$ff,#0 + + @ Note that because mod has special form, i.e. consists of + @ 0xffffffff, 1 and 0s, we can conditionally synthesize it by + @ using value of borrow as a whole or extracting single bit. + @ Follow $ff register... + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + str $a0,[$r_ptr,#0] + adcs $a2,$a2,$ff + str $a1,[$r_ptr,#4] + adcs $a3,$a3,#0 + str $a2,[$r_ptr,#8] + adcs $a4,$a4,#0 + str $a3,[$r_ptr,#12] + adcs $a5,$a5,#0 + str $a4,[$r_ptr,#16] + adcs $a6,$a6,$ff,lsr#31 + str $a5,[$r_ptr,#20] + adcs $a7,$a7,$ff + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_add,.-__ecp_nistz256_add + +@ void ecp_nistz256_mul_by_3(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_mul_by_3 +.type ecp_nistz256_mul_by_3,%function +.align 4 +ecp_nistz256_mul_by_3: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_mul_by_3 +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3 + +.type __ecp_nistz256_mul_by_3,%function +.align 4 +__ecp_nistz256_mul_by_3: + str lr,[sp,#-4]! @ push lr + + @ As multiplication by 3 is performed as 2*n+n, below are inline + @ copies of __ecp_nistz256_mul_by_2 and __ecp_nistz256_add, see + @ corresponding subroutines for details. + + ldr $a0,[$a_ptr,#0] + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + adds $a0,$a0,$a0 @ a[0:7]+=a[0:7] + ldr $a3,[$a_ptr,#12] + adcs $a1,$a1,$a1 + ldr $a4,[$a_ptr,#16] + adcs $a2,$a2,$a2 + ldr $a5,[$a_ptr,#20] + adcs $a3,$a3,$a3 + ldr $a6,[$a_ptr,#24] + adcs $a4,$a4,$a4 + ldr $a7,[$a_ptr,#28] + adcs $a5,$a5,$a5 + adcs $a6,$a6,$a6 + mov $ff,#0 + adcs $a7,$a7,$a7 + adc $ff,$ff,#0 + + subs $a0,$a0,#-1 @ .Lreduce_by_sub but without stores + sbcs $a1,$a1,#-1 + sbcs $a2,$a2,#-1 + sbcs $a3,$a3,#0 + sbcs $a4,$a4,#0 + sbcs $a5,$a5,#0 + sbcs $a6,$a6,#1 + sbcs $a7,$a7,#-1 + sbc $ff,$ff,#0 + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + adcs $a2,$a2,$ff + adcs $a3,$a3,#0 + adcs $a4,$a4,#0 + ldr $b_ptr,[$a_ptr,#0] + adcs $a5,$a5,#0 + ldr $t1,[$a_ptr,#4] + adcs $a6,$a6,$ff,lsr#31 + ldr $t2,[$a_ptr,#8] + adc $a7,$a7,$ff + + ldr $t0,[$a_ptr,#12] + adds $a0,$a0,$b_ptr @ 2*a[0:7]+=a[0:7] + ldr $b_ptr,[$a_ptr,#16] + adcs $a1,$a1,$t1 + ldr $t1,[$a_ptr,#20] + adcs $a2,$a2,$t2 + ldr $t2,[$a_ptr,#24] + adcs $a3,$a3,$t0 + ldr $t3,[$a_ptr,#28] + adcs $a4,$a4,$b_ptr + adcs $a5,$a5,$t1 + adcs $a6,$a6,$t2 + mov $ff,#0 + adcs $a7,$a7,$t3 + adc $ff,$ff,#0 + ldr lr,[sp],#4 @ pop lr + + b .Lreduce_by_sub +.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3 + +@ void ecp_nistz256_div_by_2(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_div_by_2 +.type ecp_nistz256_div_by_2,%function +.align 4 +ecp_nistz256_div_by_2: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_div_by_2 +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2 + +.type __ecp_nistz256_div_by_2,%function +.align 4 +__ecp_nistz256_div_by_2: + @ ret = (a is odd ? a+mod : a) >> 1 + + ldr $a0,[$a_ptr,#0] + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + mov $ff,$a0,lsl#31 @ place least significant bit to most + @ significant position, now arithmetic + @ right shift by 31 will produce -1 or + @ 0, while logical right shift 1 or 0, + @ this is how modulus is conditionally + @ synthesized in this case... + ldr $a3,[$a_ptr,#12] + adds $a0,$a0,$ff,asr#31 + ldr $a4,[$a_ptr,#16] + adcs $a1,$a1,$ff,asr#31 + ldr $a5,[$a_ptr,#20] + adcs $a2,$a2,$ff,asr#31 + ldr $a6,[$a_ptr,#24] + adcs $a3,$a3,#0 + ldr $a7,[$a_ptr,#28] + adcs $a4,$a4,#0 + mov $a0,$a0,lsr#1 @ a[0:7]>>=1, we can start early + @ because it doesn't affect flags + adcs $a5,$a5,#0 + orr $a0,$a0,$a1,lsl#31 + adcs $a6,$a6,$ff,lsr#31 + mov $b_ptr,#0 + adcs $a7,$a7,$ff,asr#31 + mov $a1,$a1,lsr#1 + adc $b_ptr,$b_ptr,#0 @ top-most carry bit from addition + + orr $a1,$a1,$a2,lsl#31 + mov $a2,$a2,lsr#1 + str $a0,[$r_ptr,#0] + orr $a2,$a2,$a3,lsl#31 + mov $a3,$a3,lsr#1 + str $a1,[$r_ptr,#4] + orr $a3,$a3,$a4,lsl#31 + mov $a4,$a4,lsr#1 + str $a2,[$r_ptr,#8] + orr $a4,$a4,$a5,lsl#31 + mov $a5,$a5,lsr#1 + str $a3,[$r_ptr,#12] + orr $a5,$a5,$a6,lsl#31 + mov $a6,$a6,lsr#1 + str $a4,[$r_ptr,#16] + orr $a6,$a6,$a7,lsl#31 + mov $a7,$a7,lsr#1 + str $a5,[$r_ptr,#20] + orr $a7,$a7,$b_ptr,lsl#31 @ don't forget the top-most carry bit + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2 + +@ void ecp_nistz256_sub(BN_ULONG r0[8],const BN_ULONG r1[8], +@ const BN_ULONG r2[8]); +.globl ecp_nistz256_sub +.type ecp_nistz256_sub,%function +.align 4 +ecp_nistz256_sub: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_sub +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_sub,.-ecp_nistz256_sub + +.type __ecp_nistz256_sub,%function +.align 4 +__ecp_nistz256_sub: + str lr,[sp,#-4]! @ push lr + + ldr $a0,[$a_ptr,#0] + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + ldr $a3,[$a_ptr,#12] + ldr $a4,[$a_ptr,#16] + ldr $t0,[$b_ptr,#0] + ldr $a5,[$a_ptr,#20] + ldr $t1,[$b_ptr,#4] + ldr $a6,[$a_ptr,#24] + ldr $t2,[$b_ptr,#8] + ldr $a7,[$a_ptr,#28] + ldr $t3,[$b_ptr,#12] + subs $a0,$a0,$t0 + ldr $t0,[$b_ptr,#16] + sbcs $a1,$a1,$t1 + ldr $t1,[$b_ptr,#20] + sbcs $a2,$a2,$t2 + ldr $t2,[$b_ptr,#24] + sbcs $a3,$a3,$t3 + ldr $t3,[$b_ptr,#28] + sbcs $a4,$a4,$t0 + sbcs $a5,$a5,$t1 + sbcs $a6,$a6,$t2 + sbcs $a7,$a7,$t3 + sbc $ff,$ff,$ff @ broadcast borrow bit + ldr lr,[sp],#4 @ pop lr + +.Lreduce_by_add: + + @ if a-b borrows, add modulus. + @ + @ Note that because mod has special form, i.e. consists of + @ 0xffffffff, 1 and 0s, we can conditionally synthesize it by + @ broadcasting borrow bit to a register, $ff, and using it as + @ a whole or extracting single bit. + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + str $a0,[$r_ptr,#0] + adcs $a2,$a2,$ff + str $a1,[$r_ptr,#4] + adcs $a3,$a3,#0 + str $a2,[$r_ptr,#8] + adcs $a4,$a4,#0 + str $a3,[$r_ptr,#12] + adcs $a5,$a5,#0 + str $a4,[$r_ptr,#16] + adcs $a6,$a6,$ff,lsr#31 + str $a5,[$r_ptr,#20] + adcs $a7,$a7,$ff + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_sub,.-__ecp_nistz256_sub + +@ void ecp_nistz256_neg(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_neg +.type ecp_nistz256_neg,%function +.align 4 +ecp_nistz256_neg: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_neg +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_neg,.-ecp_nistz256_neg + +.type __ecp_nistz256_neg,%function +.align 4 +__ecp_nistz256_neg: + ldr $a0,[$a_ptr,#0] + eor $ff,$ff,$ff + ldr $a1,[$a_ptr,#4] + ldr $a2,[$a_ptr,#8] + subs $a0,$ff,$a0 + ldr $a3,[$a_ptr,#12] + sbcs $a1,$ff,$a1 + ldr $a4,[$a_ptr,#16] + sbcs $a2,$ff,$a2 + ldr $a5,[$a_ptr,#20] + sbcs $a3,$ff,$a3 + ldr $a6,[$a_ptr,#24] + sbcs $a4,$ff,$a4 + ldr $a7,[$a_ptr,#28] + sbcs $a5,$ff,$a5 + sbcs $a6,$ff,$a6 + sbcs $a7,$ff,$a7 + sbc $ff,$ff,$ff + + b .Lreduce_by_add +.size __ecp_nistz256_neg,.-__ecp_nistz256_neg +___ +{ +my @acc=map("r$_",(3..11)); +my ($t0,$t1,$bj,$t2,$t3)=map("r$_",(0,1,2,12,14)); + +$code.=<<___; +@ void ecp_nistz256_sqr_mont(BN_ULONG r0[8],const BN_ULONG r1[8]); +.globl ecp_nistz256_sqr_mont +.type ecp_nistz256_sqr_mont,%function +.align 4 +ecp_nistz256_sqr_mont: + mov $b_ptr,$a_ptr + b .Lecp_nistz256_mul_mont +.size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont + +@ void ecp_nistz256_mul_mont(BN_ULONG r0[8],const BN_ULONG r1[8], +@ const BN_ULONG r2[8]); +.globl ecp_nistz256_mul_mont +.type ecp_nistz256_mul_mont,%function +.align 4 +ecp_nistz256_mul_mont: +.Lecp_nistz256_mul_mont: + stmdb sp!,{r4-r12,lr} + bl __ecp_nistz256_mul_mont +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont + +.type __ecp_nistz256_mul_mont,%function +.align 4 +__ecp_nistz256_mul_mont: + stmdb sp!,{r0-r2,lr} @ make a copy of arguments too + + ldr $bj,[$b_ptr,#0] @ b[0] + ldmia $a_ptr,{@acc[1]-@acc[8]} + + umull @acc[0],$t3,@acc[1],$bj @ r[0]=a[0]*b[0] + stmdb sp!,{$acc[1]-@acc[8]} @ copy a[0-7] to stack, so + @ that it can be addressed + @ without spending register + @ on address + umull @acc[1],$t0,@acc[2],$bj @ r[1]=a[1]*b[0] + umull @acc[2],$t1,@acc[3],$bj + adds @acc[1],@acc[1],$t3 @ accumulate high part of mult + umull @acc[3],$t2,@acc[4],$bj + adcs @acc[2],@acc[2],$t0 + umull @acc[4],$t3,@acc[5],$bj + adcs @acc[3],@acc[3],$t1 + umull @acc[5],$t0,@acc[6],$bj + adcs @acc[4],@acc[4],$t2 + umull @acc[6],$t1,@acc[7],$bj + adcs @acc[5],@acc[5],$t3 + umull @acc[7],$t2,@acc[8],$bj + adcs @acc[6],@acc[6],$t0 + adcs @acc[7],@acc[7],$t1 + eor $t3,$t3,$t3 @ first overflow bit is zero + adc @acc[8],$t2,#0 +___ +for(my $i=1;$i<8;$i++) { +my $t4=@acc[0]; + + # Reduction iteration is normally performed by accumulating + # result of multiplication of modulus by "magic" digit [and + # omitting least significant word, which is guaranteed to + # be 0], but thanks to special form of modulus and "magic" + # digit being equal to least significant word, it can be + # performed with additions and subtractions alone. Indeed: + # + # ffff.0001.0000.0000.0000.ffff.ffff.ffff + # * abcd + # + xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we + # rewrite above as: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + abcd.0000.abcd.0000.0000.abcd.0000.0000.0000 + # - abcd.0000.0000.0000.0000.0000.0000.abcd + # + # or marking redundant operations: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.---- + # + abcd.0000.abcd.0000.0000.abcd.----.----.---- + # - abcd.----.----.----.----.----.----.---- + +$code.=<<___; + @ multiplication-less reduction $i + adds @acc[3],@acc[3],@acc[0] @ r[3]+=r[0] + ldr $bj,[sp,#40] @ restore b_ptr + adcs @acc[4],@acc[4],#0 @ r[4]+=0 + adcs @acc[5],@acc[5],#0 @ r[5]+=0 + adcs @acc[6],@acc[6],@acc[0] @ r[6]+=r[0] + ldr $t1,[sp,#0] @ load a[0] + adcs @acc[7],@acc[7],#0 @ r[7]+=0 + ldr $bj,[$bj,#4*$i] @ load b[i] + adcs @acc[8],@acc[8],@acc[0] @ r[8]+=r[0] + eor $t0,$t0,$t0 + adc $t3,$t3,#0 @ overflow bit + subs @acc[7],@acc[7],@acc[0] @ r[7]-=r[0] + ldr $t2,[sp,#4] @ a[1] + sbcs @acc[8],@acc[8],#0 @ r[8]-=0 + umlal @acc[1],$t0,$t1,$bj @ "r[0]"+=a[0]*b[i] + eor $t1,$t1,$t1 + sbc @acc[0],$t3,#0 @ overflow bit, keep in mind + @ that netto result is + @ addition of a value which + @ makes underflow impossible + + ldr $t3,[sp,#8] @ a[2] + umlal @acc[2],$t1,$t2,$bj @ "r[1]"+=a[1]*b[i] + str @acc[0],[sp,#36] @ temporarily offload overflow + eor $t2,$t2,$t2 + ldr $t4,[sp,#12] @ a[3], $t4 is alias @acc[0] + umlal @acc[3],$t2,$t3,$bj @ "r[2]"+=a[2]*b[i] + eor $t3,$t3,$t3 + adds @acc[2],@acc[2],$t0 @ accumulate high part of mult + ldr $t0,[sp,#16] @ a[4] + umlal @acc[4],$t3,$t4,$bj @ "r[3]"+=a[3]*b[i] + eor $t4,$t4,$t4 + adcs @acc[3],@acc[3],$t1 + ldr $t1,[sp,#20] @ a[5] + umlal @acc[5],$t4,$t0,$bj @ "r[4]"+=a[4]*b[i] + eor $t0,$t0,$t0 + adcs @acc[4],@acc[4],$t2 + ldr $t2,[sp,#24] @ a[6] + umlal @acc[6],$t0,$t1,$bj @ "r[5]"+=a[5]*b[i] + eor $t1,$t1,$t1 + adcs @acc[5],@acc[5],$t3 + ldr $t3,[sp,#28] @ a[7] + umlal @acc[7],$t1,$t2,$bj @ "r[6]"+=a[6]*b[i] + eor $t2,$t2,$t2 + adcs @acc[6],@acc[6],$t4 + ldr @acc[0],[sp,#36] @ restore overflow bit + umlal @acc[8],$t2,$t3,$bj @ "r[7]"+=a[7]*b[i] + eor $t3,$t3,$t3 + adcs @acc[7],@acc[7],$t0 + adcs @acc[8],@acc[8],$t1 + adcs @acc[0],$acc[0],$t2 + adc $t3,$t3,#0 @ new overflow bit +___ + push(@acc,shift(@acc)); # rotate registers, so that + # "r[i]" becomes r[i] +} +$code.=<<___; + @ last multiplication-less reduction + adds @acc[3],@acc[3],@acc[0] + ldr $r_ptr,[sp,#32] @ restore r_ptr + adcs @acc[4],@acc[4],#0 + adcs @acc[5],@acc[5],#0 + adcs @acc[6],@acc[6],@acc[0] + adcs @acc[7],@acc[7],#0 + adcs @acc[8],@acc[8],@acc[0] + adc $t3,$t3,#0 + subs @acc[7],@acc[7],@acc[0] + sbcs @acc[8],@acc[8],#0 + sbc @acc[0],$t3,#0 @ overflow bit + + @ Final step is "if result > mod, subtract mod", but we do it + @ "other way around", namely subtract modulus from result + @ and if it borrowed, add modulus back. + + adds @acc[1],@acc[1],#1 @ subs @acc[1],@acc[1],#-1 + adcs @acc[2],@acc[2],#0 @ sbcs @acc[2],@acc[2],#-1 + adcs @acc[3],@acc[3],#0 @ sbcs @acc[3],@acc[3],#-1 + sbcs @acc[4],@acc[4],#0 + sbcs @acc[5],@acc[5],#0 + sbcs @acc[6],@acc[6],#0 + sbcs @acc[7],@acc[7],#1 + adcs @acc[8],@acc[8],#0 @ sbcs @acc[8],@acc[8],#-1 + ldr lr,[sp,#44] @ restore lr + sbc @acc[0],@acc[0],#0 @ broadcast borrow bit + add sp,sp,#48 + + @ Note that because mod has special form, i.e. consists of + @ 0xffffffff, 1 and 0s, we can conditionally synthesize it by + @ broadcasting borrow bit to a register, @acc[0], and using it as + @ a whole or extracting single bit. + + adds @acc[1],@acc[1],@acc[0] @ add modulus or zero + adcs @acc[2],@acc[2],@acc[0] + str @acc[1],[$r_ptr,#0] + adcs @acc[3],@acc[3],@acc[0] + str @acc[2],[$r_ptr,#4] + adcs @acc[4],@acc[4],#0 + str @acc[3],[$r_ptr,#8] + adcs @acc[5],@acc[5],#0 + str @acc[4],[$r_ptr,#12] + adcs @acc[6],@acc[6],#0 + str @acc[5],[$r_ptr,#16] + adcs @acc[7],@acc[7],@acc[0],lsr#31 + str @acc[6],[$r_ptr,#20] + adc @acc[8],@acc[8],@acc[0] + str @acc[7],[$r_ptr,#24] + str @acc[8],[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont +___ +} + +{ +my ($out,$inp,$index,$mask)=map("r$_",(0..3)); +$code.=<<___; +@ void ecp_nistz256_scatter_w5(void *r0,const P256_POINT *r1, +@ int r2); +.globl ecp_nistz256_scatter_w5 +.type ecp_nistz256_scatter_w5,%function +.align 5 +ecp_nistz256_scatter_w5: + stmdb sp!,{r4-r11} + + add $out,$out,$index,lsl#2 + + ldmia $inp!,{r4-r11} @ X + str r4,[$out,#64*0-4] + str r5,[$out,#64*1-4] + str r6,[$out,#64*2-4] + str r7,[$out,#64*3-4] + str r8,[$out,#64*4-4] + str r9,[$out,#64*5-4] + str r10,[$out,#64*6-4] + str r11,[$out,#64*7-4] + add $out,$out,#64*8 + + ldmia $inp!,{r4-r11} @ Y + str r4,[$out,#64*0-4] + str r5,[$out,#64*1-4] + str r6,[$out,#64*2-4] + str r7,[$out,#64*3-4] + str r8,[$out,#64*4-4] + str r9,[$out,#64*5-4] + str r10,[$out,#64*6-4] + str r11,[$out,#64*7-4] + add $out,$out,#64*8 + + ldmia $inp,{r4-r11} @ Z + str r4,[$out,#64*0-4] + str r5,[$out,#64*1-4] + str r6,[$out,#64*2-4] + str r7,[$out,#64*3-4] + str r8,[$out,#64*4-4] + str r9,[$out,#64*5-4] + str r10,[$out,#64*6-4] + str r11,[$out,#64*7-4] + + ldmia sp!,{r4-r11} +#if __ARM_ARCH__>=5 || defined(__thumb__) + bx lr +#else + mov pc,lr +#endif +.size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5 + +@ void ecp_nistz256_gather_w5(P256_POINT *r0,const void *r1, +@ int r2); +.globl ecp_nistz256_gather_w5 +.type ecp_nistz256_gather_w5,%function +.align 5 +ecp_nistz256_gather_w5: + stmdb sp!,{r4-r11} + + cmp $index,#0 + mov $mask,#0 +#ifdef __thumb2__ + itt ne +#endif + subne $index,$index,#1 + movne $mask,#-1 + add $inp,$inp,$index,lsl#2 + + ldr r4,[$inp,#64*0] + ldr r5,[$inp,#64*1] + ldr r6,[$inp,#64*2] + and r4,r4,$mask + ldr r7,[$inp,#64*3] + and r5,r5,$mask + ldr r8,[$inp,#64*4] + and r6,r6,$mask + ldr r9,[$inp,#64*5] + and r7,r7,$mask + ldr r10,[$inp,#64*6] + and r8,r8,$mask + ldr r11,[$inp,#64*7] + add $inp,$inp,#64*8 + and r9,r9,$mask + and r10,r10,$mask + and r11,r11,$mask + stmia $out!,{r4-r11} @ X + + ldr r4,[$inp,#64*0] + ldr r5,[$inp,#64*1] + ldr r6,[$inp,#64*2] + and r4,r4,$mask + ldr r7,[$inp,#64*3] + and r5,r5,$mask + ldr r8,[$inp,#64*4] + and r6,r6,$mask + ldr r9,[$inp,#64*5] + and r7,r7,$mask + ldr r10,[$inp,#64*6] + and r8,r8,$mask + ldr r11,[$inp,#64*7] + add $inp,$inp,#64*8 + and r9,r9,$mask + and r10,r10,$mask + and r11,r11,$mask + stmia $out!,{r4-r11} @ Y + + ldr r4,[$inp,#64*0] + ldr r5,[$inp,#64*1] + ldr r6,[$inp,#64*2] + and r4,r4,$mask + ldr r7,[$inp,#64*3] + and r5,r5,$mask + ldr r8,[$inp,#64*4] + and r6,r6,$mask + ldr r9,[$inp,#64*5] + and r7,r7,$mask + ldr r10,[$inp,#64*6] + and r8,r8,$mask + ldr r11,[$inp,#64*7] + and r9,r9,$mask + and r10,r10,$mask + and r11,r11,$mask + stmia $out,{r4-r11} @ Z + + ldmia sp!,{r4-r11} +#if __ARM_ARCH__>=5 || defined(__thumb__) + bx lr +#else + mov pc,lr +#endif +.size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5 + +@ void ecp_nistz256_scatter_w7(void *r0,const P256_POINT_AFFINE *r1, +@ int r2); +.globl ecp_nistz256_scatter_w7 +.type ecp_nistz256_scatter_w7,%function +.align 5 +ecp_nistz256_scatter_w7: + add $out,$out,$index + mov $index,#64/4 +.Loop_scatter_w7: + ldr $mask,[$inp],#4 + subs $index,$index,#1 + strb $mask,[$out,#64*0-1] + mov $mask,$mask,lsr#8 + strb $mask,[$out,#64*1-1] + mov $mask,$mask,lsr#8 + strb $mask,[$out,#64*2-1] + mov $mask,$mask,lsr#8 + strb $mask,[$out,#64*3-1] + add $out,$out,#64*4 + bne .Loop_scatter_w7 + +#if __ARM_ARCH__>=5 || defined(__thumb__) + bx lr +#else + mov pc,lr +#endif +.size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7 + +@ void ecp_nistz256_gather_w7(P256_POINT_AFFINE *r0,const void *r1, +@ int r2); +.globl ecp_nistz256_gather_w7 +.type ecp_nistz256_gather_w7,%function +.align 5 +ecp_nistz256_gather_w7: + stmdb sp!,{r4-r7} + + cmp $index,#0 + mov $mask,#0 +#ifdef __thumb2__ + itt ne +#endif + subne $index,$index,#1 + movne $mask,#-1 + add $inp,$inp,$index + mov $index,#64/4 + nop +.Loop_gather_w7: + ldrb r4,[$inp,#64*0] + subs $index,$index,#1 + ldrb r5,[$inp,#64*1] + ldrb r6,[$inp,#64*2] + ldrb r7,[$inp,#64*3] + add $inp,$inp,#64*4 + orr r4,r4,r5,lsl#8 + orr r4,r4,r6,lsl#16 + orr r4,r4,r7,lsl#24 + and r4,r4,$mask + str r4,[$out],#4 + bne .Loop_gather_w7 + + ldmia sp!,{r4-r7} +#if __ARM_ARCH__>=5 || defined(__thumb__) + bx lr +#else + mov pc,lr +#endif +.size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7 +___ +} +if (0) { +# In comparison to integer-only equivalent of below subroutine: +# +# Cortex-A8 +10% +# Cortex-A9 -10% +# Snapdragon S4 +5% +# +# As not all time is spent in multiplication, overall impact is deemed +# too low to care about. + +my ($A0,$A1,$A2,$A3,$Bi,$zero,$temp)=map("d$_",(0..7)); +my $mask="q4"; +my $mult="q5"; +my @AxB=map("q$_",(8..15)); + +my ($rptr,$aptr,$bptr,$toutptr)=map("r$_",(0..3)); + +$code.=<<___; +#if __ARM_ARCH__>=7 +.fpu neon + +.globl ecp_nistz256_mul_mont_neon +.type ecp_nistz256_mul_mont_neon,%function +.align 5 +ecp_nistz256_mul_mont_neon: + mov ip,sp + stmdb sp!,{r4-r9} + vstmdb sp!,{q4-q5} @ ABI specification says so + + sub $toutptr,sp,#40 + vld1.32 {${Bi}[0]},[$bptr,:32]! + veor $zero,$zero,$zero + vld1.32 {$A0-$A3}, [$aptr] @ can't specify :32 :-( + vzip.16 $Bi,$zero + mov sp,$toutptr @ alloca + vmov.i64 $mask,#0xffff + + vmull.u32 @AxB[0],$Bi,${A0}[0] + vmull.u32 @AxB[1],$Bi,${A0}[1] + vmull.u32 @AxB[2],$Bi,${A1}[0] + vmull.u32 @AxB[3],$Bi,${A1}[1] + vshr.u64 $temp,@AxB[0]#lo,#16 + vmull.u32 @AxB[4],$Bi,${A2}[0] + vadd.u64 @AxB[0]#hi,@AxB[0]#hi,$temp + vmull.u32 @AxB[5],$Bi,${A2}[1] + vshr.u64 $temp,@AxB[0]#hi,#16 @ upper 32 bits of a[0]*b[0] + vmull.u32 @AxB[6],$Bi,${A3}[0] + vand.u64 @AxB[0],@AxB[0],$mask @ lower 32 bits of a[0]*b[0] + vmull.u32 @AxB[7],$Bi,${A3}[1] +___ +for($i=1;$i<8;$i++) { +$code.=<<___; + vld1.32 {${Bi}[0]},[$bptr,:32]! + veor $zero,$zero,$zero + vadd.u64 @AxB[1]#lo,@AxB[1]#lo,$temp @ reduction + vshl.u64 $mult,@AxB[0],#32 + vadd.u64 @AxB[3],@AxB[3],@AxB[0] + vsub.u64 $mult,$mult,@AxB[0] + vzip.16 $Bi,$zero + vadd.u64 @AxB[6],@AxB[6],@AxB[0] + vadd.u64 @AxB[7],@AxB[7],$mult +___ + push(@AxB,shift(@AxB)); +$code.=<<___; + vmlal.u32 @AxB[0],$Bi,${A0}[0] + vmlal.u32 @AxB[1],$Bi,${A0}[1] + vmlal.u32 @AxB[2],$Bi,${A1}[0] + vmlal.u32 @AxB[3],$Bi,${A1}[1] + vshr.u64 $temp,@AxB[0]#lo,#16 + vmlal.u32 @AxB[4],$Bi,${A2}[0] + vadd.u64 @AxB[0]#hi,@AxB[0]#hi,$temp + vmlal.u32 @AxB[5],$Bi,${A2}[1] + vshr.u64 $temp,@AxB[0]#hi,#16 @ upper 33 bits of a[0]*b[i]+t[0] + vmlal.u32 @AxB[6],$Bi,${A3}[0] + vand.u64 @AxB[0],@AxB[0],$mask @ lower 32 bits of a[0]*b[0] + vmull.u32 @AxB[7],$Bi,${A3}[1] +___ +} +$code.=<<___; + vadd.u64 @AxB[1]#lo,@AxB[1]#lo,$temp @ last reduction + vshl.u64 $mult,@AxB[0],#32 + vadd.u64 @AxB[3],@AxB[3],@AxB[0] + vsub.u64 $mult,$mult,@AxB[0] + vadd.u64 @AxB[6],@AxB[6],@AxB[0] + vadd.u64 @AxB[7],@AxB[7],$mult + + vshr.u64 $temp,@AxB[1]#lo,#16 @ convert + vadd.u64 @AxB[1]#hi,@AxB[1]#hi,$temp + vshr.u64 $temp,@AxB[1]#hi,#16 + vzip.16 @AxB[1]#lo,@AxB[1]#hi +___ +foreach (2..7) { +$code.=<<___; + vadd.u64 @AxB[$_]#lo,@AxB[$_]#lo,$temp + vst1.32 {@AxB[$_-1]#lo[0]},[$toutptr,:32]! + vshr.u64 $temp,@AxB[$_]#lo,#16 + vadd.u64 @AxB[$_]#hi,@AxB[$_]#hi,$temp + vshr.u64 $temp,@AxB[$_]#hi,#16 + vzip.16 @AxB[$_]#lo,@AxB[$_]#hi +___ +} +$code.=<<___; + vst1.32 {@AxB[7]#lo[0]},[$toutptr,:32]! + vst1.32 {$temp},[$toutptr] @ upper 33 bits + + ldr r1,[sp,#0] + ldr r2,[sp,#4] + ldr r3,[sp,#8] + subs r1,r1,#-1 + ldr r4,[sp,#12] + sbcs r2,r2,#-1 + ldr r5,[sp,#16] + sbcs r3,r3,#-1 + ldr r6,[sp,#20] + sbcs r4,r4,#0 + ldr r7,[sp,#24] + sbcs r5,r5,#0 + ldr r8,[sp,#28] + sbcs r6,r6,#0 + ldr r9,[sp,#32] @ top-most bit + sbcs r7,r7,#1 + sub sp,ip,#40+16 + sbcs r8,r8,#-1 + sbc r9,r9,#0 + vldmia sp!,{q4-q5} + + adds r1,r1,r9 + adcs r2,r2,r9 + str r1,[$rptr,#0] + adcs r3,r3,r9 + str r2,[$rptr,#4] + adcs r4,r4,#0 + str r3,[$rptr,#8] + adcs r5,r5,#0 + str r4,[$rptr,#12] + adcs r6,r6,#0 + str r5,[$rptr,#16] + adcs r7,r7,r9,lsr#31 + str r6,[$rptr,#20] + adcs r8,r8,r9 + str r7,[$rptr,#24] + str r8,[$rptr,#28] + + ldmia sp!,{r4-r9} + bx lr +.size ecp_nistz256_mul_mont_neon,.-ecp_nistz256_mul_mont_neon +#endif +___ +} + +{{{ +######################################################################## +# Below $aN assignment matches order in which 256-bit result appears in +# register bank at return from __ecp_nistz256_mul_mont, so that we can +# skip over reloading it from memory. This means that below functions +# use custom calling sequence accepting 256-bit input in registers, +# output pointer in r0, $r_ptr, and optional pointer in r2, $b_ptr. +# +# See their "normal" counterparts for insights on calculations. + +my ($a0,$a1,$a2,$a3,$a4,$a5,$a6,$a7, + $t0,$t1,$t2,$t3)=map("r$_",(11,3..10,12,14,1)); +my $ff=$b_ptr; + +$code.=<<___; +.type __ecp_nistz256_sub_from,%function +.align 5 +__ecp_nistz256_sub_from: + str lr,[sp,#-4]! @ push lr + + ldr $t0,[$b_ptr,#0] + ldr $t1,[$b_ptr,#4] + ldr $t2,[$b_ptr,#8] + ldr $t3,[$b_ptr,#12] + subs $a0,$a0,$t0 + ldr $t0,[$b_ptr,#16] + sbcs $a1,$a1,$t1 + ldr $t1,[$b_ptr,#20] + sbcs $a2,$a2,$t2 + ldr $t2,[$b_ptr,#24] + sbcs $a3,$a3,$t3 + ldr $t3,[$b_ptr,#28] + sbcs $a4,$a4,$t0 + sbcs $a5,$a5,$t1 + sbcs $a6,$a6,$t2 + sbcs $a7,$a7,$t3 + sbc $ff,$ff,$ff @ broadcast borrow bit + ldr lr,[sp],#4 @ pop lr + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + str $a0,[$r_ptr,#0] + adcs $a2,$a2,$ff + str $a1,[$r_ptr,#4] + adcs $a3,$a3,#0 + str $a2,[$r_ptr,#8] + adcs $a4,$a4,#0 + str $a3,[$r_ptr,#12] + adcs $a5,$a5,#0 + str $a4,[$r_ptr,#16] + adcs $a6,$a6,$ff,lsr#31 + str $a5,[$r_ptr,#20] + adcs $a7,$a7,$ff + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from + +.type __ecp_nistz256_sub_morf,%function +.align 5 +__ecp_nistz256_sub_morf: + str lr,[sp,#-4]! @ push lr + + ldr $t0,[$b_ptr,#0] + ldr $t1,[$b_ptr,#4] + ldr $t2,[$b_ptr,#8] + ldr $t3,[$b_ptr,#12] + subs $a0,$t0,$a0 + ldr $t0,[$b_ptr,#16] + sbcs $a1,$t1,$a1 + ldr $t1,[$b_ptr,#20] + sbcs $a2,$t2,$a2 + ldr $t2,[$b_ptr,#24] + sbcs $a3,$t3,$a3 + ldr $t3,[$b_ptr,#28] + sbcs $a4,$t0,$a4 + sbcs $a5,$t1,$a5 + sbcs $a6,$t2,$a6 + sbcs $a7,$t3,$a7 + sbc $ff,$ff,$ff @ broadcast borrow bit + ldr lr,[sp],#4 @ pop lr + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + str $a0,[$r_ptr,#0] + adcs $a2,$a2,$ff + str $a1,[$r_ptr,#4] + adcs $a3,$a3,#0 + str $a2,[$r_ptr,#8] + adcs $a4,$a4,#0 + str $a3,[$r_ptr,#12] + adcs $a5,$a5,#0 + str $a4,[$r_ptr,#16] + adcs $a6,$a6,$ff,lsr#31 + str $a5,[$r_ptr,#20] + adcs $a7,$a7,$ff + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf + +.type __ecp_nistz256_add_self,%function +.align 4 +__ecp_nistz256_add_self: + adds $a0,$a0,$a0 @ a[0:7]+=a[0:7] + adcs $a1,$a1,$a1 + adcs $a2,$a2,$a2 + adcs $a3,$a3,$a3 + adcs $a4,$a4,$a4 + adcs $a5,$a5,$a5 + adcs $a6,$a6,$a6 + mov $ff,#0 + adcs $a7,$a7,$a7 + adc $ff,$ff,#0 + + @ if a+b >= modulus, subtract modulus. + @ + @ But since comparison implies subtraction, we subtract + @ modulus and then add it back if subraction borrowed. + + subs $a0,$a0,#-1 + sbcs $a1,$a1,#-1 + sbcs $a2,$a2,#-1 + sbcs $a3,$a3,#0 + sbcs $a4,$a4,#0 + sbcs $a5,$a5,#0 + sbcs $a6,$a6,#1 + sbcs $a7,$a7,#-1 + sbc $ff,$ff,#0 + + @ Note that because mod has special form, i.e. consists of + @ 0xffffffff, 1 and 0s, we can conditionally synthesize it by + @ using value of borrow as a whole or extracting single bit. + @ Follow $ff register... + + adds $a0,$a0,$ff @ add synthesized modulus + adcs $a1,$a1,$ff + str $a0,[$r_ptr,#0] + adcs $a2,$a2,$ff + str $a1,[$r_ptr,#4] + adcs $a3,$a3,#0 + str $a2,[$r_ptr,#8] + adcs $a4,$a4,#0 + str $a3,[$r_ptr,#12] + adcs $a5,$a5,#0 + str $a4,[$r_ptr,#16] + adcs $a6,$a6,$ff,lsr#31 + str $a5,[$r_ptr,#20] + adcs $a7,$a7,$ff + str $a6,[$r_ptr,#24] + str $a7,[$r_ptr,#28] + + mov pc,lr +.size __ecp_nistz256_add_self,.-__ecp_nistz256_add_self + +___ + +######################################################################## +# following subroutines are "literal" implementation of those found in +# ecp_nistz256.c +# +######################################################################## +# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp); +# +{ +my ($S,$M,$Zsqr,$in_x,$tmp0)=map(32*$_,(0..4)); +# above map() describes stack layout with 5 temporary +# 256-bit vectors on top. Then note that we push +# starting from r0, which means that we have copy of +# input arguments just below these temporary vectors. + +$code.=<<___; +.globl ecp_nistz256_point_double +.type ecp_nistz256_point_double,%function +.align 5 +ecp_nistz256_point_double: + stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional + sub sp,sp,#32*5 + +.Lpoint_double_shortcut: + add r3,sp,#$in_x + ldmia $a_ptr!,{r4-r11} @ copy in_x + stmia r3,{r4-r11} + + add $r_ptr,sp,#$S + bl __ecp_nistz256_mul_by_2 @ p256_mul_by_2(S, in_y); + + add $b_ptr,$a_ptr,#32 + add $a_ptr,$a_ptr,#32 + add $r_ptr,sp,#$Zsqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Zsqr, in_z); + + add $a_ptr,sp,#$S + add $b_ptr,sp,#$S + add $r_ptr,sp,#$S + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(S, S); + + ldr $b_ptr,[sp,#32*5+4] + add $a_ptr,$b_ptr,#32 + add $b_ptr,$b_ptr,#64 + add $r_ptr,sp,#$tmp0 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(tmp0, in_z, in_y); + + ldr $r_ptr,[sp,#32*5] + add $r_ptr,$r_ptr,#64 + bl __ecp_nistz256_add_self @ p256_mul_by_2(res_z, tmp0); + + add $a_ptr,sp,#$in_x + add $b_ptr,sp,#$Zsqr + add $r_ptr,sp,#$M + bl __ecp_nistz256_add @ p256_add(M, in_x, Zsqr); + + add $a_ptr,sp,#$in_x + add $b_ptr,sp,#$Zsqr + add $r_ptr,sp,#$Zsqr + bl __ecp_nistz256_sub @ p256_sub(Zsqr, in_x, Zsqr); + + add $a_ptr,sp,#$S + add $b_ptr,sp,#$S + add $r_ptr,sp,#$tmp0 + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(tmp0, S); + + add $a_ptr,sp,#$Zsqr + add $b_ptr,sp,#$M + add $r_ptr,sp,#$M + bl __ecp_nistz256_mul_mont @ p256_mul_mont(M, M, Zsqr); + + ldr $r_ptr,[sp,#32*5] + add $a_ptr,sp,#$tmp0 + add $r_ptr,$r_ptr,#32 + bl __ecp_nistz256_div_by_2 @ p256_div_by_2(res_y, tmp0); + + add $a_ptr,sp,#$M + add $r_ptr,sp,#$M + bl __ecp_nistz256_mul_by_3 @ p256_mul_by_3(M, M); + + add $a_ptr,sp,#$in_x + add $b_ptr,sp,#$S + add $r_ptr,sp,#$S + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S, S, in_x); + + add $r_ptr,sp,#$tmp0 + bl __ecp_nistz256_add_self @ p256_mul_by_2(tmp0, S); + + ldr $r_ptr,[sp,#32*5] + add $a_ptr,sp,#$M + add $b_ptr,sp,#$M + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(res_x, M); + + add $b_ptr,sp,#$tmp0 + bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, tmp0); + + add $b_ptr,sp,#$S + add $r_ptr,sp,#$S + bl __ecp_nistz256_sub_morf @ p256_sub(S, S, res_x); + + add $a_ptr,sp,#$M + add $b_ptr,sp,#$S + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S, S, M); + + ldr $r_ptr,[sp,#32*5] + add $b_ptr,$r_ptr,#32 + add $r_ptr,$r_ptr,#32 + bl __ecp_nistz256_sub_from @ p256_sub(res_y, S, res_y); + + add sp,sp,#32*5+16 @ +16 means "skip even over saved r0-r3" +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_point_double,.-ecp_nistz256_point_double +___ +} + +######################################################################## +# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT *in2); +{ +my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y,$in2_z, + $H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2)=map(32*$_,(0..17)); +my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); +# above map() describes stack layout with 18 temporary +# 256-bit vectors on top. Then note that we push +# starting from r0, which means that we have copy of +# input arguments just below these temporary vectors. +# We use three of them for !in1infty, !in2intfy and +# result of check for zero. + +$code.=<<___; +.globl ecp_nistz256_point_add +.type ecp_nistz256_point_add,%function +.align 5 +ecp_nistz256_point_add: + stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional + sub sp,sp,#32*18+16 + + ldmia $b_ptr!,{r4-r11} @ copy in2_x + add r3,sp,#$in2_x + stmia r3!,{r4-r11} + ldmia $b_ptr!,{r4-r11} @ copy in2_y + stmia r3!,{r4-r11} + ldmia $b_ptr,{r4-r11} @ copy in2_z + orr r12,r4,r5 + orr r12,r12,r6 + orr r12,r12,r7 + orr r12,r12,r8 + orr r12,r12,r9 + orr r12,r12,r10 + orr r12,r12,r11 + cmp r12,#0 +#ifdef __thumb2__ + it ne +#endif + movne r12,#-1 + stmia r3,{r4-r11} + str r12,[sp,#32*18+8] @ !in2infty + + ldmia $a_ptr!,{r4-r11} @ copy in1_x + add r3,sp,#$in1_x + stmia r3!,{r4-r11} + ldmia $a_ptr!,{r4-r11} @ copy in1_y + stmia r3!,{r4-r11} + ldmia $a_ptr,{r4-r11} @ copy in1_z + orr r12,r4,r5 + orr r12,r12,r6 + orr r12,r12,r7 + orr r12,r12,r8 + orr r12,r12,r9 + orr r12,r12,r10 + orr r12,r12,r11 + cmp r12,#0 +#ifdef __thumb2__ + it ne +#endif + movne r12,#-1 + stmia r3,{r4-r11} + str r12,[sp,#32*18+4] @ !in1infty + + add $a_ptr,sp,#$in2_z + add $b_ptr,sp,#$in2_z + add $r_ptr,sp,#$Z2sqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z2sqr, in2_z); + + add $a_ptr,sp,#$in1_z + add $b_ptr,sp,#$in1_z + add $r_ptr,sp,#$Z1sqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z1sqr, in1_z); + + add $a_ptr,sp,#$in2_z + add $b_ptr,sp,#$Z2sqr + add $r_ptr,sp,#$S1 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S1, Z2sqr, in2_z); + + add $a_ptr,sp,#$in1_z + add $b_ptr,sp,#$Z1sqr + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, Z1sqr, in1_z); + + add $a_ptr,sp,#$in1_y + add $b_ptr,sp,#$S1 + add $r_ptr,sp,#$S1 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S1, S1, in1_y); + + add $a_ptr,sp,#$in2_y + add $b_ptr,sp,#$S2 + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S2, in2_y); + + add $b_ptr,sp,#$S1 + add $r_ptr,sp,#$R + bl __ecp_nistz256_sub_from @ p256_sub(R, S2, S1); + + orr $a0,$a0,$a1 @ see if result is zero + orr $a2,$a2,$a3 + orr $a4,$a4,$a5 + orr $a0,$a0,$a2 + orr $a4,$a4,$a6 + orr $a0,$a0,$a7 + add $a_ptr,sp,#$in1_x + orr $a0,$a0,$a4 + add $b_ptr,sp,#$Z2sqr + str $a0,[sp,#32*18+12] + + add $r_ptr,sp,#$U1 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(U1, in1_x, Z2sqr); + + add $a_ptr,sp,#$in2_x + add $b_ptr,sp,#$Z1sqr + add $r_ptr,sp,#$U2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, in2_x, Z1sqr); + + add $b_ptr,sp,#$U1 + add $r_ptr,sp,#$H + bl __ecp_nistz256_sub_from @ p256_sub(H, U2, U1); + + orr $a0,$a0,$a1 @ see if result is zero + orr $a2,$a2,$a3 + orr $a4,$a4,$a5 + orr $a0,$a0,$a2 + orr $a4,$a4,$a6 + orr $a0,$a0,$a7 + orrs $a0,$a0,$a4 + + bne .Ladd_proceed @ is_equal(U1,U2)? + + ldr $t0,[sp,#32*18+4] + ldr $t1,[sp,#32*18+8] + ldr $t2,[sp,#32*18+12] + tst $t0,$t1 + beq .Ladd_proceed @ (in1infty || in2infty)? + tst $t2,$t2 + beq .Ladd_double @ is_equal(S1,S2)? + + ldr $r_ptr,[sp,#32*18+16] + eor r4,r4,r4 + eor r5,r5,r5 + eor r6,r6,r6 + eor r7,r7,r7 + eor r8,r8,r8 + eor r9,r9,r9 + eor r10,r10,r10 + eor r11,r11,r11 + stmia $r_ptr!,{r4-r11} + stmia $r_ptr!,{r4-r11} + stmia $r_ptr!,{r4-r11} + b .Ladd_done + +.align 4 +.Ladd_double: + ldr $a_ptr,[sp,#32*18+20] + add sp,sp,#32*(18-5)+16 @ difference in frame sizes + b .Lpoint_double_shortcut + +.align 4 +.Ladd_proceed: + add $a_ptr,sp,#$R + add $b_ptr,sp,#$R + add $r_ptr,sp,#$Rsqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Rsqr, R); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$in1_z + add $r_ptr,sp,#$res_z + bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, H, in1_z); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$H + add $r_ptr,sp,#$Hsqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Hsqr, H); + + add $a_ptr,sp,#$in2_z + add $b_ptr,sp,#$res_z + add $r_ptr,sp,#$res_z + bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, res_z, in2_z); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$Hsqr + add $r_ptr,sp,#$Hcub + bl __ecp_nistz256_mul_mont @ p256_mul_mont(Hcub, Hsqr, H); + + add $a_ptr,sp,#$Hsqr + add $b_ptr,sp,#$U1 + add $r_ptr,sp,#$U2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, U1, Hsqr); + + add $r_ptr,sp,#$Hsqr + bl __ecp_nistz256_add_self @ p256_mul_by_2(Hsqr, U2); + + add $b_ptr,sp,#$Rsqr + add $r_ptr,sp,#$res_x + bl __ecp_nistz256_sub_morf @ p256_sub(res_x, Rsqr, Hsqr); + + add $b_ptr,sp,#$Hcub + bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, Hcub); + + add $b_ptr,sp,#$U2 + add $r_ptr,sp,#$res_y + bl __ecp_nistz256_sub_morf @ p256_sub(res_y, U2, res_x); + + add $a_ptr,sp,#$Hcub + add $b_ptr,sp,#$S1 + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S1, Hcub); + + add $a_ptr,sp,#$R + add $b_ptr,sp,#$res_y + add $r_ptr,sp,#$res_y + bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_y, res_y, R); + + add $b_ptr,sp,#$S2 + bl __ecp_nistz256_sub_from @ p256_sub(res_y, res_y, S2); + + ldr r11,[sp,#32*18+4] @ !in1intfy + ldr r12,[sp,#32*18+8] @ !in2intfy + add r1,sp,#$res_x + add r2,sp,#$in2_x + and r10,r11,r12 + mvn r11,r11 + add r3,sp,#$in1_x + and r11,r11,r12 + mvn r12,r12 + ldr $r_ptr,[sp,#32*18+16] +___ +for($i=0;$i<96;$i+=8) { # conditional moves +$code.=<<___; + ldmia r1!,{r4-r5} @ res_x + ldmia r2!,{r6-r7} @ in2_x + ldmia r3!,{r8-r9} @ in1_x + and r4,r4,r10 + and r5,r5,r10 + and r6,r6,r11 + and r7,r7,r11 + and r8,r8,r12 + and r9,r9,r12 + orr r4,r4,r6 + orr r5,r5,r7 + orr r4,r4,r8 + orr r5,r5,r9 + stmia $r_ptr!,{r4-r5} +___ +} +$code.=<<___; +.Ladd_done: + add sp,sp,#32*18+16+16 @ +16 means "skip even over saved r0-r3" +#if __ARM_ARCH__>=5 || defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_point_add,.-ecp_nistz256_point_add +___ +} + +######################################################################## +# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT_AFFINE *in2); +{ +my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y, + $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..14)); +my $Z1sqr = $S2; +# above map() describes stack layout with 18 temporary +# 256-bit vectors on top. Then note that we push +# starting from r0, which means that we have copy of +# input arguments just below these temporary vectors. +# We use two of them for !in1infty, !in2intfy. + +my @ONE_mont=(1,0,0,-1,-1,-1,-2,0); + +$code.=<<___; +.globl ecp_nistz256_point_add_affine +.type ecp_nistz256_point_add_affine,%function +.align 5 +ecp_nistz256_point_add_affine: + stmdb sp!,{r0-r12,lr} @ push from r0, unusual, but intentional + sub sp,sp,#32*15 + + ldmia $a_ptr!,{r4-r11} @ copy in1_x + add r3,sp,#$in1_x + stmia r3!,{r4-r11} + ldmia $a_ptr!,{r4-r11} @ copy in1_y + stmia r3!,{r4-r11} + ldmia $a_ptr,{r4-r11} @ copy in1_z + orr r12,r4,r5 + orr r12,r12,r6 + orr r12,r12,r7 + orr r12,r12,r8 + orr r12,r12,r9 + orr r12,r12,r10 + orr r12,r12,r11 + cmp r12,#0 +#ifdef __thumb2__ + it ne +#endif + movne r12,#-1 + stmia r3,{r4-r11} + str r12,[sp,#32*15+4] @ !in1infty + + ldmia $b_ptr!,{r4-r11} @ copy in2_x + add r3,sp,#$in2_x + orr r12,r4,r5 + orr r12,r12,r6 + orr r12,r12,r7 + orr r12,r12,r8 + orr r12,r12,r9 + orr r12,r12,r10 + orr r12,r12,r11 + stmia r3!,{r4-r11} + ldmia $b_ptr!,{r4-r11} @ copy in2_y + orr r12,r12,r4 + orr r12,r12,r5 + orr r12,r12,r6 + orr r12,r12,r7 + orr r12,r12,r8 + orr r12,r12,r9 + orr r12,r12,r10 + orr r12,r12,r11 + stmia r3!,{r4-r11} + cmp r12,#0 +#ifdef __thumb2__ + it ne +#endif + movne r12,#-1 + str r12,[sp,#32*15+8] @ !in2infty + + add $a_ptr,sp,#$in1_z + add $b_ptr,sp,#$in1_z + add $r_ptr,sp,#$Z1sqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Z1sqr, in1_z); + + add $a_ptr,sp,#$Z1sqr + add $b_ptr,sp,#$in2_x + add $r_ptr,sp,#$U2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, Z1sqr, in2_x); + + add $b_ptr,sp,#$in1_x + add $r_ptr,sp,#$H + bl __ecp_nistz256_sub_from @ p256_sub(H, U2, in1_x); + + add $a_ptr,sp,#$Z1sqr + add $b_ptr,sp,#$in1_z + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, Z1sqr, in1_z); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$in1_z + add $r_ptr,sp,#$res_z + bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_z, H, in1_z); + + add $a_ptr,sp,#$in2_y + add $b_ptr,sp,#$S2 + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, S2, in2_y); + + add $b_ptr,sp,#$in1_y + add $r_ptr,sp,#$R + bl __ecp_nistz256_sub_from @ p256_sub(R, S2, in1_y); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$H + add $r_ptr,sp,#$Hsqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Hsqr, H); + + add $a_ptr,sp,#$R + add $b_ptr,sp,#$R + add $r_ptr,sp,#$Rsqr + bl __ecp_nistz256_mul_mont @ p256_sqr_mont(Rsqr, R); + + add $a_ptr,sp,#$H + add $b_ptr,sp,#$Hsqr + add $r_ptr,sp,#$Hcub + bl __ecp_nistz256_mul_mont @ p256_mul_mont(Hcub, Hsqr, H); + + add $a_ptr,sp,#$Hsqr + add $b_ptr,sp,#$in1_x + add $r_ptr,sp,#$U2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(U2, in1_x, Hsqr); + + add $r_ptr,sp,#$Hsqr + bl __ecp_nistz256_add_self @ p256_mul_by_2(Hsqr, U2); + + add $b_ptr,sp,#$Rsqr + add $r_ptr,sp,#$res_x + bl __ecp_nistz256_sub_morf @ p256_sub(res_x, Rsqr, Hsqr); + + add $b_ptr,sp,#$Hcub + bl __ecp_nistz256_sub_from @ p256_sub(res_x, res_x, Hcub); + + add $b_ptr,sp,#$U2 + add $r_ptr,sp,#$res_y + bl __ecp_nistz256_sub_morf @ p256_sub(res_y, U2, res_x); + + add $a_ptr,sp,#$Hcub + add $b_ptr,sp,#$in1_y + add $r_ptr,sp,#$S2 + bl __ecp_nistz256_mul_mont @ p256_mul_mont(S2, in1_y, Hcub); + + add $a_ptr,sp,#$R + add $b_ptr,sp,#$res_y + add $r_ptr,sp,#$res_y + bl __ecp_nistz256_mul_mont @ p256_mul_mont(res_y, res_y, R); + + add $b_ptr,sp,#$S2 + bl __ecp_nistz256_sub_from @ p256_sub(res_y, res_y, S2); + + ldr r11,[sp,#32*15+4] @ !in1intfy + ldr r12,[sp,#32*15+8] @ !in2intfy + add r1,sp,#$res_x + add r2,sp,#$in2_x + and r10,r11,r12 + mvn r11,r11 + add r3,sp,#$in1_x + and r11,r11,r12 + mvn r12,r12 + ldr $r_ptr,[sp,#32*15] +___ +for($i=0;$i<64;$i+=8) { # conditional moves +$code.=<<___; + ldmia r1!,{r4-r5} @ res_x + ldmia r2!,{r6-r7} @ in2_x + ldmia r3!,{r8-r9} @ in1_x + and r4,r4,r10 + and r5,r5,r10 + and r6,r6,r11 + and r7,r7,r11 + and r8,r8,r12 + and r9,r9,r12 + orr r4,r4,r6 + orr r5,r5,r7 + orr r4,r4,r8 + orr r5,r5,r9 + stmia $r_ptr!,{r4-r5} +___ +} +for(;$i<96;$i+=8) { +my $j=($i-64)/4; +$code.=<<___; + ldmia r1!,{r4-r5} @ res_z + ldmia r3!,{r8-r9} @ in1_z + and r4,r4,r10 + and r5,r5,r10 + and r6,r11,#@ONE_mont[$j] + and r7,r11,#@ONE_mont[$j+1] + and r8,r8,r12 + and r9,r9,r12 + orr r4,r4,r6 + orr r5,r5,r7 + orr r4,r4,r8 + orr r5,r5,r9 + stmia $r_ptr!,{r4-r5} +___ +} +$code.=<<___; + add sp,sp,#32*15+16 @ +16 means "skip even over saved r0-r3" +#if __ARM_ARCH__>=5 || !defined(__thumb__) + ldmia sp!,{r4-r12,pc} +#else + ldmia sp!,{r4-r12,lr} + bx lr @ interoperable with Thumb ISA:-) +#endif +.size ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine +___ +} }}} + +foreach (split("\n",$code)) { + s/\`([^\`]*)\`/eval $1/geo; + + s/\bq([0-9]+)#(lo|hi)/sprintf "d%d",2*$1+($2 eq "hi")/geo; + + print $_,"\n"; +} +close STDOUT; # enforce flush diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv8.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv8.pl new file mode 100644 index 0000000..cdc9161 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-armv8.pl @@ -0,0 +1,1558 @@ +#! /usr/bin/env perl +# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +# ==================================================================== +# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL +# project. The module is, however, dual licensed under OpenSSL and +# CRYPTOGAMS licenses depending on where you obtain it. For further +# details see http://www.openssl.org/~appro/cryptogams/. +# ==================================================================== +# +# ECP_NISTZ256 module for ARMv8. +# +# February 2015. +# +# Original ECP_NISTZ256 submission targeting x86_64 is detailed in +# http://eprint.iacr.org/2013/816. +# +# with/without -DECP_NISTZ256_ASM +# Apple A7 +120-360% +# Cortex-A53 +120-400% +# Cortex-A57 +120-350% +# X-Gene +200-330% +# Denver +140-400% +# +# Ranges denote minimum and maximum improvement coefficients depending +# on benchmark. Lower coefficients are for ECDSA sign, server-side +# operation. Keep in mind that +400% means 5x improvement. + +$flavour = shift; +while (($output=shift) && ($output!~/\w[\w\-]*\.\w+$/)) {} + +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or +( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or +die "can't locate arm-xlate.pl"; + +open OUT,"| \"$^X\" $xlate $flavour $output"; +*STDOUT=*OUT; + +{ +my ($rp,$ap,$bp,$bi,$a0,$a1,$a2,$a3,$t0,$t1,$t2,$t3,$poly1,$poly3, + $acc0,$acc1,$acc2,$acc3,$acc4,$acc5) = + map("x$_",(0..17,19,20)); + +my ($acc6,$acc7)=($ap,$bp); # used in __ecp_nistz256_sqr_mont + +$code.=<<___; +#include "arm_arch.h" + +.text +___ +######################################################################## +# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7 +# +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +open TABLE,"<ecp_nistz256_table.c" or +open TABLE,"<${dir}../ecp_nistz256_table.c" or +die "failed to open ecp_nistz256_table.c:",$!; + +use integer; + +foreach(<TABLE>) { + s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo; +} +close TABLE; + +# See ecp_nistz256_table.c for explanation for why it's 64*16*37. +# 64*16*37-1 is because $#arr returns last valid index or @arr, not +# amount of elements. +die "insane number of elements" if ($#arr != 64*16*37-1); + +$code.=<<___; +.globl ecp_nistz256_precomputed +.type ecp_nistz256_precomputed,%object +.align 12 +ecp_nistz256_precomputed: +___ +######################################################################## +# this conversion smashes P256_POINT_AFFINE by individual bytes with +# 64 byte interval, similar to +# 1111222233334444 +# 1234123412341234 +for(1..37) { + @tbl = splice(@arr,0,64*16); + for($i=0;$i<64;$i++) { + undef @line; + for($j=0;$j<64;$j++) { + push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff; + } + $code.=".byte\t"; + $code.=join(',',map { sprintf "0x%02x",$_} @line); + $code.="\n"; + } +} +$code.=<<___; +.size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed +.align 5 +.Lpoly: +.quad 0xffffffffffffffff,0x00000000ffffffff,0x0000000000000000,0xffffffff00000001 +.LRR: // 2^512 mod P precomputed for NIST P256 polynomial +.quad 0x0000000000000003,0xfffffffbffffffff,0xfffffffffffffffe,0x00000004fffffffd +.Lone_mont: +.quad 0x0000000000000001,0xffffffff00000000,0xffffffffffffffff,0x00000000fffffffe +.Lone: +.quad 1,0,0,0 +.asciz "ECP_NISTZ256 for ARMv8, CRYPTOGAMS by <appro\@openssl.org>" + +// void ecp_nistz256_to_mont(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_to_mont +.type ecp_nistz256_to_mont,%function +.align 6 +ecp_nistz256_to_mont: + stp x29,x30,[sp,#-32]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + + ldr $bi,.LRR // bp[0] + ldp $a0,$a1,[$ap] + ldp $a2,$a3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + adr $bp,.LRR // &bp[0] + + bl __ecp_nistz256_mul_mont + + ldp x19,x20,[sp,#16] + ldp x29,x30,[sp],#32 + ret +.size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont + +// void ecp_nistz256_from_mont(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_from_mont +.type ecp_nistz256_from_mont,%function +.align 4 +ecp_nistz256_from_mont: + stp x29,x30,[sp,#-32]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + + mov $bi,#1 // bp[0] + ldp $a0,$a1,[$ap] + ldp $a2,$a3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + adr $bp,.Lone // &bp[0] + + bl __ecp_nistz256_mul_mont + + ldp x19,x20,[sp,#16] + ldp x29,x30,[sp],#32 + ret +.size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont + +// void ecp_nistz256_mul_mont(BN_ULONG x0[4],const BN_ULONG x1[4], +// const BN_ULONG x2[4]); +.globl ecp_nistz256_mul_mont +.type ecp_nistz256_mul_mont,%function +.align 4 +ecp_nistz256_mul_mont: + stp x29,x30,[sp,#-32]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + + ldr $bi,[$bp] // bp[0] + ldp $a0,$a1,[$ap] + ldp $a2,$a3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_mul_mont + + ldp x19,x20,[sp,#16] + ldp x29,x30,[sp],#32 + ret +.size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont + +// void ecp_nistz256_sqr_mont(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_sqr_mont +.type ecp_nistz256_sqr_mont,%function +.align 4 +ecp_nistz256_sqr_mont: + stp x29,x30,[sp,#-32]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + + ldp $a0,$a1,[$ap] + ldp $a2,$a3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_sqr_mont + + ldp x19,x20,[sp,#16] + ldp x29,x30,[sp],#32 + ret +.size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont + +// void ecp_nistz256_add(BN_ULONG x0[4],const BN_ULONG x1[4], +// const BN_ULONG x2[4]); +.globl ecp_nistz256_add +.type ecp_nistz256_add,%function +.align 4 +ecp_nistz256_add: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + ldp $acc0,$acc1,[$ap] + ldp $t0,$t1,[$bp] + ldp $acc2,$acc3,[$ap,#16] + ldp $t2,$t3,[$bp,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_add + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_add,.-ecp_nistz256_add + +// void ecp_nistz256_div_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_div_by_2 +.type ecp_nistz256_div_by_2,%function +.align 4 +ecp_nistz256_div_by_2: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + ldp $acc0,$acc1,[$ap] + ldp $acc2,$acc3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_div_by_2 + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2 + +// void ecp_nistz256_mul_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_mul_by_2 +.type ecp_nistz256_mul_by_2,%function +.align 4 +ecp_nistz256_mul_by_2: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + ldp $acc0,$acc1,[$ap] + ldp $acc2,$acc3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + mov $t0,$acc0 + mov $t1,$acc1 + mov $t2,$acc2 + mov $t3,$acc3 + + bl __ecp_nistz256_add // ret = a+a // 2*a + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2 + +// void ecp_nistz256_mul_by_3(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_mul_by_3 +.type ecp_nistz256_mul_by_3,%function +.align 4 +ecp_nistz256_mul_by_3: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + ldp $acc0,$acc1,[$ap] + ldp $acc2,$acc3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + mov $t0,$acc0 + mov $t1,$acc1 + mov $t2,$acc2 + mov $t3,$acc3 + mov $a0,$acc0 + mov $a1,$acc1 + mov $a2,$acc2 + mov $a3,$acc3 + + bl __ecp_nistz256_add // ret = a+a // 2*a + + mov $t0,$a0 + mov $t1,$a1 + mov $t2,$a2 + mov $t3,$a3 + + bl __ecp_nistz256_add // ret += a // 2*a+a=3*a + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3 + +// void ecp_nistz256_sub(BN_ULONG x0[4],const BN_ULONG x1[4], +// const BN_ULONG x2[4]); +.globl ecp_nistz256_sub +.type ecp_nistz256_sub,%function +.align 4 +ecp_nistz256_sub: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + ldp $acc0,$acc1,[$ap] + ldp $acc2,$acc3,[$ap,#16] + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_sub_from + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_sub,.-ecp_nistz256_sub + +// void ecp_nistz256_neg(BN_ULONG x0[4],const BN_ULONG x1[4]); +.globl ecp_nistz256_neg +.type ecp_nistz256_neg,%function +.align 4 +ecp_nistz256_neg: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + mov $bp,$ap + mov $acc0,xzr // a = 0 + mov $acc1,xzr + mov $acc2,xzr + mov $acc3,xzr + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + bl __ecp_nistz256_sub_from + + ldp x29,x30,[sp],#16 + ret +.size ecp_nistz256_neg,.-ecp_nistz256_neg + +// note that __ecp_nistz256_mul_mont expects a[0-3] input pre-loaded +// to $a0-$a3 and b[0] - to $bi +.type __ecp_nistz256_mul_mont,%function +.align 4 +__ecp_nistz256_mul_mont: + mul $acc0,$a0,$bi // a[0]*b[0] + umulh $t0,$a0,$bi + + mul $acc1,$a1,$bi // a[1]*b[0] + umulh $t1,$a1,$bi + + mul $acc2,$a2,$bi // a[2]*b[0] + umulh $t2,$a2,$bi + + mul $acc3,$a3,$bi // a[3]*b[0] + umulh $t3,$a3,$bi + ldr $bi,[$bp,#8] // b[1] + + adds $acc1,$acc1,$t0 // accumulate high parts of multiplication + lsl $t0,$acc0,#32 + adcs $acc2,$acc2,$t1 + lsr $t1,$acc0,#32 + adcs $acc3,$acc3,$t2 + adc $acc4,xzr,$t3 + mov $acc5,xzr +___ +for($i=1;$i<4;$i++) { + # Reduction iteration is normally performed by accumulating + # result of multiplication of modulus by "magic" digit [and + # omitting least significant word, which is guaranteed to + # be 0], but thanks to special form of modulus and "magic" + # digit being equal to least significant word, it can be + # performed with additions and subtractions alone. Indeed: + # + # ffff0001.00000000.0000ffff.ffffffff + # * abcdefgh + # + xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh + # + # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we + # rewrite above as: + # + # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh + # + abcdefgh.abcdefgh.0000abcd.efgh0000.00000000 + # - 0000abcd.efgh0000.00000000.00000000.abcdefgh + # + # or marking redundant operations: + # + # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.-------- + # + abcdefgh.abcdefgh.0000abcd.efgh0000.-------- + # - 0000abcd.efgh0000.--------.--------.-------- + +$code.=<<___; + subs $t2,$acc0,$t0 // "*0xffff0001" + sbc $t3,$acc0,$t1 + adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0] + mul $t0,$a0,$bi // lo(a[0]*b[i]) + adcs $acc1,$acc2,$t1 + mul $t1,$a1,$bi // lo(a[1]*b[i]) + adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001 + mul $t2,$a2,$bi // lo(a[2]*b[i]) + adcs $acc3,$acc4,$t3 + mul $t3,$a3,$bi // lo(a[3]*b[i]) + adc $acc4,$acc5,xzr + + adds $acc0,$acc0,$t0 // accumulate low parts of multiplication + umulh $t0,$a0,$bi // hi(a[0]*b[i]) + adcs $acc1,$acc1,$t1 + umulh $t1,$a1,$bi // hi(a[1]*b[i]) + adcs $acc2,$acc2,$t2 + umulh $t2,$a2,$bi // hi(a[2]*b[i]) + adcs $acc3,$acc3,$t3 + umulh $t3,$a3,$bi // hi(a[3]*b[i]) + adc $acc4,$acc4,xzr +___ +$code.=<<___ if ($i<3); + ldr $bi,[$bp,#8*($i+1)] // b[$i+1] +___ +$code.=<<___; + adds $acc1,$acc1,$t0 // accumulate high parts of multiplication + lsl $t0,$acc0,#32 + adcs $acc2,$acc2,$t1 + lsr $t1,$acc0,#32 + adcs $acc3,$acc3,$t2 + adcs $acc4,$acc4,$t3 + adc $acc5,xzr,xzr +___ +} +$code.=<<___; + // last reduction + subs $t2,$acc0,$t0 // "*0xffff0001" + sbc $t3,$acc0,$t1 + adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0] + adcs $acc1,$acc2,$t1 + adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001 + adcs $acc3,$acc4,$t3 + adc $acc4,$acc5,xzr + + adds $t0,$acc0,#1 // subs $t0,$acc0,#-1 // tmp = ret-modulus + sbcs $t1,$acc1,$poly1 + sbcs $t2,$acc2,xzr + sbcs $t3,$acc3,$poly3 + sbcs xzr,$acc4,xzr // did it borrow? + + csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus + csel $acc1,$acc1,$t1,lo + csel $acc2,$acc2,$t2,lo + stp $acc0,$acc1,[$rp] + csel $acc3,$acc3,$t3,lo + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont + +// note that __ecp_nistz256_sqr_mont expects a[0-3] input pre-loaded +// to $a0-$a3 +.type __ecp_nistz256_sqr_mont,%function +.align 4 +__ecp_nistz256_sqr_mont: + // | | | | | |a1*a0| | + // | | | | |a2*a0| | | + // | |a3*a2|a3*a0| | | | + // | | | |a2*a1| | | | + // | | |a3*a1| | | | | + // *| | | | | | | | 2| + // +|a3*a3|a2*a2|a1*a1|a0*a0| + // |--+--+--+--+--+--+--+--| + // |A7|A6|A5|A4|A3|A2|A1|A0|, where Ax is $accx, i.e. follow $accx + // + // "can't overflow" below mark carrying into high part of + // multiplication result, which can't overflow, because it + // can never be all ones. + + mul $acc1,$a1,$a0 // a[1]*a[0] + umulh $t1,$a1,$a0 + mul $acc2,$a2,$a0 // a[2]*a[0] + umulh $t2,$a2,$a0 + mul $acc3,$a3,$a0 // a[3]*a[0] + umulh $acc4,$a3,$a0 + + adds $acc2,$acc2,$t1 // accumulate high parts of multiplication + mul $t0,$a2,$a1 // a[2]*a[1] + umulh $t1,$a2,$a1 + adcs $acc3,$acc3,$t2 + mul $t2,$a3,$a1 // a[3]*a[1] + umulh $t3,$a3,$a1 + adc $acc4,$acc4,xzr // can't overflow + + mul $acc5,$a3,$a2 // a[3]*a[2] + umulh $acc6,$a3,$a2 + + adds $t1,$t1,$t2 // accumulate high parts of multiplication + mul $acc0,$a0,$a0 // a[0]*a[0] + adc $t2,$t3,xzr // can't overflow + + adds $acc3,$acc3,$t0 // accumulate low parts of multiplication + umulh $a0,$a0,$a0 + adcs $acc4,$acc4,$t1 + mul $t1,$a1,$a1 // a[1]*a[1] + adcs $acc5,$acc5,$t2 + umulh $a1,$a1,$a1 + adc $acc6,$acc6,xzr // can't overflow + + adds $acc1,$acc1,$acc1 // acc[1-6]*=2 + mul $t2,$a2,$a2 // a[2]*a[2] + adcs $acc2,$acc2,$acc2 + umulh $a2,$a2,$a2 + adcs $acc3,$acc3,$acc3 + mul $t3,$a3,$a3 // a[3]*a[3] + adcs $acc4,$acc4,$acc4 + umulh $a3,$a3,$a3 + adcs $acc5,$acc5,$acc5 + adcs $acc6,$acc6,$acc6 + adc $acc7,xzr,xzr + + adds $acc1,$acc1,$a0 // +a[i]*a[i] + adcs $acc2,$acc2,$t1 + adcs $acc3,$acc3,$a1 + adcs $acc4,$acc4,$t2 + adcs $acc5,$acc5,$a2 + lsl $t0,$acc0,#32 + adcs $acc6,$acc6,$t3 + lsr $t1,$acc0,#32 + adc $acc7,$acc7,$a3 +___ +for($i=0;$i<3;$i++) { # reductions, see commentary in + # multiplication for details +$code.=<<___; + subs $t2,$acc0,$t0 // "*0xffff0001" + sbc $t3,$acc0,$t1 + adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0] + adcs $acc1,$acc2,$t1 + lsl $t0,$acc0,#32 + adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001 + lsr $t1,$acc0,#32 + adc $acc3,$t3,xzr // can't overflow +___ +} +$code.=<<___; + subs $t2,$acc0,$t0 // "*0xffff0001" + sbc $t3,$acc0,$t1 + adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0] + adcs $acc1,$acc2,$t1 + adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001 + adc $acc3,$t3,xzr // can't overflow + + adds $acc0,$acc0,$acc4 // accumulate upper half + adcs $acc1,$acc1,$acc5 + adcs $acc2,$acc2,$acc6 + adcs $acc3,$acc3,$acc7 + adc $acc4,xzr,xzr + + adds $t0,$acc0,#1 // subs $t0,$acc0,#-1 // tmp = ret-modulus + sbcs $t1,$acc1,$poly1 + sbcs $t2,$acc2,xzr + sbcs $t3,$acc3,$poly3 + sbcs xzr,$acc4,xzr // did it borrow? + + csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus + csel $acc1,$acc1,$t1,lo + csel $acc2,$acc2,$t2,lo + stp $acc0,$acc1,[$rp] + csel $acc3,$acc3,$t3,lo + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_sqr_mont,.-__ecp_nistz256_sqr_mont + +// Note that __ecp_nistz256_add expects both input vectors pre-loaded to +// $a0-$a3 and $t0-$t3. This is done because it's used in multiple +// contexts, e.g. in multiplication by 2 and 3... +.type __ecp_nistz256_add,%function +.align 4 +__ecp_nistz256_add: + adds $acc0,$acc0,$t0 // ret = a+b + adcs $acc1,$acc1,$t1 + adcs $acc2,$acc2,$t2 + adcs $acc3,$acc3,$t3 + adc $ap,xzr,xzr // zap $ap + + adds $t0,$acc0,#1 // subs $t0,$a0,#-1 // tmp = ret-modulus + sbcs $t1,$acc1,$poly1 + sbcs $t2,$acc2,xzr + sbcs $t3,$acc3,$poly3 + sbcs xzr,$ap,xzr // did subtraction borrow? + + csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus + csel $acc1,$acc1,$t1,lo + csel $acc2,$acc2,$t2,lo + stp $acc0,$acc1,[$rp] + csel $acc3,$acc3,$t3,lo + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_add,.-__ecp_nistz256_add + +.type __ecp_nistz256_sub_from,%function +.align 4 +__ecp_nistz256_sub_from: + ldp $t0,$t1,[$bp] + ldp $t2,$t3,[$bp,#16] + subs $acc0,$acc0,$t0 // ret = a-b + sbcs $acc1,$acc1,$t1 + sbcs $acc2,$acc2,$t2 + sbcs $acc3,$acc3,$t3 + sbc $ap,xzr,xzr // zap $ap + + subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = ret+modulus + adcs $t1,$acc1,$poly1 + adcs $t2,$acc2,xzr + adc $t3,$acc3,$poly3 + cmp $ap,xzr // did subtraction borrow? + + csel $acc0,$acc0,$t0,eq // ret = borrow ? ret+modulus : ret + csel $acc1,$acc1,$t1,eq + csel $acc2,$acc2,$t2,eq + stp $acc0,$acc1,[$rp] + csel $acc3,$acc3,$t3,eq + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from + +.type __ecp_nistz256_sub_morf,%function +.align 4 +__ecp_nistz256_sub_morf: + ldp $t0,$t1,[$bp] + ldp $t2,$t3,[$bp,#16] + subs $acc0,$t0,$acc0 // ret = b-a + sbcs $acc1,$t1,$acc1 + sbcs $acc2,$t2,$acc2 + sbcs $acc3,$t3,$acc3 + sbc $ap,xzr,xzr // zap $ap + + subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = ret+modulus + adcs $t1,$acc1,$poly1 + adcs $t2,$acc2,xzr + adc $t3,$acc3,$poly3 + cmp $ap,xzr // did subtraction borrow? + + csel $acc0,$acc0,$t0,eq // ret = borrow ? ret+modulus : ret + csel $acc1,$acc1,$t1,eq + csel $acc2,$acc2,$t2,eq + stp $acc0,$acc1,[$rp] + csel $acc3,$acc3,$t3,eq + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf + +.type __ecp_nistz256_div_by_2,%function +.align 4 +__ecp_nistz256_div_by_2: + subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = a+modulus + adcs $t1,$acc1,$poly1 + adcs $t2,$acc2,xzr + adcs $t3,$acc3,$poly3 + adc $ap,xzr,xzr // zap $ap + tst $acc0,#1 // is a even? + + csel $acc0,$acc0,$t0,eq // ret = even ? a : a+modulus + csel $acc1,$acc1,$t1,eq + csel $acc2,$acc2,$t2,eq + csel $acc3,$acc3,$t3,eq + csel $ap,xzr,$ap,eq + + lsr $acc0,$acc0,#1 // ret >>= 1 + orr $acc0,$acc0,$acc1,lsl#63 + lsr $acc1,$acc1,#1 + orr $acc1,$acc1,$acc2,lsl#63 + lsr $acc2,$acc2,#1 + orr $acc2,$acc2,$acc3,lsl#63 + lsr $acc3,$acc3,#1 + stp $acc0,$acc1,[$rp] + orr $acc3,$acc3,$ap,lsl#63 + stp $acc2,$acc3,[$rp,#16] + + ret +.size __ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2 +___ +######################################################################## +# following subroutines are "literal" implementation of those found in +# ecp_nistz256.c +# +######################################################################## +# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp); +# +{ +my ($S,$M,$Zsqr,$tmp0)=map(32*$_,(0..3)); +# above map() describes stack layout with 4 temporary +# 256-bit vectors on top. +my ($rp_real,$ap_real) = map("x$_",(21,22)); + +$code.=<<___; +.globl ecp_nistz256_point_double +.type ecp_nistz256_point_double,%function +.align 5 +ecp_nistz256_point_double: + stp x29,x30,[sp,#-80]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + stp x21,x22,[sp,#32] + sub sp,sp,#32*4 + +.Ldouble_shortcut: + ldp $acc0,$acc1,[$ap,#32] + mov $rp_real,$rp + ldp $acc2,$acc3,[$ap,#48] + mov $ap_real,$ap + ldr $poly1,.Lpoly+8 + mov $t0,$acc0 + ldr $poly3,.Lpoly+24 + mov $t1,$acc1 + ldp $a0,$a1,[$ap_real,#64] // forward load for p256_sqr_mont + mov $t2,$acc2 + mov $t3,$acc3 + ldp $a2,$a3,[$ap_real,#64+16] + add $rp,sp,#$S + bl __ecp_nistz256_add // p256_mul_by_2(S, in_y); + + add $rp,sp,#$Zsqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Zsqr, in_z); + + ldp $t0,$t1,[$ap_real] + ldp $t2,$t3,[$ap_real,#16] + mov $a0,$acc0 // put Zsqr aside for p256_sub + mov $a1,$acc1 + mov $a2,$acc2 + mov $a3,$acc3 + add $rp,sp,#$M + bl __ecp_nistz256_add // p256_add(M, Zsqr, in_x); + + add $bp,$ap_real,#0 + mov $acc0,$a0 // restore Zsqr + mov $acc1,$a1 + ldp $a0,$a1,[sp,#$S] // forward load for p256_sqr_mont + mov $acc2,$a2 + mov $acc3,$a3 + ldp $a2,$a3,[sp,#$S+16] + add $rp,sp,#$Zsqr + bl __ecp_nistz256_sub_morf // p256_sub(Zsqr, in_x, Zsqr); + + add $rp,sp,#$S + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(S, S); + + ldr $bi,[$ap_real,#32] + ldp $a0,$a1,[$ap_real,#64] + ldp $a2,$a3,[$ap_real,#64+16] + add $bp,$ap_real,#32 + add $rp,sp,#$tmp0 + bl __ecp_nistz256_mul_mont // p256_mul_mont(tmp0, in_z, in_y); + + mov $t0,$acc0 + mov $t1,$acc1 + ldp $a0,$a1,[sp,#$S] // forward load for p256_sqr_mont + mov $t2,$acc2 + mov $t3,$acc3 + ldp $a2,$a3,[sp,#$S+16] + add $rp,$rp_real,#64 + bl __ecp_nistz256_add // p256_mul_by_2(res_z, tmp0); + + add $rp,sp,#$tmp0 + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(tmp0, S); + + ldr $bi,[sp,#$Zsqr] // forward load for p256_mul_mont + ldp $a0,$a1,[sp,#$M] + ldp $a2,$a3,[sp,#$M+16] + add $rp,$rp_real,#32 + bl __ecp_nistz256_div_by_2 // p256_div_by_2(res_y, tmp0); + + add $bp,sp,#$Zsqr + add $rp,sp,#$M + bl __ecp_nistz256_mul_mont // p256_mul_mont(M, M, Zsqr); + + mov $t0,$acc0 // duplicate M + mov $t1,$acc1 + mov $t2,$acc2 + mov $t3,$acc3 + mov $a0,$acc0 // put M aside + mov $a1,$acc1 + mov $a2,$acc2 + mov $a3,$acc3 + add $rp,sp,#$M + bl __ecp_nistz256_add + mov $t0,$a0 // restore M + mov $t1,$a1 + ldr $bi,[$ap_real] // forward load for p256_mul_mont + mov $t2,$a2 + ldp $a0,$a1,[sp,#$S] + mov $t3,$a3 + ldp $a2,$a3,[sp,#$S+16] + bl __ecp_nistz256_add // p256_mul_by_3(M, M); + + add $bp,$ap_real,#0 + add $rp,sp,#$S + bl __ecp_nistz256_mul_mont // p256_mul_mont(S, S, in_x); + + mov $t0,$acc0 + mov $t1,$acc1 + ldp $a0,$a1,[sp,#$M] // forward load for p256_sqr_mont + mov $t2,$acc2 + mov $t3,$acc3 + ldp $a2,$a3,[sp,#$M+16] + add $rp,sp,#$tmp0 + bl __ecp_nistz256_add // p256_mul_by_2(tmp0, S); + + add $rp,$rp_real,#0 + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(res_x, M); + + add $bp,sp,#$tmp0 + bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, tmp0); + + add $bp,sp,#$S + add $rp,sp,#$S + bl __ecp_nistz256_sub_morf // p256_sub(S, S, res_x); + + ldr $bi,[sp,#$M] + mov $a0,$acc0 // copy S + mov $a1,$acc1 + mov $a2,$acc2 + mov $a3,$acc3 + add $bp,sp,#$M + bl __ecp_nistz256_mul_mont // p256_mul_mont(S, S, M); + + add $bp,$rp_real,#32 + add $rp,$rp_real,#32 + bl __ecp_nistz256_sub_from // p256_sub(res_y, S, res_y); + + add sp,x29,#0 // destroy frame + ldp x19,x20,[x29,#16] + ldp x21,x22,[x29,#32] + ldp x29,x30,[sp],#80 + ret +.size ecp_nistz256_point_double,.-ecp_nistz256_point_double +___ +} + +######################################################################## +# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT *in2); +{ +my ($res_x,$res_y,$res_z, + $H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2)=map(32*$_,(0..11)); +my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); +# above map() describes stack layout with 12 temporary +# 256-bit vectors on top. +my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26)); + +$code.=<<___; +.globl ecp_nistz256_point_add +.type ecp_nistz256_point_add,%function +.align 5 +ecp_nistz256_point_add: + stp x29,x30,[sp,#-80]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + stp x21,x22,[sp,#32] + stp x23,x24,[sp,#48] + stp x25,x26,[sp,#64] + sub sp,sp,#32*12 + + ldp $a0,$a1,[$bp,#64] // in2_z + ldp $a2,$a3,[$bp,#64+16] + mov $rp_real,$rp + mov $ap_real,$ap + mov $bp_real,$bp + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + orr $t0,$a0,$a1 + orr $t2,$a2,$a3 + orr $in2infty,$t0,$t2 + cmp $in2infty,#0 + csetm $in2infty,ne // !in2infty + add $rp,sp,#$Z2sqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z2sqr, in2_z); + + ldp $a0,$a1,[$ap_real,#64] // in1_z + ldp $a2,$a3,[$ap_real,#64+16] + orr $t0,$a0,$a1 + orr $t2,$a2,$a3 + orr $in1infty,$t0,$t2 + cmp $in1infty,#0 + csetm $in1infty,ne // !in1infty + add $rp,sp,#$Z1sqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z1sqr, in1_z); + + ldr $bi,[$bp_real,#64] + ldp $a0,$a1,[sp,#$Z2sqr] + ldp $a2,$a3,[sp,#$Z2sqr+16] + add $bp,$bp_real,#64 + add $rp,sp,#$S1 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S1, Z2sqr, in2_z); + + ldr $bi,[$ap_real,#64] + ldp $a0,$a1,[sp,#$Z1sqr] + ldp $a2,$a3,[sp,#$Z1sqr+16] + add $bp,$ap_real,#64 + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, Z1sqr, in1_z); + + ldr $bi,[$ap_real,#32] + ldp $a0,$a1,[sp,#$S1] + ldp $a2,$a3,[sp,#$S1+16] + add $bp,$ap_real,#32 + add $rp,sp,#$S1 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S1, S1, in1_y); + + ldr $bi,[$bp_real,#32] + ldp $a0,$a1,[sp,#$S2] + ldp $a2,$a3,[sp,#$S2+16] + add $bp,$bp_real,#32 + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S2, in2_y); + + add $bp,sp,#$S1 + ldr $bi,[sp,#$Z2sqr] // forward load for p256_mul_mont + ldp $a0,$a1,[$ap_real] + ldp $a2,$a3,[$ap_real,#16] + add $rp,sp,#$R + bl __ecp_nistz256_sub_from // p256_sub(R, S2, S1); + + orr $acc0,$acc0,$acc1 // see if result is zero + orr $acc2,$acc2,$acc3 + orr $temp,$acc0,$acc2 + + add $bp,sp,#$Z2sqr + add $rp,sp,#$U1 + bl __ecp_nistz256_mul_mont // p256_mul_mont(U1, in1_x, Z2sqr); + + ldr $bi,[sp,#$Z1sqr] + ldp $a0,$a1,[$bp_real] + ldp $a2,$a3,[$bp_real,#16] + add $bp,sp,#$Z1sqr + add $rp,sp,#$U2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, in2_x, Z1sqr); + + add $bp,sp,#$U1 + ldp $a0,$a1,[sp,#$R] // forward load for p256_sqr_mont + ldp $a2,$a3,[sp,#$R+16] + add $rp,sp,#$H + bl __ecp_nistz256_sub_from // p256_sub(H, U2, U1); + + orr $acc0,$acc0,$acc1 // see if result is zero + orr $acc2,$acc2,$acc3 + orr $acc0,$acc0,$acc2 + tst $acc0,$acc0 + b.ne .Ladd_proceed // is_equal(U1,U2)? + + tst $in1infty,$in2infty + b.eq .Ladd_proceed // (in1infty || in2infty)? + + tst $temp,$temp + b.eq .Ladd_double // is_equal(S1,S2)? + + eor $a0,$a0,$a0 + eor $a1,$a1,$a1 + stp $a0,$a1,[$rp_real] + stp $a0,$a1,[$rp_real,#16] + stp $a0,$a1,[$rp_real,#32] + stp $a0,$a1,[$rp_real,#48] + stp $a0,$a1,[$rp_real,#64] + stp $a0,$a1,[$rp_real,#80] + b .Ladd_done + +.align 4 +.Ladd_double: + mov $ap,$ap_real + mov $rp,$rp_real + ldp x23,x24,[x29,#48] + ldp x25,x26,[x29,#64] + add sp,sp,#32*(12-4) // difference in stack frames + b .Ldouble_shortcut + +.align 4 +.Ladd_proceed: + add $rp,sp,#$Rsqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Rsqr, R); + + ldr $bi,[$ap_real,#64] + ldp $a0,$a1,[sp,#$H] + ldp $a2,$a3,[sp,#$H+16] + add $bp,$ap_real,#64 + add $rp,sp,#$res_z + bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, H, in1_z); + + ldp $a0,$a1,[sp,#$H] + ldp $a2,$a3,[sp,#$H+16] + add $rp,sp,#$Hsqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Hsqr, H); + + ldr $bi,[$bp_real,#64] + ldp $a0,$a1,[sp,#$res_z] + ldp $a2,$a3,[sp,#$res_z+16] + add $bp,$bp_real,#64 + add $rp,sp,#$res_z + bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, res_z, in2_z); + + ldr $bi,[sp,#$H] + ldp $a0,$a1,[sp,#$Hsqr] + ldp $a2,$a3,[sp,#$Hsqr+16] + add $bp,sp,#$H + add $rp,sp,#$Hcub + bl __ecp_nistz256_mul_mont // p256_mul_mont(Hcub, Hsqr, H); + + ldr $bi,[sp,#$Hsqr] + ldp $a0,$a1,[sp,#$U1] + ldp $a2,$a3,[sp,#$U1+16] + add $bp,sp,#$Hsqr + add $rp,sp,#$U2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, U1, Hsqr); + + mov $t0,$acc0 + mov $t1,$acc1 + mov $t2,$acc2 + mov $t3,$acc3 + add $rp,sp,#$Hsqr + bl __ecp_nistz256_add // p256_mul_by_2(Hsqr, U2); + + add $bp,sp,#$Rsqr + add $rp,sp,#$res_x + bl __ecp_nistz256_sub_morf // p256_sub(res_x, Rsqr, Hsqr); + + add $bp,sp,#$Hcub + bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, Hcub); + + add $bp,sp,#$U2 + ldr $bi,[sp,#$Hcub] // forward load for p256_mul_mont + ldp $a0,$a1,[sp,#$S1] + ldp $a2,$a3,[sp,#$S1+16] + add $rp,sp,#$res_y + bl __ecp_nistz256_sub_morf // p256_sub(res_y, U2, res_x); + + add $bp,sp,#$Hcub + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S1, Hcub); + + ldr $bi,[sp,#$R] + ldp $a0,$a1,[sp,#$res_y] + ldp $a2,$a3,[sp,#$res_y+16] + add $bp,sp,#$R + add $rp,sp,#$res_y + bl __ecp_nistz256_mul_mont // p256_mul_mont(res_y, res_y, R); + + add $bp,sp,#$S2 + bl __ecp_nistz256_sub_from // p256_sub(res_y, res_y, S2); + + ldp $a0,$a1,[sp,#$res_x] // res + ldp $a2,$a3,[sp,#$res_x+16] + ldp $t0,$t1,[$bp_real] // in2 + ldp $t2,$t3,[$bp_real,#16] +___ +for($i=0;$i<64;$i+=32) { # conditional moves +$code.=<<___; + ldp $acc0,$acc1,[$ap_real,#$i] // in1 + cmp $in1infty,#0 // !$in1intfy, remember? + ldp $acc2,$acc3,[$ap_real,#$i+16] + csel $t0,$a0,$t0,ne + csel $t1,$a1,$t1,ne + ldp $a0,$a1,[sp,#$res_x+$i+32] // res + csel $t2,$a2,$t2,ne + csel $t3,$a3,$t3,ne + cmp $in2infty,#0 // !$in2intfy, remember? + ldp $a2,$a3,[sp,#$res_x+$i+48] + csel $acc0,$t0,$acc0,ne + csel $acc1,$t1,$acc1,ne + ldp $t0,$t1,[$bp_real,#$i+32] // in2 + csel $acc2,$t2,$acc2,ne + csel $acc3,$t3,$acc3,ne + ldp $t2,$t3,[$bp_real,#$i+48] + stp $acc0,$acc1,[$rp_real,#$i] + stp $acc2,$acc3,[$rp_real,#$i+16] +___ +} +$code.=<<___; + ldp $acc0,$acc1,[$ap_real,#$i] // in1 + cmp $in1infty,#0 // !$in1intfy, remember? + ldp $acc2,$acc3,[$ap_real,#$i+16] + csel $t0,$a0,$t0,ne + csel $t1,$a1,$t1,ne + csel $t2,$a2,$t2,ne + csel $t3,$a3,$t3,ne + cmp $in2infty,#0 // !$in2intfy, remember? + csel $acc0,$t0,$acc0,ne + csel $acc1,$t1,$acc1,ne + csel $acc2,$t2,$acc2,ne + csel $acc3,$t3,$acc3,ne + stp $acc0,$acc1,[$rp_real,#$i] + stp $acc2,$acc3,[$rp_real,#$i+16] + +.Ladd_done: + add sp,x29,#0 // destroy frame + ldp x19,x20,[x29,#16] + ldp x21,x22,[x29,#32] + ldp x23,x24,[x29,#48] + ldp x25,x26,[x29,#64] + ldp x29,x30,[sp],#80 + ret +.size ecp_nistz256_point_add,.-ecp_nistz256_point_add +___ +} + +######################################################################## +# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT_AFFINE *in2); +{ +my ($res_x,$res_y,$res_z, + $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..9)); +my $Z1sqr = $S2; +# above map() describes stack layout with 10 temporary +# 256-bit vectors on top. +my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26)); + +$code.=<<___; +.globl ecp_nistz256_point_add_affine +.type ecp_nistz256_point_add_affine,%function +.align 5 +ecp_nistz256_point_add_affine: + stp x29,x30,[sp,#-80]! + add x29,sp,#0 + stp x19,x20,[sp,#16] + stp x21,x22,[sp,#32] + stp x23,x24,[sp,#48] + stp x25,x26,[sp,#64] + sub sp,sp,#32*10 + + mov $rp_real,$rp + mov $ap_real,$ap + mov $bp_real,$bp + ldr $poly1,.Lpoly+8 + ldr $poly3,.Lpoly+24 + + ldp $a0,$a1,[$ap,#64] // in1_z + ldp $a2,$a3,[$ap,#64+16] + orr $t0,$a0,$a1 + orr $t2,$a2,$a3 + orr $in1infty,$t0,$t2 + cmp $in1infty,#0 + csetm $in1infty,ne // !in1infty + + ldp $acc0,$acc1,[$bp] // in2_x + ldp $acc2,$acc3,[$bp,#16] + ldp $t0,$t1,[$bp,#32] // in2_y + ldp $t2,$t3,[$bp,#48] + orr $acc0,$acc0,$acc1 + orr $acc2,$acc2,$acc3 + orr $t0,$t0,$t1 + orr $t2,$t2,$t3 + orr $acc0,$acc0,$acc2 + orr $t0,$t0,$t2 + orr $in2infty,$acc0,$t0 + cmp $in2infty,#0 + csetm $in2infty,ne // !in2infty + + add $rp,sp,#$Z1sqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z1sqr, in1_z); + + mov $a0,$acc0 + mov $a1,$acc1 + mov $a2,$acc2 + mov $a3,$acc3 + ldr $bi,[$bp_real] + add $bp,$bp_real,#0 + add $rp,sp,#$U2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, Z1sqr, in2_x); + + add $bp,$ap_real,#0 + ldr $bi,[$ap_real,#64] // forward load for p256_mul_mont + ldp $a0,$a1,[sp,#$Z1sqr] + ldp $a2,$a3,[sp,#$Z1sqr+16] + add $rp,sp,#$H + bl __ecp_nistz256_sub_from // p256_sub(H, U2, in1_x); + + add $bp,$ap_real,#64 + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, Z1sqr, in1_z); + + ldr $bi,[$ap_real,#64] + ldp $a0,$a1,[sp,#$H] + ldp $a2,$a3,[sp,#$H+16] + add $bp,$ap_real,#64 + add $rp,sp,#$res_z + bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, H, in1_z); + + ldr $bi,[$bp_real,#32] + ldp $a0,$a1,[sp,#$S2] + ldp $a2,$a3,[sp,#$S2+16] + add $bp,$bp_real,#32 + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S2, in2_y); + + add $bp,$ap_real,#32 + ldp $a0,$a1,[sp,#$H] // forward load for p256_sqr_mont + ldp $a2,$a3,[sp,#$H+16] + add $rp,sp,#$R + bl __ecp_nistz256_sub_from // p256_sub(R, S2, in1_y); + + add $rp,sp,#$Hsqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Hsqr, H); + + ldp $a0,$a1,[sp,#$R] + ldp $a2,$a3,[sp,#$R+16] + add $rp,sp,#$Rsqr + bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Rsqr, R); + + ldr $bi,[sp,#$H] + ldp $a0,$a1,[sp,#$Hsqr] + ldp $a2,$a3,[sp,#$Hsqr+16] + add $bp,sp,#$H + add $rp,sp,#$Hcub + bl __ecp_nistz256_mul_mont // p256_mul_mont(Hcub, Hsqr, H); + + ldr $bi,[$ap_real] + ldp $a0,$a1,[sp,#$Hsqr] + ldp $a2,$a3,[sp,#$Hsqr+16] + add $bp,$ap_real,#0 + add $rp,sp,#$U2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, in1_x, Hsqr); + + mov $t0,$acc0 + mov $t1,$acc1 + mov $t2,$acc2 + mov $t3,$acc3 + add $rp,sp,#$Hsqr + bl __ecp_nistz256_add // p256_mul_by_2(Hsqr, U2); + + add $bp,sp,#$Rsqr + add $rp,sp,#$res_x + bl __ecp_nistz256_sub_morf // p256_sub(res_x, Rsqr, Hsqr); + + add $bp,sp,#$Hcub + bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, Hcub); + + add $bp,sp,#$U2 + ldr $bi,[$ap_real,#32] // forward load for p256_mul_mont + ldp $a0,$a1,[sp,#$Hcub] + ldp $a2,$a3,[sp,#$Hcub+16] + add $rp,sp,#$res_y + bl __ecp_nistz256_sub_morf // p256_sub(res_y, U2, res_x); + + add $bp,$ap_real,#32 + add $rp,sp,#$S2 + bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, in1_y, Hcub); + + ldr $bi,[sp,#$R] + ldp $a0,$a1,[sp,#$res_y] + ldp $a2,$a3,[sp,#$res_y+16] + add $bp,sp,#$R + add $rp,sp,#$res_y + bl __ecp_nistz256_mul_mont // p256_mul_mont(res_y, res_y, R); + + add $bp,sp,#$S2 + bl __ecp_nistz256_sub_from // p256_sub(res_y, res_y, S2); + + ldp $a0,$a1,[sp,#$res_x] // res + ldp $a2,$a3,[sp,#$res_x+16] + ldp $t0,$t1,[$bp_real] // in2 + ldp $t2,$t3,[$bp_real,#16] +___ +for($i=0;$i<64;$i+=32) { # conditional moves +$code.=<<___; + ldp $acc0,$acc1,[$ap_real,#$i] // in1 + cmp $in1infty,#0 // !$in1intfy, remember? + ldp $acc2,$acc3,[$ap_real,#$i+16] + csel $t0,$a0,$t0,ne + csel $t1,$a1,$t1,ne + ldp $a0,$a1,[sp,#$res_x+$i+32] // res + csel $t2,$a2,$t2,ne + csel $t3,$a3,$t3,ne + cmp $in2infty,#0 // !$in2intfy, remember? + ldp $a2,$a3,[sp,#$res_x+$i+48] + csel $acc0,$t0,$acc0,ne + csel $acc1,$t1,$acc1,ne + ldp $t0,$t1,[$bp_real,#$i+32] // in2 + csel $acc2,$t2,$acc2,ne + csel $acc3,$t3,$acc3,ne + ldp $t2,$t3,[$bp_real,#$i+48] + stp $acc0,$acc1,[$rp_real,#$i] + stp $acc2,$acc3,[$rp_real,#$i+16] +___ +$code.=<<___ if ($i == 0); + adr $bp_real,.Lone_mont-64 +___ +} +$code.=<<___; + ldp $acc0,$acc1,[$ap_real,#$i] // in1 + cmp $in1infty,#0 // !$in1intfy, remember? + ldp $acc2,$acc3,[$ap_real,#$i+16] + csel $t0,$a0,$t0,ne + csel $t1,$a1,$t1,ne + csel $t2,$a2,$t2,ne + csel $t3,$a3,$t3,ne + cmp $in2infty,#0 // !$in2intfy, remember? + csel $acc0,$t0,$acc0,ne + csel $acc1,$t1,$acc1,ne + csel $acc2,$t2,$acc2,ne + csel $acc3,$t3,$acc3,ne + stp $acc0,$acc1,[$rp_real,#$i] + stp $acc2,$acc3,[$rp_real,#$i+16] + + add sp,x29,#0 // destroy frame + ldp x19,x20,[x29,#16] + ldp x21,x22,[x29,#32] + ldp x23,x24,[x29,#48] + ldp x25,x26,[x29,#64] + ldp x29,x30,[sp],#80 + ret +.size ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine +___ +} } + +######################################################################## +# scatter-gather subroutines +{ +my ($out,$inp,$index,$mask)=map("x$_",(0..3)); +$code.=<<___; +// void ecp_nistz256_scatter_w5(void *x0,const P256_POINT *x1, +// int x2); +.globl ecp_nistz256_scatter_w5 +.type ecp_nistz256_scatter_w5,%function +.align 4 +ecp_nistz256_scatter_w5: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + add $out,$out,$index,lsl#2 + + ldp x4,x5,[$inp] // X + ldp x6,x7,[$inp,#16] + str w4,[$out,#64*0-4] + lsr x4,x4,#32 + str w5,[$out,#64*1-4] + lsr x5,x5,#32 + str w6,[$out,#64*2-4] + lsr x6,x6,#32 + str w7,[$out,#64*3-4] + lsr x7,x7,#32 + str w4,[$out,#64*4-4] + str w5,[$out,#64*5-4] + str w6,[$out,#64*6-4] + str w7,[$out,#64*7-4] + add $out,$out,#64*8 + + ldp x4,x5,[$inp,#32] // Y + ldp x6,x7,[$inp,#48] + str w4,[$out,#64*0-4] + lsr x4,x4,#32 + str w5,[$out,#64*1-4] + lsr x5,x5,#32 + str w6,[$out,#64*2-4] + lsr x6,x6,#32 + str w7,[$out,#64*3-4] + lsr x7,x7,#32 + str w4,[$out,#64*4-4] + str w5,[$out,#64*5-4] + str w6,[$out,#64*6-4] + str w7,[$out,#64*7-4] + add $out,$out,#64*8 + + ldp x4,x5,[$inp,#64] // Z + ldp x6,x7,[$inp,#80] + str w4,[$out,#64*0-4] + lsr x4,x4,#32 + str w5,[$out,#64*1-4] + lsr x5,x5,#32 + str w6,[$out,#64*2-4] + lsr x6,x6,#32 + str w7,[$out,#64*3-4] + lsr x7,x7,#32 + str w4,[$out,#64*4-4] + str w5,[$out,#64*5-4] + str w6,[$out,#64*6-4] + str w7,[$out,#64*7-4] + + ldr x29,[sp],#16 + ret +.size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5 + +// void ecp_nistz256_gather_w5(P256_POINT *x0,const void *x1, +// int x2); +.globl ecp_nistz256_gather_w5 +.type ecp_nistz256_gather_w5,%function +.align 4 +ecp_nistz256_gather_w5: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + cmp $index,xzr + csetm x3,ne + add $index,$index,x3 + add $inp,$inp,$index,lsl#2 + + ldr w4,[$inp,#64*0] + ldr w5,[$inp,#64*1] + ldr w6,[$inp,#64*2] + ldr w7,[$inp,#64*3] + ldr w8,[$inp,#64*4] + ldr w9,[$inp,#64*5] + ldr w10,[$inp,#64*6] + ldr w11,[$inp,#64*7] + add $inp,$inp,#64*8 + orr x4,x4,x8,lsl#32 + orr x5,x5,x9,lsl#32 + orr x6,x6,x10,lsl#32 + orr x7,x7,x11,lsl#32 + csel x4,x4,xzr,ne + csel x5,x5,xzr,ne + csel x6,x6,xzr,ne + csel x7,x7,xzr,ne + stp x4,x5,[$out] // X + stp x6,x7,[$out,#16] + + ldr w4,[$inp,#64*0] + ldr w5,[$inp,#64*1] + ldr w6,[$inp,#64*2] + ldr w7,[$inp,#64*3] + ldr w8,[$inp,#64*4] + ldr w9,[$inp,#64*5] + ldr w10,[$inp,#64*6] + ldr w11,[$inp,#64*7] + add $inp,$inp,#64*8 + orr x4,x4,x8,lsl#32 + orr x5,x5,x9,lsl#32 + orr x6,x6,x10,lsl#32 + orr x7,x7,x11,lsl#32 + csel x4,x4,xzr,ne + csel x5,x5,xzr,ne + csel x6,x6,xzr,ne + csel x7,x7,xzr,ne + stp x4,x5,[$out,#32] // Y + stp x6,x7,[$out,#48] + + ldr w4,[$inp,#64*0] + ldr w5,[$inp,#64*1] + ldr w6,[$inp,#64*2] + ldr w7,[$inp,#64*3] + ldr w8,[$inp,#64*4] + ldr w9,[$inp,#64*5] + ldr w10,[$inp,#64*6] + ldr w11,[$inp,#64*7] + orr x4,x4,x8,lsl#32 + orr x5,x5,x9,lsl#32 + orr x6,x6,x10,lsl#32 + orr x7,x7,x11,lsl#32 + csel x4,x4,xzr,ne + csel x5,x5,xzr,ne + csel x6,x6,xzr,ne + csel x7,x7,xzr,ne + stp x4,x5,[$out,#64] // Z + stp x6,x7,[$out,#80] + + ldr x29,[sp],#16 + ret +.size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5 + +// void ecp_nistz256_scatter_w7(void *x0,const P256_POINT_AFFINE *x1, +// int x2); +.globl ecp_nistz256_scatter_w7 +.type ecp_nistz256_scatter_w7,%function +.align 4 +ecp_nistz256_scatter_w7: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + add $out,$out,$index + mov $index,#64/8 +.Loop_scatter_w7: + ldr x3,[$inp],#8 + subs $index,$index,#1 + prfm pstl1strm,[$out,#4096+64*0] + prfm pstl1strm,[$out,#4096+64*1] + prfm pstl1strm,[$out,#4096+64*2] + prfm pstl1strm,[$out,#4096+64*3] + prfm pstl1strm,[$out,#4096+64*4] + prfm pstl1strm,[$out,#4096+64*5] + prfm pstl1strm,[$out,#4096+64*6] + prfm pstl1strm,[$out,#4096+64*7] + strb w3,[$out,#64*0-1] + lsr x3,x3,#8 + strb w3,[$out,#64*1-1] + lsr x3,x3,#8 + strb w3,[$out,#64*2-1] + lsr x3,x3,#8 + strb w3,[$out,#64*3-1] + lsr x3,x3,#8 + strb w3,[$out,#64*4-1] + lsr x3,x3,#8 + strb w3,[$out,#64*5-1] + lsr x3,x3,#8 + strb w3,[$out,#64*6-1] + lsr x3,x3,#8 + strb w3,[$out,#64*7-1] + add $out,$out,#64*8 + b.ne .Loop_scatter_w7 + + ldr x29,[sp],#16 + ret +.size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7 + +// void ecp_nistz256_gather_w7(P256_POINT_AFFINE *x0,const void *x1, +// int x2); +.globl ecp_nistz256_gather_w7 +.type ecp_nistz256_gather_w7,%function +.align 4 +ecp_nistz256_gather_w7: + stp x29,x30,[sp,#-16]! + add x29,sp,#0 + + cmp $index,xzr + csetm x3,ne + add $index,$index,x3 + add $inp,$inp,$index + mov $index,#64/8 + nop +.Loop_gather_w7: + ldrb w4,[$inp,#64*0] + prfm pldl1strm,[$inp,#4096+64*0] + subs $index,$index,#1 + ldrb w5,[$inp,#64*1] + prfm pldl1strm,[$inp,#4096+64*1] + ldrb w6,[$inp,#64*2] + prfm pldl1strm,[$inp,#4096+64*2] + ldrb w7,[$inp,#64*3] + prfm pldl1strm,[$inp,#4096+64*3] + ldrb w8,[$inp,#64*4] + prfm pldl1strm,[$inp,#4096+64*4] + ldrb w9,[$inp,#64*5] + prfm pldl1strm,[$inp,#4096+64*5] + ldrb w10,[$inp,#64*6] + prfm pldl1strm,[$inp,#4096+64*6] + ldrb w11,[$inp,#64*7] + prfm pldl1strm,[$inp,#4096+64*7] + add $inp,$inp,#64*8 + orr x4,x4,x5,lsl#8 + orr x6,x6,x7,lsl#8 + orr x8,x8,x9,lsl#8 + orr x4,x4,x6,lsl#16 + orr x10,x10,x11,lsl#8 + orr x4,x4,x8,lsl#32 + orr x4,x4,x10,lsl#48 + and x4,x4,x3 + str x4,[$out],#8 + b.ne .Loop_gather_w7 + + ldr x29,[sp],#16 + ret +.size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7 +___ +} + +foreach (split("\n",$code)) { + s/\`([^\`]*)\`/eval $1/ge; + + print $_,"\n"; +} +close STDOUT; # enforce flush diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-avx2.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-avx2.pl new file mode 100755 index 0000000..3bdd2cf --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-avx2.pl @@ -0,0 +1,2100 @@ +#! /usr/bin/env perl +# Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +############################################################################## +# # +# Copyright 2014 Intel Corporation # +# # +# Licensed under the Apache License, Version 2.0 (the "License"); # +# you may not use this file except in compliance with the License. # +# You may obtain a copy of the License at # +# # +# http://www.apache.org/licenses/LICENSE-2.0 # +# # +# Unless required by applicable law or agreed to in writing, software # +# distributed under the License is distributed on an "AS IS" BASIS, # +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # +# See the License for the specific language governing permissions and # +# limitations under the License. # +# # +############################################################################## +# # +# Developers and authors: # +# Shay Gueron (1, 2), and Vlad Krasnov (1) # +# (1) Intel Corporation, Israel Development Center # +# (2) University of Haifa # +# Reference: # +# S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with# +# 256 Bit Primes" # +# # +############################################################################## + +$flavour = shift; +$output = shift; +if ($flavour =~ /\./) { $output = $flavour; undef $flavour; } + +$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/); + +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or +( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or +die "can't locate x86_64-xlate.pl"; + +open OUT,"| \"$^X\" $xlate $flavour $output"; +*STDOUT=*OUT; + +if (`$ENV{CC} -Wa,-v -c -o /dev/null -x assembler /dev/null 2>&1` + =~ /GNU assembler version ([2-9]\.[0-9]+)/) { + $avx = ($1>=2.19) + ($1>=2.22); + $addx = ($1>=2.23); +} + +if (!$addx && $win64 && ($flavour =~ /nasm/ || $ENV{ASM} =~ /nasm/) && + `nasm -v 2>&1` =~ /NASM version ([2-9]\.[0-9]+)/) { + $avx = ($1>=2.09) + ($1>=2.10); + $addx = ($1>=2.10); +} + +if (!$addx && $win64 && ($flavour =~ /masm/ || $ENV{ASM} =~ /ml64/) && + `ml64 2>&1` =~ /Version ([0-9]+)\./) { + $avx = ($1>=10) + ($1>=11); + $addx = ($1>=12); +} + +if (!$addx && `$ENV{CC} -v 2>&1` =~ /(^clang version|based on LLVM) ([3-9])\.([0-9]+)/) { + my $ver = $2 + $3/100.0; # 3.1->3.01, 3.10->3.10 + $avx = ($ver>=3.0) + ($ver>=3.01); + $addx = ($ver>=3.03); +} + +if ($avx>=2) {{ +$digit_size = "\$29"; +$n_digits = "\$9"; + +$code.=<<___; +.text + +.align 64 +.LAVX2_AND_MASK: +.LAVX2_POLY: +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x000001ff, 0x000001ff, 0x000001ff, 0x000001ff +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x00040000, 0x00040000, 0x00040000, 0x00040000 +.quad 0x1fe00000, 0x1fe00000, 0x1fe00000, 0x1fe00000 +.quad 0x00ffffff, 0x00ffffff, 0x00ffffff, 0x00ffffff + +.LAVX2_POLY_x2: +.quad 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC +.quad 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC +.quad 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC +.quad 0x400007FC, 0x400007FC, 0x400007FC, 0x400007FC +.quad 0x3FFFFFFE, 0x3FFFFFFE, 0x3FFFFFFE, 0x3FFFFFFE +.quad 0x3FFFFFFE, 0x3FFFFFFE, 0x3FFFFFFE, 0x3FFFFFFE +.quad 0x400FFFFE, 0x400FFFFE, 0x400FFFFE, 0x400FFFFE +.quad 0x7F7FFFFE, 0x7F7FFFFE, 0x7F7FFFFE, 0x7F7FFFFE +.quad 0x03FFFFFC, 0x03FFFFFC, 0x03FFFFFC, 0x03FFFFFC + +.LAVX2_POLY_x8: +.quad 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8 +.quad 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8 +.quad 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8, 0xFFFFFFF8 +.quad 0x80000FF8, 0x80000FF8, 0x80000FF8, 0x80000FF8 +.quad 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC +.quad 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC, 0x7FFFFFFC +.quad 0x801FFFFC, 0x801FFFFC, 0x801FFFFC, 0x801FFFFC +.quad 0xFEFFFFFC, 0xFEFFFFFC, 0xFEFFFFFC, 0xFEFFFFFC +.quad 0x07FFFFF8, 0x07FFFFF8, 0x07FFFFF8, 0x07FFFFF8 + +.LONE: +.quad 0x00000020, 0x00000020, 0x00000020, 0x00000020 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x1fffc000, 0x1fffc000, 0x1fffc000, 0x1fffc000 +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1f7fffff, 0x1f7fffff, 0x1f7fffff, 0x1f7fffff +.quad 0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 + +# RR = 2^266 mod p in AVX2 format, to transform from the native OpenSSL +# Montgomery form (*2^256) to our format (*2^261) + +.LTO_MONT_AVX2: +.quad 0x00000400, 0x00000400, 0x00000400, 0x00000400 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x1ff80000, 0x1ff80000, 0x1ff80000, 0x1ff80000 +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x0fffffff, 0x0fffffff, 0x0fffffff, 0x0fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x00000003, 0x00000003, 0x00000003, 0x00000003 + +.LFROM_MONT_AVX2: +.quad 0x00000001, 0x00000001, 0x00000001, 0x00000001 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 +.quad 0x1ffffe00, 0x1ffffe00, 0x1ffffe00, 0x1ffffe00 +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff +.quad 0x1ffbffff, 0x1ffbffff, 0x1ffbffff, 0x1ffbffff +.quad 0x001fffff, 0x001fffff, 0x001fffff, 0x001fffff +.quad 0x00000000, 0x00000000, 0x00000000, 0x00000000 + +.LIntOne: +.long 1,1,1,1,1,1,1,1 +___ + +{ +# This function receives a pointer to an array of four affine points +# (X, Y, <1>) and rearanges the data for AVX2 execution, while +# converting it to 2^29 radix redundant form + +my ($X0,$X1,$X2,$X3, $Y0,$Y1,$Y2,$Y3, + $T0,$T1,$T2,$T3, $T4,$T5,$T6,$T7)=map("%ymm$_",(0..15)); + +$code.=<<___; +.globl ecp_nistz256_avx2_transpose_convert +.type ecp_nistz256_avx2_transpose_convert,\@function,2 +.align 64 +ecp_nistz256_avx2_transpose_convert: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -8-16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + # Load the data + vmovdqa 32*0(%rsi), $X0 + lea 112(%rsi), %rax # size optimization + vmovdqa 32*1(%rsi), $Y0 + lea .LAVX2_AND_MASK(%rip), %rdx + vmovdqa 32*2(%rsi), $X1 + vmovdqa 32*3(%rsi), $Y1 + vmovdqa 32*4-112(%rax), $X2 + vmovdqa 32*5-112(%rax), $Y2 + vmovdqa 32*6-112(%rax), $X3 + vmovdqa 32*7-112(%rax), $Y3 + + # Transpose X and Y independently + vpunpcklqdq $X1, $X0, $T0 # T0 = [B2 A2 B0 A0] + vpunpcklqdq $X3, $X2, $T1 # T1 = [D2 C2 D0 C0] + vpunpckhqdq $X1, $X0, $T2 # T2 = [B3 A3 B1 A1] + vpunpckhqdq $X3, $X2, $T3 # T3 = [D3 C3 D1 C1] + + vpunpcklqdq $Y1, $Y0, $T4 + vpunpcklqdq $Y3, $Y2, $T5 + vpunpckhqdq $Y1, $Y0, $T6 + vpunpckhqdq $Y3, $Y2, $T7 + + vperm2i128 \$0x20, $T1, $T0, $X0 # X0 = [D0 C0 B0 A0] + vperm2i128 \$0x20, $T3, $T2, $X1 # X1 = [D1 C1 B1 A1] + vperm2i128 \$0x31, $T1, $T0, $X2 # X2 = [D2 C2 B2 A2] + vperm2i128 \$0x31, $T3, $T2, $X3 # X3 = [D3 C3 B3 A3] + + vperm2i128 \$0x20, $T5, $T4, $Y0 + vperm2i128 \$0x20, $T7, $T6, $Y1 + vperm2i128 \$0x31, $T5, $T4, $Y2 + vperm2i128 \$0x31, $T7, $T6, $Y3 + vmovdqa (%rdx), $T7 + + vpand (%rdx), $X0, $T0 # out[0] = in[0] & mask; + vpsrlq \$29, $X0, $X0 + vpand $T7, $X0, $T1 # out[1] = (in[0] >> shift) & mask; + vpsrlq \$29, $X0, $X0 + vpsllq \$6, $X1, $T2 + vpxor $X0, $T2, $T2 + vpand $T7, $T2, $T2 # out[2] = ((in[0] >> (shift*2)) ^ (in[1] << (64-shift*2))) & mask; + vpsrlq \$23, $X1, $X1 + vpand $T7, $X1, $T3 # out[3] = (in[1] >> ((shift*3)%64)) & mask; + vpsrlq \$29, $X1, $X1 + vpsllq \$12, $X2, $T4 + vpxor $X1, $T4, $T4 + vpand $T7, $T4, $T4 # out[4] = ((in[1] >> ((shift*4)%64)) ^ (in[2] << (64*2-shift*4))) & mask; + vpsrlq \$17, $X2, $X2 + vpand $T7, $X2, $T5 # out[5] = (in[2] >> ((shift*5)%64)) & mask; + vpsrlq \$29, $X2, $X2 + vpsllq \$18, $X3, $T6 + vpxor $X2, $T6, $T6 + vpand $T7, $T6, $T6 # out[6] = ((in[2] >> ((shift*6)%64)) ^ (in[3] << (64*3-shift*6))) & mask; + vpsrlq \$11, $X3, $X3 + vmovdqa $T0, 32*0(%rdi) + lea 112(%rdi), %rax # size optimization + vpand $T7, $X3, $T0 # out[7] = (in[3] >> ((shift*7)%64)) & mask; + vpsrlq \$29, $X3, $X3 # out[8] = (in[3] >> ((shift*8)%64)) & mask; + + vmovdqa $T1, 32*1(%rdi) + vmovdqa $T2, 32*2(%rdi) + vmovdqa $T3, 32*3(%rdi) + vmovdqa $T4, 32*4-112(%rax) + vmovdqa $T5, 32*5-112(%rax) + vmovdqa $T6, 32*6-112(%rax) + vmovdqa $T0, 32*7-112(%rax) + vmovdqa $X3, 32*8-112(%rax) + lea 448(%rdi), %rax # size optimization + + vpand $T7, $Y0, $T0 # out[0] = in[0] & mask; + vpsrlq \$29, $Y0, $Y0 + vpand $T7, $Y0, $T1 # out[1] = (in[0] >> shift) & mask; + vpsrlq \$29, $Y0, $Y0 + vpsllq \$6, $Y1, $T2 + vpxor $Y0, $T2, $T2 + vpand $T7, $T2, $T2 # out[2] = ((in[0] >> (shift*2)) ^ (in[1] << (64-shift*2))) & mask; + vpsrlq \$23, $Y1, $Y1 + vpand $T7, $Y1, $T3 # out[3] = (in[1] >> ((shift*3)%64)) & mask; + vpsrlq \$29, $Y1, $Y1 + vpsllq \$12, $Y2, $T4 + vpxor $Y1, $T4, $T4 + vpand $T7, $T4, $T4 # out[4] = ((in[1] >> ((shift*4)%64)) ^ (in[2] << (64*2-shift*4))) & mask; + vpsrlq \$17, $Y2, $Y2 + vpand $T7, $Y2, $T5 # out[5] = (in[2] >> ((shift*5)%64)) & mask; + vpsrlq \$29, $Y2, $Y2 + vpsllq \$18, $Y3, $T6 + vpxor $Y2, $T6, $T6 + vpand $T7, $T6, $T6 # out[6] = ((in[2] >> ((shift*6)%64)) ^ (in[3] << (64*3-shift*6))) & mask; + vpsrlq \$11, $Y3, $Y3 + vmovdqa $T0, 32*9-448(%rax) + vpand $T7, $Y3, $T0 # out[7] = (in[3] >> ((shift*7)%64)) & mask; + vpsrlq \$29, $Y3, $Y3 # out[8] = (in[3] >> ((shift*8)%64)) & mask; + + vmovdqa $T1, 32*10-448(%rax) + vmovdqa $T2, 32*11-448(%rax) + vmovdqa $T3, 32*12-448(%rax) + vmovdqa $T4, 32*13-448(%rax) + vmovdqa $T5, 32*14-448(%rax) + vmovdqa $T6, 32*15-448(%rax) + vmovdqa $T0, 32*16-448(%rax) + vmovdqa $Y3, 32*17-448(%rax) + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps 16*0(%rsp), %xmm6 + movaps 16*1(%rsp), %xmm7 + movaps 16*2(%rsp), %xmm8 + movaps 16*3(%rsp), %xmm9 + movaps 16*4(%rsp), %xmm10 + movaps 16*5(%rsp), %xmm11 + movaps 16*6(%rsp), %xmm12 + movaps 16*7(%rsp), %xmm13 + movaps 16*8(%rsp), %xmm14 + movaps 16*9(%rsp), %xmm15 + lea 8+16*10(%rsp), %rsp +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_transpose_convert,.-ecp_nistz256_avx2_transpose_convert +___ +} +{ +################################################################################ +# This function receives a pointer to an array of four AVX2 formatted points +# (X, Y, Z) convert the data to normal representation, and rearanges the data + +my ($D0,$D1,$D2,$D3, $D4,$D5,$D6,$D7, $D8)=map("%ymm$_",(0..8)); +my ($T0,$T1,$T2,$T3, $T4,$T5,$T6)=map("%ymm$_",(9..15)); + +$code.=<<___; + +.globl ecp_nistz256_avx2_convert_transpose_back +.type ecp_nistz256_avx2_convert_transpose_back,\@function,2 +.align 32 +ecp_nistz256_avx2_convert_transpose_back: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -8-16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + mov \$3, %ecx + +.Lconv_loop: + vmovdqa 32*0(%rsi), $D0 + lea 160(%rsi), %rax # size optimization + vmovdqa 32*1(%rsi), $D1 + vmovdqa 32*2(%rsi), $D2 + vmovdqa 32*3(%rsi), $D3 + vmovdqa 32*4-160(%rax), $D4 + vmovdqa 32*5-160(%rax), $D5 + vmovdqa 32*6-160(%rax), $D6 + vmovdqa 32*7-160(%rax), $D7 + vmovdqa 32*8-160(%rax), $D8 + + vpsllq \$29, $D1, $D1 + vpsllq \$58, $D2, $T0 + vpaddq $D1, $D0, $D0 + vpaddq $T0, $D0, $D0 # out[0] = (in[0]) ^ (in[1] << shift*1) ^ (in[2] << shift*2); + + vpsrlq \$6, $D2, $D2 + vpsllq \$23, $D3, $D3 + vpsllq \$52, $D4, $T1 + vpaddq $D2, $D3, $D3 + vpaddq $D3, $T1, $D1 # out[1] = (in[2] >> (64*1-shift*2)) ^ (in[3] << shift*3%64) ^ (in[4] << shift*4%64); + + vpsrlq \$12, $D4, $D4 + vpsllq \$17, $D5, $D5 + vpsllq \$46, $D6, $T2 + vpaddq $D4, $D5, $D5 + vpaddq $D5, $T2, $D2 # out[2] = (in[4] >> (64*2-shift*4)) ^ (in[5] << shift*5%64) ^ (in[6] << shift*6%64); + + vpsrlq \$18, $D6, $D6 + vpsllq \$11, $D7, $D7 + vpsllq \$40, $D8, $T3 + vpaddq $D6, $D7, $D7 + vpaddq $D7, $T3, $D3 # out[3] = (in[6] >> (64*3-shift*6)) ^ (in[7] << shift*7%64) ^ (in[8] << shift*8%64); + + vpunpcklqdq $D1, $D0, $T0 # T0 = [B2 A2 B0 A0] + vpunpcklqdq $D3, $D2, $T1 # T1 = [D2 C2 D0 C0] + vpunpckhqdq $D1, $D0, $T2 # T2 = [B3 A3 B1 A1] + vpunpckhqdq $D3, $D2, $T3 # T3 = [D3 C3 D1 C1] + + vperm2i128 \$0x20, $T1, $T0, $D0 # X0 = [D0 C0 B0 A0] + vperm2i128 \$0x20, $T3, $T2, $D1 # X1 = [D1 C1 B1 A1] + vperm2i128 \$0x31, $T1, $T0, $D2 # X2 = [D2 C2 B2 A2] + vperm2i128 \$0x31, $T3, $T2, $D3 # X3 = [D3 C3 B3 A3] + + vmovdqa $D0, 32*0(%rdi) + vmovdqa $D1, 32*3(%rdi) + vmovdqa $D2, 32*6(%rdi) + vmovdqa $D3, 32*9(%rdi) + + lea 32*9(%rsi), %rsi + lea 32*1(%rdi), %rdi + + dec %ecx + jnz .Lconv_loop + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps 16*0(%rsp), %xmm6 + movaps 16*1(%rsp), %xmm7 + movaps 16*2(%rsp), %xmm8 + movaps 16*3(%rsp), %xmm9 + movaps 16*4(%rsp), %xmm10 + movaps 16*5(%rsp), %xmm11 + movaps 16*6(%rsp), %xmm12 + movaps 16*7(%rsp), %xmm13 + movaps 16*8(%rsp), %xmm14 + movaps 16*9(%rsp), %xmm15 + lea 8+16*10(%rsp), %rsp +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_convert_transpose_back,.-ecp_nistz256_avx2_convert_transpose_back +___ +} +{ +my ($r_ptr,$a_ptr,$b_ptr,$itr)=("%rdi","%rsi","%rdx","%ecx"); +my ($ACC0,$ACC1,$ACC2,$ACC3,$ACC4,$ACC5,$ACC6,$ACC7,$ACC8)=map("%ymm$_",(0..8)); +my ($B,$Y,$T0,$AND_MASK,$OVERFLOW)=map("%ymm$_",(9..13)); + +sub NORMALIZE { +my $ret=<<___; + vpsrlq $digit_size, $ACC0, $T0 + vpand $AND_MASK, $ACC0, $ACC0 + vpaddq $T0, $ACC1, $ACC1 + + vpsrlq $digit_size, $ACC1, $T0 + vpand $AND_MASK, $ACC1, $ACC1 + vpaddq $T0, $ACC2, $ACC2 + + vpsrlq $digit_size, $ACC2, $T0 + vpand $AND_MASK, $ACC2, $ACC2 + vpaddq $T0, $ACC3, $ACC3 + + vpsrlq $digit_size, $ACC3, $T0 + vpand $AND_MASK, $ACC3, $ACC3 + vpaddq $T0, $ACC4, $ACC4 + + vpsrlq $digit_size, $ACC4, $T0 + vpand $AND_MASK, $ACC4, $ACC4 + vpaddq $T0, $ACC5, $ACC5 + + vpsrlq $digit_size, $ACC5, $T0 + vpand $AND_MASK, $ACC5, $ACC5 + vpaddq $T0, $ACC6, $ACC6 + + vpsrlq $digit_size, $ACC6, $T0 + vpand $AND_MASK, $ACC6, $ACC6 + vpaddq $T0, $ACC7, $ACC7 + + vpsrlq $digit_size, $ACC7, $T0 + vpand $AND_MASK, $ACC7, $ACC7 + vpaddq $T0, $ACC8, $ACC8 + #vpand $AND_MASK, $ACC8, $ACC8 +___ + $ret; +} + +sub STORE { +my $ret=<<___; + vmovdqa $ACC0, 32*0(%rdi) + lea 160(%rdi), %rax # size optimization + vmovdqa $ACC1, 32*1(%rdi) + vmovdqa $ACC2, 32*2(%rdi) + vmovdqa $ACC3, 32*3(%rdi) + vmovdqa $ACC4, 32*4-160(%rax) + vmovdqa $ACC5, 32*5-160(%rax) + vmovdqa $ACC6, 32*6-160(%rax) + vmovdqa $ACC7, 32*7-160(%rax) + vmovdqa $ACC8, 32*8-160(%rax) +___ + $ret; +} + +$code.=<<___; +.type avx2_normalize,\@abi-omnipotent +.align 32 +avx2_normalize: + vpsrlq $digit_size, $ACC0, $T0 + vpand $AND_MASK, $ACC0, $ACC0 + vpaddq $T0, $ACC1, $ACC1 + + vpsrlq $digit_size, $ACC1, $T0 + vpand $AND_MASK, $ACC1, $ACC1 + vpaddq $T0, $ACC2, $ACC2 + + vpsrlq $digit_size, $ACC2, $T0 + vpand $AND_MASK, $ACC2, $ACC2 + vpaddq $T0, $ACC3, $ACC3 + + vpsrlq $digit_size, $ACC3, $T0 + vpand $AND_MASK, $ACC3, $ACC3 + vpaddq $T0, $ACC4, $ACC4 + + vpsrlq $digit_size, $ACC4, $T0 + vpand $AND_MASK, $ACC4, $ACC4 + vpaddq $T0, $ACC5, $ACC5 + + vpsrlq $digit_size, $ACC5, $T0 + vpand $AND_MASK, $ACC5, $ACC5 + vpaddq $T0, $ACC6, $ACC6 + + vpsrlq $digit_size, $ACC6, $T0 + vpand $AND_MASK, $ACC6, $ACC6 + vpaddq $T0, $ACC7, $ACC7 + + vpsrlq $digit_size, $ACC7, $T0 + vpand $AND_MASK, $ACC7, $ACC7 + vpaddq $T0, $ACC8, $ACC8 + #vpand $AND_MASK, $ACC8, $ACC8 + + ret +.size avx2_normalize,.-avx2_normalize + +.type avx2_normalize_n_store,\@abi-omnipotent +.align 32 +avx2_normalize_n_store: + vpsrlq $digit_size, $ACC0, $T0 + vpand $AND_MASK, $ACC0, $ACC0 + vpaddq $T0, $ACC1, $ACC1 + + vpsrlq $digit_size, $ACC1, $T0 + vpand $AND_MASK, $ACC1, $ACC1 + vmovdqa $ACC0, 32*0(%rdi) + lea 160(%rdi), %rax # size optimization + vpaddq $T0, $ACC2, $ACC2 + + vpsrlq $digit_size, $ACC2, $T0 + vpand $AND_MASK, $ACC2, $ACC2 + vmovdqa $ACC1, 32*1(%rdi) + vpaddq $T0, $ACC3, $ACC3 + + vpsrlq $digit_size, $ACC3, $T0 + vpand $AND_MASK, $ACC3, $ACC3 + vmovdqa $ACC2, 32*2(%rdi) + vpaddq $T0, $ACC4, $ACC4 + + vpsrlq $digit_size, $ACC4, $T0 + vpand $AND_MASK, $ACC4, $ACC4 + vmovdqa $ACC3, 32*3(%rdi) + vpaddq $T0, $ACC5, $ACC5 + + vpsrlq $digit_size, $ACC5, $T0 + vpand $AND_MASK, $ACC5, $ACC5 + vmovdqa $ACC4, 32*4-160(%rax) + vpaddq $T0, $ACC6, $ACC6 + + vpsrlq $digit_size, $ACC6, $T0 + vpand $AND_MASK, $ACC6, $ACC6 + vmovdqa $ACC5, 32*5-160(%rax) + vpaddq $T0, $ACC7, $ACC7 + + vpsrlq $digit_size, $ACC7, $T0 + vpand $AND_MASK, $ACC7, $ACC7 + vmovdqa $ACC6, 32*6-160(%rax) + vpaddq $T0, $ACC8, $ACC8 + #vpand $AND_MASK, $ACC8, $ACC8 + vmovdqa $ACC7, 32*7-160(%rax) + vmovdqa $ACC8, 32*8-160(%rax) + + ret +.size avx2_normalize_n_store,.-avx2_normalize_n_store + +################################################################################ +# void avx2_mul_x4(void* RESULTx4, void *Ax4, void *Bx4); +.type avx2_mul_x4,\@abi-omnipotent +.align 32 +avx2_mul_x4: + lea .LAVX2_POLY(%rip), %rax + + vpxor $ACC0, $ACC0, $ACC0 + vpxor $ACC1, $ACC1, $ACC1 + vpxor $ACC2, $ACC2, $ACC2 + vpxor $ACC3, $ACC3, $ACC3 + vpxor $ACC4, $ACC4, $ACC4 + vpxor $ACC5, $ACC5, $ACC5 + vpxor $ACC6, $ACC6, $ACC6 + vpxor $ACC7, $ACC7, $ACC7 + + vmovdqa 32*7(%rax), %ymm14 + vmovdqa 32*8(%rax), %ymm15 + + mov $n_digits, $itr + lea -512($a_ptr), $a_ptr # strategic bias to control u-op density + jmp .Lavx2_mul_x4_loop + +.align 32 +.Lavx2_mul_x4_loop: + vmovdqa 32*0($b_ptr), $B + lea 32*1($b_ptr), $b_ptr + + vpmuludq 32*0+512($a_ptr), $B, $T0 + vpmuludq 32*1+512($a_ptr), $B, $OVERFLOW # borrow $OVERFLOW + vpaddq $T0, $ACC0, $ACC0 + vpmuludq 32*2+512($a_ptr), $B, $T0 + vpaddq $OVERFLOW, $ACC1, $ACC1 + vpand $AND_MASK, $ACC0, $Y + vpmuludq 32*3+512($a_ptr), $B, $OVERFLOW + vpaddq $T0, $ACC2, $ACC2 + vpmuludq 32*4+512($a_ptr), $B, $T0 + vpaddq $OVERFLOW, $ACC3, $ACC3 + vpmuludq 32*5+512($a_ptr), $B, $OVERFLOW + vpaddq $T0, $ACC4, $ACC4 + vpmuludq 32*6+512($a_ptr), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*7+512($a_ptr), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + # Skip some multiplications, optimizing for the constant poly + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*8+512($a_ptr), $B, $ACC8 + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + .byte 0x67 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $OVERFLOW + .byte 0x67 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $T0 + vpaddq $OVERFLOW, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $OVERFLOW + vpaddq $T0, $ACC7, $ACC6 + vpaddq $OVERFLOW, $ACC8, $ACC7 + + dec $itr + jnz .Lavx2_mul_x4_loop + + vpxor $ACC8, $ACC8, $ACC8 + + ret +.size avx2_mul_x4,.-avx2_mul_x4 + +# Function optimized for the constant 1 +################################################################################ +# void avx2_mul_by1_x4(void* RESULTx4, void *Ax4); +.type avx2_mul_by1_x4,\@abi-omnipotent +.align 32 +avx2_mul_by1_x4: + lea .LAVX2_POLY(%rip), %rax + + vpxor $ACC0, $ACC0, $ACC0 + vpxor $ACC1, $ACC1, $ACC1 + vpxor $ACC2, $ACC2, $ACC2 + vpxor $ACC3, $ACC3, $ACC3 + vpxor $ACC4, $ACC4, $ACC4 + vpxor $ACC5, $ACC5, $ACC5 + vpxor $ACC6, $ACC6, $ACC6 + vpxor $ACC7, $ACC7, $ACC7 + vpxor $ACC8, $ACC8, $ACC8 + + vmovdqa 32*3+.LONE(%rip), %ymm14 + vmovdqa 32*7+.LONE(%rip), %ymm15 + + mov $n_digits, $itr + jmp .Lavx2_mul_by1_x4_loop + +.align 32 +.Lavx2_mul_by1_x4_loop: + vmovdqa 32*0($a_ptr), $B + .byte 0x48,0x8d,0xb6,0x20,0,0,0 # lea 32*1($a_ptr), $a_ptr + + vpsllq \$5, $B, $OVERFLOW + vpmuludq %ymm14, $B, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC3 + .byte 0x67 + vpmuludq $AND_MASK, $B, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $T0, $ACC4, $ACC4 + vpaddq $T0, $ACC5, $ACC5 + vpaddq $T0, $ACC6, $ACC6 + vpsllq \$23, $B, $T0 + + .byte 0x67,0x67 + vpmuludq %ymm15, $B, $OVERFLOW + vpsubq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + .byte 0x67,0x67 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $OVERFLOW + vmovdqa $ACC5, $ACC4 + vpmuludq 32*7(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC6, $ACC5 + vpaddq $T0, $ACC7, $ACC6 + vpmuludq 32*8(%rax), $Y, $ACC7 + + dec $itr + jnz .Lavx2_mul_by1_x4_loop + + ret +.size avx2_mul_by1_x4,.-avx2_mul_by1_x4 + +################################################################################ +# void avx2_sqr_x4(void* RESULTx4, void *Ax4, void *Bx4); +.type avx2_sqr_x4,\@abi-omnipotent +.align 32 +avx2_sqr_x4: + lea .LAVX2_POLY(%rip), %rax + + vmovdqa 32*7(%rax), %ymm14 + vmovdqa 32*8(%rax), %ymm15 + + vmovdqa 32*0($a_ptr), $B + vmovdqa 32*1($a_ptr), $ACC1 + vmovdqa 32*2($a_ptr), $ACC2 + vmovdqa 32*3($a_ptr), $ACC3 + vmovdqa 32*4($a_ptr), $ACC4 + vmovdqa 32*5($a_ptr), $ACC5 + vmovdqa 32*6($a_ptr), $ACC6 + vmovdqa 32*7($a_ptr), $ACC7 + vpaddq $ACC1, $ACC1, $ACC1 # 2*$ACC0..7 + vmovdqa 32*8($a_ptr), $ACC8 + vpaddq $ACC2, $ACC2, $ACC2 + vmovdqa $ACC1, 32*0(%rcx) + vpaddq $ACC3, $ACC3, $ACC3 + vmovdqa $ACC2, 32*1(%rcx) + vpaddq $ACC4, $ACC4, $ACC4 + vmovdqa $ACC3, 32*2(%rcx) + vpaddq $ACC5, $ACC5, $ACC5 + vmovdqa $ACC4, 32*3(%rcx) + vpaddq $ACC6, $ACC6, $ACC6 + vmovdqa $ACC5, 32*4(%rcx) + vpaddq $ACC7, $ACC7, $ACC7 + vmovdqa $ACC6, 32*5(%rcx) + vpaddq $ACC8, $ACC8, $ACC8 + vmovdqa $ACC7, 32*6(%rcx) + vmovdqa $ACC8, 32*7(%rcx) + + #itr 1 + vpmuludq $B, $B, $ACC0 + vpmuludq $B, $ACC1, $ACC1 + vpand $AND_MASK, $ACC0, $Y + vpmuludq $B, $ACC2, $ACC2 + vpmuludq $B, $ACC3, $ACC3 + vpmuludq $B, $ACC4, $ACC4 + vpmuludq $B, $ACC5, $ACC5 + vpmuludq $B, $ACC6, $ACC6 + vpmuludq $AND_MASK, $Y, $T0 + vpmuludq $B, $ACC7, $ACC7 + vpmuludq $B, $ACC8, $ACC8 + vmovdqa 32*1($a_ptr), $B + + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 2 + vpmuludq $B, $B, $OVERFLOW + vpand $AND_MASK, $ACC0, $Y + vpmuludq 32*1(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC1, $ACC1 + vpmuludq 32*2(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC2, $ACC2 + vpmuludq 32*3(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC3, $ACC3 + vpmuludq 32*4(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC4, $ACC4 + vpmuludq 32*5(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*2($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 3 + vpmuludq $B, $B, $T0 + vpand $AND_MASK, $ACC0, $Y + vpmuludq 32*2(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC2, $ACC2 + vpmuludq 32*3(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC3, $ACC3 + vpmuludq 32*4(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC4, $ACC4 + vpmuludq 32*5(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*3($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 4 + vpmuludq $B, $B, $OVERFLOW + vpmuludq 32*3(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC3, $ACC3 + vpmuludq 32*4(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC4, $ACC4 + vpmuludq 32*5(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*4($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 5 + vpmuludq $B, $B, $T0 + vpmuludq 32*4(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC4, $ACC4 + vpmuludq 32*5(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*5($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3+.LAVX2_POLY(%rip), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 6 + vpmuludq $B, $B, $OVERFLOW + vpmuludq 32*5(%rcx), $B, $T0 + vpaddq $OVERFLOW, $ACC5, $ACC5 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*6($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 7 + vpmuludq $B, $B, $T0 + vpmuludq 32*6(%rcx), $B, $OVERFLOW + vpaddq $T0, $ACC6, $ACC6 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*7($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 8 + vpmuludq $B, $B, $OVERFLOW + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC7 + vpmuludq 32*7(%rcx), $B, $ACC8 + vmovdqa 32*8($a_ptr), $B + vpaddq $T0, $ACC0, $OVERFLOW + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpand $AND_MASK, $ACC0, $Y + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + #itr 9 + vpmuludq $B, $B, $ACC8 + + vpmuludq $AND_MASK, $Y, $T0 + vpaddq $T0, $ACC0, $OVERFLOW + vpsrlq $digit_size, $OVERFLOW, $OVERFLOW + vpaddq $T0, $ACC1, $ACC0 + vpaddq $T0, $ACC2, $ACC1 + vpmuludq 32*3(%rax), $Y, $T0 + vpaddq $OVERFLOW, $ACC0, $ACC0 + vpaddq $T0, $ACC3, $ACC2 + vmovdqa $ACC4, $ACC3 + vpsllq \$18, $Y, $T0 + vmovdqa $ACC5, $ACC4 + vpmuludq %ymm14, $Y, $OVERFLOW + vpaddq $T0, $ACC6, $ACC5 + vpmuludq %ymm15, $Y, $T0 + vpaddq $OVERFLOW, $ACC7, $ACC6 + vpaddq $T0, $ACC8, $ACC7 + + vpxor $ACC8, $ACC8, $ACC8 + + ret +.size avx2_sqr_x4,.-avx2_sqr_x4 + +################################################################################ +# void avx2_sub_x4(void* RESULTx4, void *Ax4, void *Bx4); +.type avx2_sub_x4,\@abi-omnipotent +.align 32 +avx2_sub_x4: + vmovdqa 32*0($a_ptr), $ACC0 + lea 160($a_ptr), $a_ptr + lea .LAVX2_POLY_x8+128(%rip), %rax + lea 128($b_ptr), $b_ptr + vmovdqa 32*1-160($a_ptr), $ACC1 + vmovdqa 32*2-160($a_ptr), $ACC2 + vmovdqa 32*3-160($a_ptr), $ACC3 + vmovdqa 32*4-160($a_ptr), $ACC4 + vmovdqa 32*5-160($a_ptr), $ACC5 + vmovdqa 32*6-160($a_ptr), $ACC6 + vmovdqa 32*7-160($a_ptr), $ACC7 + vmovdqa 32*8-160($a_ptr), $ACC8 + + vpaddq 32*0-128(%rax), $ACC0, $ACC0 + vpaddq 32*1-128(%rax), $ACC1, $ACC1 + vpaddq 32*2-128(%rax), $ACC2, $ACC2 + vpaddq 32*3-128(%rax), $ACC3, $ACC3 + vpaddq 32*4-128(%rax), $ACC4, $ACC4 + vpaddq 32*5-128(%rax), $ACC5, $ACC5 + vpaddq 32*6-128(%rax), $ACC6, $ACC6 + vpaddq 32*7-128(%rax), $ACC7, $ACC7 + vpaddq 32*8-128(%rax), $ACC8, $ACC8 + + vpsubq 32*0-128($b_ptr), $ACC0, $ACC0 + vpsubq 32*1-128($b_ptr), $ACC1, $ACC1 + vpsubq 32*2-128($b_ptr), $ACC2, $ACC2 + vpsubq 32*3-128($b_ptr), $ACC3, $ACC3 + vpsubq 32*4-128($b_ptr), $ACC4, $ACC4 + vpsubq 32*5-128($b_ptr), $ACC5, $ACC5 + vpsubq 32*6-128($b_ptr), $ACC6, $ACC6 + vpsubq 32*7-128($b_ptr), $ACC7, $ACC7 + vpsubq 32*8-128($b_ptr), $ACC8, $ACC8 + + ret +.size avx2_sub_x4,.-avx2_sub_x4 + +.type avx2_select_n_store,\@abi-omnipotent +.align 32 +avx2_select_n_store: + vmovdqa `8+32*9*8`(%rsp), $Y + vpor `8+32*9*8+32`(%rsp), $Y, $Y + + vpandn $ACC0, $Y, $ACC0 + vpandn $ACC1, $Y, $ACC1 + vpandn $ACC2, $Y, $ACC2 + vpandn $ACC3, $Y, $ACC3 + vpandn $ACC4, $Y, $ACC4 + vpandn $ACC5, $Y, $ACC5 + vpandn $ACC6, $Y, $ACC6 + vmovdqa `8+32*9*8+32`(%rsp), $B + vpandn $ACC7, $Y, $ACC7 + vpandn `8+32*9*8`(%rsp), $B, $B + vpandn $ACC8, $Y, $ACC8 + + vpand 32*0(%rsi), $B, $T0 + lea 160(%rsi), %rax + vpand 32*1(%rsi), $B, $Y + vpxor $T0, $ACC0, $ACC0 + vpand 32*2(%rsi), $B, $T0 + vpxor $Y, $ACC1, $ACC1 + vpand 32*3(%rsi), $B, $Y + vpxor $T0, $ACC2, $ACC2 + vpand 32*4-160(%rax), $B, $T0 + vpxor $Y, $ACC3, $ACC3 + vpand 32*5-160(%rax), $B, $Y + vpxor $T0, $ACC4, $ACC4 + vpand 32*6-160(%rax), $B, $T0 + vpxor $Y, $ACC5, $ACC5 + vpand 32*7-160(%rax), $B, $Y + vpxor $T0, $ACC6, $ACC6 + vpand 32*8-160(%rax), $B, $T0 + vmovdqa `8+32*9*8+32`(%rsp), $B + vpxor $Y, $ACC7, $ACC7 + + vpand 32*0(%rdx), $B, $Y + lea 160(%rdx), %rax + vpxor $T0, $ACC8, $ACC8 + vpand 32*1(%rdx), $B, $T0 + vpxor $Y, $ACC0, $ACC0 + vpand 32*2(%rdx), $B, $Y + vpxor $T0, $ACC1, $ACC1 + vpand 32*3(%rdx), $B, $T0 + vpxor $Y, $ACC2, $ACC2 + vpand 32*4-160(%rax), $B, $Y + vpxor $T0, $ACC3, $ACC3 + vpand 32*5-160(%rax), $B, $T0 + vpxor $Y, $ACC4, $ACC4 + vpand 32*6-160(%rax), $B, $Y + vpxor $T0, $ACC5, $ACC5 + vpand 32*7-160(%rax), $B, $T0 + vpxor $Y, $ACC6, $ACC6 + vpand 32*8-160(%rax), $B, $Y + vpxor $T0, $ACC7, $ACC7 + vpxor $Y, $ACC8, $ACC8 + `&STORE` + + ret +.size avx2_select_n_store,.-avx2_select_n_store +___ +$code.=<<___ if (0); # inlined +################################################################################ +# void avx2_mul_by2_x4(void* RESULTx4, void *Ax4); +.type avx2_mul_by2_x4,\@abi-omnipotent +.align 32 +avx2_mul_by2_x4: + vmovdqa 32*0($a_ptr), $ACC0 + lea 160($a_ptr), %rax + vmovdqa 32*1($a_ptr), $ACC1 + vmovdqa 32*2($a_ptr), $ACC2 + vmovdqa 32*3($a_ptr), $ACC3 + vmovdqa 32*4-160(%rax), $ACC4 + vmovdqa 32*5-160(%rax), $ACC5 + vmovdqa 32*6-160(%rax), $ACC6 + vmovdqa 32*7-160(%rax), $ACC7 + vmovdqa 32*8-160(%rax), $ACC8 + + vpaddq $ACC0, $ACC0, $ACC0 + vpaddq $ACC1, $ACC1, $ACC1 + vpaddq $ACC2, $ACC2, $ACC2 + vpaddq $ACC3, $ACC3, $ACC3 + vpaddq $ACC4, $ACC4, $ACC4 + vpaddq $ACC5, $ACC5, $ACC5 + vpaddq $ACC6, $ACC6, $ACC6 + vpaddq $ACC7, $ACC7, $ACC7 + vpaddq $ACC8, $ACC8, $ACC8 + + ret +.size avx2_mul_by2_x4,.-avx2_mul_by2_x4 +___ +my ($r_ptr_in,$a_ptr_in,$b_ptr_in)=("%rdi","%rsi","%rdx"); +my ($r_ptr,$a_ptr,$b_ptr)=("%r8","%r9","%r10"); + +$code.=<<___; +################################################################################ +# void ecp_nistz256_avx2_point_add_affine_x4(void* RESULTx4, void *Ax4, void *Bx4); +.globl ecp_nistz256_avx2_point_add_affine_x4 +.type ecp_nistz256_avx2_point_add_affine_x4,\@function,3 +.align 32 +ecp_nistz256_avx2_point_add_affine_x4: + mov %rsp, %rax + push %rbp + vzeroupper +___ +$code.=<<___ if ($win64); + lea -16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + lea -8(%rax), %rbp + +# Result + 32*0 = Result.X +# Result + 32*9 = Result.Y +# Result + 32*18 = Result.Z + +# A + 32*0 = A.X +# A + 32*9 = A.Y +# A + 32*18 = A.Z + +# B + 32*0 = B.X +# B + 32*9 = B.Y + + sub \$`32*9*8+32*2+32*8`, %rsp + and \$-64, %rsp + + mov $r_ptr_in, $r_ptr + mov $a_ptr_in, $a_ptr + mov $b_ptr_in, $b_ptr + + vmovdqa 32*0($a_ptr_in), %ymm0 + vmovdqa .LAVX2_AND_MASK(%rip), $AND_MASK + vpxor %ymm1, %ymm1, %ymm1 + lea 256($a_ptr_in), %rax # size optimization + vpor 32*1($a_ptr_in), %ymm0, %ymm0 + vpor 32*2($a_ptr_in), %ymm0, %ymm0 + vpor 32*3($a_ptr_in), %ymm0, %ymm0 + vpor 32*4-256(%rax), %ymm0, %ymm0 + lea 256(%rax), %rcx # size optimization + vpor 32*5-256(%rax), %ymm0, %ymm0 + vpor 32*6-256(%rax), %ymm0, %ymm0 + vpor 32*7-256(%rax), %ymm0, %ymm0 + vpor 32*8-256(%rax), %ymm0, %ymm0 + vpor 32*9-256(%rax), %ymm0, %ymm0 + vpor 32*10-256(%rax), %ymm0, %ymm0 + vpor 32*11-256(%rax), %ymm0, %ymm0 + vpor 32*12-512(%rcx), %ymm0, %ymm0 + vpor 32*13-512(%rcx), %ymm0, %ymm0 + vpor 32*14-512(%rcx), %ymm0, %ymm0 + vpor 32*15-512(%rcx), %ymm0, %ymm0 + vpor 32*16-512(%rcx), %ymm0, %ymm0 + vpor 32*17-512(%rcx), %ymm0, %ymm0 + vpcmpeqq %ymm1, %ymm0, %ymm0 + vmovdqa %ymm0, `32*9*8`(%rsp) + + vpxor %ymm1, %ymm1, %ymm1 + vmovdqa 32*0($b_ptr), %ymm0 + lea 256($b_ptr), %rax # size optimization + vpor 32*1($b_ptr), %ymm0, %ymm0 + vpor 32*2($b_ptr), %ymm0, %ymm0 + vpor 32*3($b_ptr), %ymm0, %ymm0 + vpor 32*4-256(%rax), %ymm0, %ymm0 + lea 256(%rax), %rcx # size optimization + vpor 32*5-256(%rax), %ymm0, %ymm0 + vpor 32*6-256(%rax), %ymm0, %ymm0 + vpor 32*7-256(%rax), %ymm0, %ymm0 + vpor 32*8-256(%rax), %ymm0, %ymm0 + vpor 32*9-256(%rax), %ymm0, %ymm0 + vpor 32*10-256(%rax), %ymm0, %ymm0 + vpor 32*11-256(%rax), %ymm0, %ymm0 + vpor 32*12-512(%rcx), %ymm0, %ymm0 + vpor 32*13-512(%rcx), %ymm0, %ymm0 + vpor 32*14-512(%rcx), %ymm0, %ymm0 + vpor 32*15-512(%rcx), %ymm0, %ymm0 + vpor 32*16-512(%rcx), %ymm0, %ymm0 + vpor 32*17-512(%rcx), %ymm0, %ymm0 + vpcmpeqq %ymm1, %ymm0, %ymm0 + vmovdqa %ymm0, `32*9*8+32`(%rsp) + + # Z1^2 = Z1*Z1 + lea `32*9*2`($a_ptr), %rsi + lea `32*9*2`(%rsp), %rdi + lea `32*9*8+32*2`(%rsp), %rcx # temporary vector + call avx2_sqr_x4 + call avx2_normalize_n_store + + # U2 = X2*Z1^2 + lea `32*9*0`($b_ptr), %rsi + lea `32*9*2`(%rsp), %rdx + lea `32*9*0`(%rsp), %rdi + call avx2_mul_x4 + #call avx2_normalize + `&STORE` + + # S2 = Z1*Z1^2 = Z1^3 + lea `32*9*2`($a_ptr), %rsi + lea `32*9*2`(%rsp), %rdx + lea `32*9*1`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # S2 = S2*Y2 = Y2*Z1^3 + lea `32*9*1`($b_ptr), %rsi + lea `32*9*1`(%rsp), %rdx + lea `32*9*1`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # H = U2 - U1 = U2 - X1 + lea `32*9*0`(%rsp), %rsi + lea `32*9*0`($a_ptr), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # R = S2 - S1 = S2 - Y1 + lea `32*9*1`(%rsp), %rsi + lea `32*9*1`($a_ptr), %rdx + lea `32*9*4`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # Z3 = H*Z1*Z2 + lea `32*9*3`(%rsp), %rsi + lea `32*9*2`($a_ptr), %rdx + lea `32*9*2`($r_ptr), %rdi + call avx2_mul_x4 + call avx2_normalize + + lea .LONE(%rip), %rsi + lea `32*9*2`($a_ptr), %rdx + call avx2_select_n_store + + # R^2 = R^2 + lea `32*9*4`(%rsp), %rsi + lea `32*9*6`(%rsp), %rdi + lea `32*9*8+32*2`(%rsp), %rcx # temporary vector + call avx2_sqr_x4 + call avx2_normalize_n_store + + # H^2 = H^2 + lea `32*9*3`(%rsp), %rsi + lea `32*9*5`(%rsp), %rdi + call avx2_sqr_x4 + call avx2_normalize_n_store + + # H^3 = H^2*H + lea `32*9*3`(%rsp), %rsi + lea `32*9*5`(%rsp), %rdx + lea `32*9*7`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # U2 = U1*H^2 + lea `32*9*0`($a_ptr), %rsi + lea `32*9*5`(%rsp), %rdx + lea `32*9*0`(%rsp), %rdi + call avx2_mul_x4 + #call avx2_normalize + `&STORE` + + # Hsqr = U2*2 + #lea 32*9*0(%rsp), %rsi + #lea 32*9*5(%rsp), %rdi + #call avx2_mul_by2_x4 + + vpaddq $ACC0, $ACC0, $ACC0 # inlined avx2_mul_by2_x4 + lea `32*9*5`(%rsp), %rdi + vpaddq $ACC1, $ACC1, $ACC1 + vpaddq $ACC2, $ACC2, $ACC2 + vpaddq $ACC3, $ACC3, $ACC3 + vpaddq $ACC4, $ACC4, $ACC4 + vpaddq $ACC5, $ACC5, $ACC5 + vpaddq $ACC6, $ACC6, $ACC6 + vpaddq $ACC7, $ACC7, $ACC7 + vpaddq $ACC8, $ACC8, $ACC8 + call avx2_normalize_n_store + + # X3 = R^2 - H^3 + #lea 32*9*6(%rsp), %rsi + #lea 32*9*7(%rsp), %rdx + #lea 32*9*5(%rsp), %rcx + #lea 32*9*0($r_ptr), %rdi + #call avx2_sub_x4 + #NORMALIZE + #STORE + + # X3 = X3 - U2*2 + #lea 32*9*0($r_ptr), %rsi + #lea 32*9*0($r_ptr), %rdi + #call avx2_sub_x4 + #NORMALIZE + #STORE + + lea `32*9*6+128`(%rsp), %rsi + lea .LAVX2_POLY_x2+128(%rip), %rax + lea `32*9*7+128`(%rsp), %rdx + lea `32*9*5+128`(%rsp), %rcx + lea `32*9*0`($r_ptr), %rdi + + vmovdqa 32*0-128(%rsi), $ACC0 + vmovdqa 32*1-128(%rsi), $ACC1 + vmovdqa 32*2-128(%rsi), $ACC2 + vmovdqa 32*3-128(%rsi), $ACC3 + vmovdqa 32*4-128(%rsi), $ACC4 + vmovdqa 32*5-128(%rsi), $ACC5 + vmovdqa 32*6-128(%rsi), $ACC6 + vmovdqa 32*7-128(%rsi), $ACC7 + vmovdqa 32*8-128(%rsi), $ACC8 + + vpaddq 32*0-128(%rax), $ACC0, $ACC0 + vpaddq 32*1-128(%rax), $ACC1, $ACC1 + vpaddq 32*2-128(%rax), $ACC2, $ACC2 + vpaddq 32*3-128(%rax), $ACC3, $ACC3 + vpaddq 32*4-128(%rax), $ACC4, $ACC4 + vpaddq 32*5-128(%rax), $ACC5, $ACC5 + vpaddq 32*6-128(%rax), $ACC6, $ACC6 + vpaddq 32*7-128(%rax), $ACC7, $ACC7 + vpaddq 32*8-128(%rax), $ACC8, $ACC8 + + vpsubq 32*0-128(%rdx), $ACC0, $ACC0 + vpsubq 32*1-128(%rdx), $ACC1, $ACC1 + vpsubq 32*2-128(%rdx), $ACC2, $ACC2 + vpsubq 32*3-128(%rdx), $ACC3, $ACC3 + vpsubq 32*4-128(%rdx), $ACC4, $ACC4 + vpsubq 32*5-128(%rdx), $ACC5, $ACC5 + vpsubq 32*6-128(%rdx), $ACC6, $ACC6 + vpsubq 32*7-128(%rdx), $ACC7, $ACC7 + vpsubq 32*8-128(%rdx), $ACC8, $ACC8 + + vpsubq 32*0-128(%rcx), $ACC0, $ACC0 + vpsubq 32*1-128(%rcx), $ACC1, $ACC1 + vpsubq 32*2-128(%rcx), $ACC2, $ACC2 + vpsubq 32*3-128(%rcx), $ACC3, $ACC3 + vpsubq 32*4-128(%rcx), $ACC4, $ACC4 + vpsubq 32*5-128(%rcx), $ACC5, $ACC5 + vpsubq 32*6-128(%rcx), $ACC6, $ACC6 + vpsubq 32*7-128(%rcx), $ACC7, $ACC7 + vpsubq 32*8-128(%rcx), $ACC8, $ACC8 + call avx2_normalize + + lea 32*0($b_ptr), %rsi + lea 32*0($a_ptr), %rdx + call avx2_select_n_store + + # H = U2 - X3 + lea `32*9*0`(%rsp), %rsi + lea `32*9*0`($r_ptr), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # + lea `32*9*3`(%rsp), %rsi + lea `32*9*4`(%rsp), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # + lea `32*9*7`(%rsp), %rsi + lea `32*9*1`($a_ptr), %rdx + lea `32*9*1`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # + lea `32*9*3`(%rsp), %rsi + lea `32*9*1`(%rsp), %rdx + lea `32*9*1`($r_ptr), %rdi + call avx2_sub_x4 + call avx2_normalize + + lea 32*9($b_ptr), %rsi + lea 32*9($a_ptr), %rdx + call avx2_select_n_store + + #lea 32*9*0($r_ptr), %rsi + #lea 32*9*0($r_ptr), %rdi + #call avx2_mul_by1_x4 + #NORMALIZE + #STORE + + lea `32*9*1`($r_ptr), %rsi + lea `32*9*1`($r_ptr), %rdi + call avx2_mul_by1_x4 + call avx2_normalize_n_store + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps %xmm6, -16*10(%rbp) + movaps %xmm7, -16*9(%rbp) + movaps %xmm8, -16*8(%rbp) + movaps %xmm9, -16*7(%rbp) + movaps %xmm10, -16*6(%rbp) + movaps %xmm11, -16*5(%rbp) + movaps %xmm12, -16*4(%rbp) + movaps %xmm13, -16*3(%rbp) + movaps %xmm14, -16*2(%rbp) + movaps %xmm15, -16*1(%rbp) +___ +$code.=<<___; + mov %rbp, %rsp + pop %rbp + ret +.size ecp_nistz256_avx2_point_add_affine_x4,.-ecp_nistz256_avx2_point_add_affine_x4 + +################################################################################ +# void ecp_nistz256_avx2_point_add_affines_x4(void* RESULTx4, void *Ax4, void *Bx4); +.globl ecp_nistz256_avx2_point_add_affines_x4 +.type ecp_nistz256_avx2_point_add_affines_x4,\@function,3 +.align 32 +ecp_nistz256_avx2_point_add_affines_x4: + mov %rsp, %rax + push %rbp + vzeroupper +___ +$code.=<<___ if ($win64); + lea -16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + lea -8(%rax), %rbp + +# Result + 32*0 = Result.X +# Result + 32*9 = Result.Y +# Result + 32*18 = Result.Z + +# A + 32*0 = A.X +# A + 32*9 = A.Y + +# B + 32*0 = B.X +# B + 32*9 = B.Y + + sub \$`32*9*8+32*2+32*8`, %rsp + and \$-64, %rsp + + mov $r_ptr_in, $r_ptr + mov $a_ptr_in, $a_ptr + mov $b_ptr_in, $b_ptr + + vmovdqa 32*0($a_ptr_in), %ymm0 + vmovdqa .LAVX2_AND_MASK(%rip), $AND_MASK + vpxor %ymm1, %ymm1, %ymm1 + lea 256($a_ptr_in), %rax # size optimization + vpor 32*1($a_ptr_in), %ymm0, %ymm0 + vpor 32*2($a_ptr_in), %ymm0, %ymm0 + vpor 32*3($a_ptr_in), %ymm0, %ymm0 + vpor 32*4-256(%rax), %ymm0, %ymm0 + lea 256(%rax), %rcx # size optimization + vpor 32*5-256(%rax), %ymm0, %ymm0 + vpor 32*6-256(%rax), %ymm0, %ymm0 + vpor 32*7-256(%rax), %ymm0, %ymm0 + vpor 32*8-256(%rax), %ymm0, %ymm0 + vpor 32*9-256(%rax), %ymm0, %ymm0 + vpor 32*10-256(%rax), %ymm0, %ymm0 + vpor 32*11-256(%rax), %ymm0, %ymm0 + vpor 32*12-512(%rcx), %ymm0, %ymm0 + vpor 32*13-512(%rcx), %ymm0, %ymm0 + vpor 32*14-512(%rcx), %ymm0, %ymm0 + vpor 32*15-512(%rcx), %ymm0, %ymm0 + vpor 32*16-512(%rcx), %ymm0, %ymm0 + vpor 32*17-512(%rcx), %ymm0, %ymm0 + vpcmpeqq %ymm1, %ymm0, %ymm0 + vmovdqa %ymm0, `32*9*8`(%rsp) + + vpxor %ymm1, %ymm1, %ymm1 + vmovdqa 32*0($b_ptr), %ymm0 + lea 256($b_ptr), %rax # size optimization + vpor 32*1($b_ptr), %ymm0, %ymm0 + vpor 32*2($b_ptr), %ymm0, %ymm0 + vpor 32*3($b_ptr), %ymm0, %ymm0 + vpor 32*4-256(%rax), %ymm0, %ymm0 + lea 256(%rax), %rcx # size optimization + vpor 32*5-256(%rax), %ymm0, %ymm0 + vpor 32*6-256(%rax), %ymm0, %ymm0 + vpor 32*7-256(%rax), %ymm0, %ymm0 + vpor 32*8-256(%rax), %ymm0, %ymm0 + vpor 32*9-256(%rax), %ymm0, %ymm0 + vpor 32*10-256(%rax), %ymm0, %ymm0 + vpor 32*11-256(%rax), %ymm0, %ymm0 + vpor 32*12-512(%rcx), %ymm0, %ymm0 + vpor 32*13-512(%rcx), %ymm0, %ymm0 + vpor 32*14-512(%rcx), %ymm0, %ymm0 + vpor 32*15-512(%rcx), %ymm0, %ymm0 + vpor 32*16-512(%rcx), %ymm0, %ymm0 + vpor 32*17-512(%rcx), %ymm0, %ymm0 + vpcmpeqq %ymm1, %ymm0, %ymm0 + vmovdqa %ymm0, `32*9*8+32`(%rsp) + + # H = U2 - U1 = X2 - X1 + lea `32*9*0`($b_ptr), %rsi + lea `32*9*0`($a_ptr), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # R = S2 - S1 = Y2 - Y1 + lea `32*9*1`($b_ptr), %rsi + lea `32*9*1`($a_ptr), %rdx + lea `32*9*4`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # Z3 = H*Z1*Z2 = H + lea `32*9*3`(%rsp), %rsi + lea `32*9*2`($r_ptr), %rdi + call avx2_mul_by1_x4 + call avx2_normalize + + vmovdqa `32*9*8`(%rsp), $B + vpor `32*9*8+32`(%rsp), $B, $B + + vpandn $ACC0, $B, $ACC0 + lea .LONE+128(%rip), %rax + vpandn $ACC1, $B, $ACC1 + vpandn $ACC2, $B, $ACC2 + vpandn $ACC3, $B, $ACC3 + vpandn $ACC4, $B, $ACC4 + vpandn $ACC5, $B, $ACC5 + vpandn $ACC6, $B, $ACC6 + vpandn $ACC7, $B, $ACC7 + + vpand 32*0-128(%rax), $B, $T0 + vpandn $ACC8, $B, $ACC8 + vpand 32*1-128(%rax), $B, $Y + vpxor $T0, $ACC0, $ACC0 + vpand 32*2-128(%rax), $B, $T0 + vpxor $Y, $ACC1, $ACC1 + vpand 32*3-128(%rax), $B, $Y + vpxor $T0, $ACC2, $ACC2 + vpand 32*4-128(%rax), $B, $T0 + vpxor $Y, $ACC3, $ACC3 + vpand 32*5-128(%rax), $B, $Y + vpxor $T0, $ACC4, $ACC4 + vpand 32*6-128(%rax), $B, $T0 + vpxor $Y, $ACC5, $ACC5 + vpand 32*7-128(%rax), $B, $Y + vpxor $T0, $ACC6, $ACC6 + vpand 32*8-128(%rax), $B, $T0 + vpxor $Y, $ACC7, $ACC7 + vpxor $T0, $ACC8, $ACC8 + `&STORE` + + # R^2 = R^2 + lea `32*9*4`(%rsp), %rsi + lea `32*9*6`(%rsp), %rdi + lea `32*9*8+32*2`(%rsp), %rcx # temporary vector + call avx2_sqr_x4 + call avx2_normalize_n_store + + # H^2 = H^2 + lea `32*9*3`(%rsp), %rsi + lea `32*9*5`(%rsp), %rdi + call avx2_sqr_x4 + call avx2_normalize_n_store + + # H^3 = H^2*H + lea `32*9*3`(%rsp), %rsi + lea `32*9*5`(%rsp), %rdx + lea `32*9*7`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # U2 = U1*H^2 + lea `32*9*0`($a_ptr), %rsi + lea `32*9*5`(%rsp), %rdx + lea `32*9*0`(%rsp), %rdi + call avx2_mul_x4 + #call avx2_normalize + `&STORE` + + # Hsqr = U2*2 + #lea 32*9*0(%rsp), %rsi + #lea 32*9*5(%rsp), %rdi + #call avx2_mul_by2_x4 + + vpaddq $ACC0, $ACC0, $ACC0 # inlined avx2_mul_by2_x4 + lea `32*9*5`(%rsp), %rdi + vpaddq $ACC1, $ACC1, $ACC1 + vpaddq $ACC2, $ACC2, $ACC2 + vpaddq $ACC3, $ACC3, $ACC3 + vpaddq $ACC4, $ACC4, $ACC4 + vpaddq $ACC5, $ACC5, $ACC5 + vpaddq $ACC6, $ACC6, $ACC6 + vpaddq $ACC7, $ACC7, $ACC7 + vpaddq $ACC8, $ACC8, $ACC8 + call avx2_normalize_n_store + + # X3 = R^2 - H^3 + #lea 32*9*6(%rsp), %rsi + #lea 32*9*7(%rsp), %rdx + #lea 32*9*5(%rsp), %rcx + #lea 32*9*0($r_ptr), %rdi + #call avx2_sub_x4 + #NORMALIZE + #STORE + + # X3 = X3 - U2*2 + #lea 32*9*0($r_ptr), %rsi + #lea 32*9*0($r_ptr), %rdi + #call avx2_sub_x4 + #NORMALIZE + #STORE + + lea `32*9*6+128`(%rsp), %rsi + lea .LAVX2_POLY_x2+128(%rip), %rax + lea `32*9*7+128`(%rsp), %rdx + lea `32*9*5+128`(%rsp), %rcx + lea `32*9*0`($r_ptr), %rdi + + vmovdqa 32*0-128(%rsi), $ACC0 + vmovdqa 32*1-128(%rsi), $ACC1 + vmovdqa 32*2-128(%rsi), $ACC2 + vmovdqa 32*3-128(%rsi), $ACC3 + vmovdqa 32*4-128(%rsi), $ACC4 + vmovdqa 32*5-128(%rsi), $ACC5 + vmovdqa 32*6-128(%rsi), $ACC6 + vmovdqa 32*7-128(%rsi), $ACC7 + vmovdqa 32*8-128(%rsi), $ACC8 + + vpaddq 32*0-128(%rax), $ACC0, $ACC0 + vpaddq 32*1-128(%rax), $ACC1, $ACC1 + vpaddq 32*2-128(%rax), $ACC2, $ACC2 + vpaddq 32*3-128(%rax), $ACC3, $ACC3 + vpaddq 32*4-128(%rax), $ACC4, $ACC4 + vpaddq 32*5-128(%rax), $ACC5, $ACC5 + vpaddq 32*6-128(%rax), $ACC6, $ACC6 + vpaddq 32*7-128(%rax), $ACC7, $ACC7 + vpaddq 32*8-128(%rax), $ACC8, $ACC8 + + vpsubq 32*0-128(%rdx), $ACC0, $ACC0 + vpsubq 32*1-128(%rdx), $ACC1, $ACC1 + vpsubq 32*2-128(%rdx), $ACC2, $ACC2 + vpsubq 32*3-128(%rdx), $ACC3, $ACC3 + vpsubq 32*4-128(%rdx), $ACC4, $ACC4 + vpsubq 32*5-128(%rdx), $ACC5, $ACC5 + vpsubq 32*6-128(%rdx), $ACC6, $ACC6 + vpsubq 32*7-128(%rdx), $ACC7, $ACC7 + vpsubq 32*8-128(%rdx), $ACC8, $ACC8 + + vpsubq 32*0-128(%rcx), $ACC0, $ACC0 + vpsubq 32*1-128(%rcx), $ACC1, $ACC1 + vpsubq 32*2-128(%rcx), $ACC2, $ACC2 + vpsubq 32*3-128(%rcx), $ACC3, $ACC3 + vpsubq 32*4-128(%rcx), $ACC4, $ACC4 + vpsubq 32*5-128(%rcx), $ACC5, $ACC5 + vpsubq 32*6-128(%rcx), $ACC6, $ACC6 + vpsubq 32*7-128(%rcx), $ACC7, $ACC7 + vpsubq 32*8-128(%rcx), $ACC8, $ACC8 + call avx2_normalize + + lea 32*0($b_ptr), %rsi + lea 32*0($a_ptr), %rdx + call avx2_select_n_store + + # H = U2 - X3 + lea `32*9*0`(%rsp), %rsi + lea `32*9*0`($r_ptr), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_sub_x4 + call avx2_normalize_n_store + + # H = H*R + lea `32*9*3`(%rsp), %rsi + lea `32*9*4`(%rsp), %rdx + lea `32*9*3`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # S2 = S1 * H^3 + lea `32*9*7`(%rsp), %rsi + lea `32*9*1`($a_ptr), %rdx + lea `32*9*1`(%rsp), %rdi + call avx2_mul_x4 + call avx2_normalize_n_store + + # + lea `32*9*3`(%rsp), %rsi + lea `32*9*1`(%rsp), %rdx + lea `32*9*1`($r_ptr), %rdi + call avx2_sub_x4 + call avx2_normalize + + lea 32*9($b_ptr), %rsi + lea 32*9($a_ptr), %rdx + call avx2_select_n_store + + #lea 32*9*0($r_ptr), %rsi + #lea 32*9*0($r_ptr), %rdi + #call avx2_mul_by1_x4 + #NORMALIZE + #STORE + + lea `32*9*1`($r_ptr), %rsi + lea `32*9*1`($r_ptr), %rdi + call avx2_mul_by1_x4 + call avx2_normalize_n_store + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps %xmm6, -16*10(%rbp) + movaps %xmm7, -16*9(%rbp) + movaps %xmm8, -16*8(%rbp) + movaps %xmm9, -16*7(%rbp) + movaps %xmm10, -16*6(%rbp) + movaps %xmm11, -16*5(%rbp) + movaps %xmm12, -16*4(%rbp) + movaps %xmm13, -16*3(%rbp) + movaps %xmm14, -16*2(%rbp) + movaps %xmm15, -16*1(%rbp) +___ +$code.=<<___; + mov %rbp, %rsp + pop %rbp + ret +.size ecp_nistz256_avx2_point_add_affines_x4,.-ecp_nistz256_avx2_point_add_affines_x4 + +################################################################################ +# void ecp_nistz256_avx2_to_mont(void* RESULTx4, void *Ax4); +.globl ecp_nistz256_avx2_to_mont +.type ecp_nistz256_avx2_to_mont,\@function,2 +.align 32 +ecp_nistz256_avx2_to_mont: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -8-16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + vmovdqa .LAVX2_AND_MASK(%rip), $AND_MASK + lea .LTO_MONT_AVX2(%rip), %rdx + call avx2_mul_x4 + call avx2_normalize_n_store + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps 16*0(%rsp), %xmm6 + movaps 16*1(%rsp), %xmm7 + movaps 16*2(%rsp), %xmm8 + movaps 16*3(%rsp), %xmm9 + movaps 16*4(%rsp), %xmm10 + movaps 16*5(%rsp), %xmm11 + movaps 16*6(%rsp), %xmm12 + movaps 16*7(%rsp), %xmm13 + movaps 16*8(%rsp), %xmm14 + movaps 16*9(%rsp), %xmm15 + lea 8+16*10(%rsp), %rsp +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_to_mont,.-ecp_nistz256_avx2_to_mont + +################################################################################ +# void ecp_nistz256_avx2_from_mont(void* RESULTx4, void *Ax4); +.globl ecp_nistz256_avx2_from_mont +.type ecp_nistz256_avx2_from_mont,\@function,2 +.align 32 +ecp_nistz256_avx2_from_mont: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -8-16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + vmovdqa .LAVX2_AND_MASK(%rip), $AND_MASK + lea .LFROM_MONT_AVX2(%rip), %rdx + call avx2_mul_x4 + call avx2_normalize_n_store + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps 16*0(%rsp), %xmm6 + movaps 16*1(%rsp), %xmm7 + movaps 16*2(%rsp), %xmm8 + movaps 16*3(%rsp), %xmm9 + movaps 16*4(%rsp), %xmm10 + movaps 16*5(%rsp), %xmm11 + movaps 16*6(%rsp), %xmm12 + movaps 16*7(%rsp), %xmm13 + movaps 16*8(%rsp), %xmm14 + movaps 16*9(%rsp), %xmm15 + lea 8+16*10(%rsp), %rsp +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_from_mont,.-ecp_nistz256_avx2_from_mont + +################################################################################ +# void ecp_nistz256_avx2_set1(void* RESULTx4); +.globl ecp_nistz256_avx2_set1 +.type ecp_nistz256_avx2_set1,\@function,1 +.align 32 +ecp_nistz256_avx2_set1: + lea .LONE+128(%rip), %rax + lea 128(%rdi), %rdi + vzeroupper + vmovdqa 32*0-128(%rax), %ymm0 + vmovdqa 32*1-128(%rax), %ymm1 + vmovdqa 32*2-128(%rax), %ymm2 + vmovdqa 32*3-128(%rax), %ymm3 + vmovdqa 32*4-128(%rax), %ymm4 + vmovdqa 32*5-128(%rax), %ymm5 + vmovdqa %ymm0, 32*0-128(%rdi) + vmovdqa 32*6-128(%rax), %ymm0 + vmovdqa %ymm1, 32*1-128(%rdi) + vmovdqa 32*7-128(%rax), %ymm1 + vmovdqa %ymm2, 32*2-128(%rdi) + vmovdqa 32*8-128(%rax), %ymm2 + vmovdqa %ymm3, 32*3-128(%rdi) + vmovdqa %ymm4, 32*4-128(%rdi) + vmovdqa %ymm5, 32*5-128(%rdi) + vmovdqa %ymm0, 32*6-128(%rdi) + vmovdqa %ymm1, 32*7-128(%rdi) + vmovdqa %ymm2, 32*8-128(%rdi) + + vzeroupper + ret +.size ecp_nistz256_avx2_set1,.-ecp_nistz256_avx2_set1 +___ +} +{ +################################################################################ +# void ecp_nistz256_avx2_multi_gather_w7(void* RESULT, void *in, +# int index0, int index1, int index2, int index3); +################################################################################ + +my ($val,$in_t,$index0,$index1,$index2,$index3)=("%rdi","%rsi","%edx","%ecx","%r8d","%r9d"); +my ($INDEX0,$INDEX1,$INDEX2,$INDEX3)=map("%ymm$_",(0..3)); +my ($R0a,$R0b,$R1a,$R1b,$R2a,$R2b,$R3a,$R3b)=map("%ymm$_",(4..11)); +my ($M0,$T0,$T1,$TMP0)=map("%ymm$_",(12..15)); + +$code.=<<___; +.globl ecp_nistz256_avx2_multi_gather_w7 +.type ecp_nistz256_avx2_multi_gather_w7,\@function,6 +.align 32 +ecp_nistz256_avx2_multi_gather_w7: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -8-16*10(%rsp), %rsp + vmovaps %xmm6, -8-16*10(%rax) + vmovaps %xmm7, -8-16*9(%rax) + vmovaps %xmm8, -8-16*8(%rax) + vmovaps %xmm9, -8-16*7(%rax) + vmovaps %xmm10, -8-16*6(%rax) + vmovaps %xmm11, -8-16*5(%rax) + vmovaps %xmm12, -8-16*4(%rax) + vmovaps %xmm13, -8-16*3(%rax) + vmovaps %xmm14, -8-16*2(%rax) + vmovaps %xmm15, -8-16*1(%rax) +___ +$code.=<<___; + lea .LIntOne(%rip), %rax + + vmovd $index0, %xmm0 + vmovd $index1, %xmm1 + vmovd $index2, %xmm2 + vmovd $index3, %xmm3 + + vpxor $R0a, $R0a, $R0a + vpxor $R0b, $R0b, $R0b + vpxor $R1a, $R1a, $R1a + vpxor $R1b, $R1b, $R1b + vpxor $R2a, $R2a, $R2a + vpxor $R2b, $R2b, $R2b + vpxor $R3a, $R3a, $R3a + vpxor $R3b, $R3b, $R3b + vmovdqa (%rax), $M0 + + vpermd $INDEX0, $R0a, $INDEX0 + vpermd $INDEX1, $R0a, $INDEX1 + vpermd $INDEX2, $R0a, $INDEX2 + vpermd $INDEX3, $R0a, $INDEX3 + + mov \$64, %ecx + lea 112($val), $val # size optimization + jmp .Lmulti_select_loop_avx2 + +# INDEX=0, corresponds to the point at infty (0,0) +.align 32 +.Lmulti_select_loop_avx2: + vpcmpeqd $INDEX0, $M0, $TMP0 + + vmovdqa `32*0+32*64*2*0`($in_t), $T0 + vmovdqa `32*1+32*64*2*0`($in_t), $T1 + vpand $TMP0, $T0, $T0 + vpand $TMP0, $T1, $T1 + vpxor $T0, $R0a, $R0a + vpxor $T1, $R0b, $R0b + + vpcmpeqd $INDEX1, $M0, $TMP0 + + vmovdqa `32*0+32*64*2*1`($in_t), $T0 + vmovdqa `32*1+32*64*2*1`($in_t), $T1 + vpand $TMP0, $T0, $T0 + vpand $TMP0, $T1, $T1 + vpxor $T0, $R1a, $R1a + vpxor $T1, $R1b, $R1b + + vpcmpeqd $INDEX2, $M0, $TMP0 + + vmovdqa `32*0+32*64*2*2`($in_t), $T0 + vmovdqa `32*1+32*64*2*2`($in_t), $T1 + vpand $TMP0, $T0, $T0 + vpand $TMP0, $T1, $T1 + vpxor $T0, $R2a, $R2a + vpxor $T1, $R2b, $R2b + + vpcmpeqd $INDEX3, $M0, $TMP0 + + vmovdqa `32*0+32*64*2*3`($in_t), $T0 + vmovdqa `32*1+32*64*2*3`($in_t), $T1 + vpand $TMP0, $T0, $T0 + vpand $TMP0, $T1, $T1 + vpxor $T0, $R3a, $R3a + vpxor $T1, $R3b, $R3b + + vpaddd (%rax), $M0, $M0 # increment + lea 32*2($in_t), $in_t + + dec %ecx + jnz .Lmulti_select_loop_avx2 + + vmovdqu $R0a, 32*0-112($val) + vmovdqu $R0b, 32*1-112($val) + vmovdqu $R1a, 32*2-112($val) + vmovdqu $R1b, 32*3-112($val) + vmovdqu $R2a, 32*4-112($val) + vmovdqu $R2b, 32*5-112($val) + vmovdqu $R3a, 32*6-112($val) + vmovdqu $R3b, 32*7-112($val) + + vzeroupper +___ +$code.=<<___ if ($win64); + movaps 16*0(%rsp), %xmm6 + movaps 16*1(%rsp), %xmm7 + movaps 16*2(%rsp), %xmm8 + movaps 16*3(%rsp), %xmm9 + movaps 16*4(%rsp), %xmm10 + movaps 16*5(%rsp), %xmm11 + movaps 16*6(%rsp), %xmm12 + movaps 16*7(%rsp), %xmm13 + movaps 16*8(%rsp), %xmm14 + movaps 16*9(%rsp), %xmm15 + lea 8+16*10(%rsp), %rsp +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_multi_gather_w7,.-ecp_nistz256_avx2_multi_gather_w7 + +.extern OPENSSL_ia32cap_P +.globl ecp_nistz_avx2_eligible +.type ecp_nistz_avx2_eligible,\@abi-omnipotent +.align 32 +ecp_nistz_avx2_eligible: + mov OPENSSL_ia32cap_P+8(%rip),%eax + shr \$5,%eax + and \$1,%eax + ret +.size ecp_nistz_avx2_eligible,.-ecp_nistz_avx2_eligible +___ +} +}} else {{ # assembler is too old +$code.=<<___; +.text + +.globl ecp_nistz256_avx2_transpose_convert +.globl ecp_nistz256_avx2_convert_transpose_back +.globl ecp_nistz256_avx2_point_add_affine_x4 +.globl ecp_nistz256_avx2_point_add_affines_x4 +.globl ecp_nistz256_avx2_to_mont +.globl ecp_nistz256_avx2_from_mont +.globl ecp_nistz256_avx2_set1 +.globl ecp_nistz256_avx2_multi_gather_w7 +.type ecp_nistz256_avx2_multi_gather_w7,\@abi-omnipotent +ecp_nistz256_avx2_transpose_convert: +ecp_nistz256_avx2_convert_transpose_back: +ecp_nistz256_avx2_point_add_affine_x4: +ecp_nistz256_avx2_point_add_affines_x4: +ecp_nistz256_avx2_to_mont: +ecp_nistz256_avx2_from_mont: +ecp_nistz256_avx2_set1: +ecp_nistz256_avx2_multi_gather_w7: + .byte 0x0f,0x0b # ud2 + ret +.size ecp_nistz256_avx2_multi_gather_w7,.-ecp_nistz256_avx2_multi_gather_w7 + +.globl ecp_nistz_avx2_eligible +.type ecp_nistz_avx2_eligible,\@abi-omnipotent +ecp_nistz_avx2_eligible: + xor %eax,%eax + ret +.size ecp_nistz_avx2_eligible,.-ecp_nistz_avx2_eligible +___ +}} + +foreach (split("\n",$code)) { + s/\`([^\`]*)\`/eval($1)/geo; + + print $_,"\n"; +} + +close STDOUT; diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-sparcv9.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-sparcv9.pl new file mode 100755 index 0000000..97201cb --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-sparcv9.pl @@ -0,0 +1,3061 @@ +#! /usr/bin/env perl +# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +# ==================================================================== +# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL +# project. The module is, however, dual licensed under OpenSSL and +# CRYPTOGAMS licenses depending on where you obtain it. For further +# details see http://www.openssl.org/~appro/cryptogams/. +# ==================================================================== +# +# ECP_NISTZ256 module for SPARCv9. +# +# February 2015. +# +# Original ECP_NISTZ256 submission targeting x86_64 is detailed in +# http://eprint.iacr.org/2013/816. In the process of adaptation +# original .c module was made 32-bit savvy in order to make this +# implementation possible. +# +# with/without -DECP_NISTZ256_ASM +# UltraSPARC III +12-18% +# SPARC T4 +99-550% (+66-150% on 32-bit Solaris) +# +# Ranges denote minimum and maximum improvement coefficients depending +# on benchmark. Lower coefficients are for ECDSA sign, server-side +# operation. Keep in mind that +200% means 3x improvement. + +$output = pop; +open STDOUT,">$output"; + +$code.=<<___; +#include "sparc_arch.h" + +#define LOCALS (STACK_BIAS+STACK_FRAME) +#ifdef __arch64__ +.register %g2,#scratch +.register %g3,#scratch +# define STACK64_FRAME STACK_FRAME +# define LOCALS64 LOCALS +#else +# define STACK64_FRAME (2047+192) +# define LOCALS64 STACK64_FRAME +#endif + +.section ".text",#alloc,#execinstr +___ +######################################################################## +# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7 +# +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +open TABLE,"<ecp_nistz256_table.c" or +open TABLE,"<${dir}../ecp_nistz256_table.c" or +die "failed to open ecp_nistz256_table.c:",$!; + +use integer; + +foreach(<TABLE>) { + s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo; +} +close TABLE; + +# See ecp_nistz256_table.c for explanation for why it's 64*16*37. +# 64*16*37-1 is because $#arr returns last valid index or @arr, not +# amount of elements. +die "insane number of elements" if ($#arr != 64*16*37-1); + +$code.=<<___; +.globl ecp_nistz256_precomputed +.align 4096 +ecp_nistz256_precomputed: +___ +######################################################################## +# this conversion smashes P256_POINT_AFFINE by individual bytes with +# 64 byte interval, similar to +# 1111222233334444 +# 1234123412341234 +for(1..37) { + @tbl = splice(@arr,0,64*16); + for($i=0;$i<64;$i++) { + undef @line; + for($j=0;$j<64;$j++) { + push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff; + } + $code.=".byte\t"; + $code.=join(',',map { sprintf "0x%02x",$_} @line); + $code.="\n"; + } +} + +{{{ +my ($rp,$ap,$bp)=map("%i$_",(0..2)); +my @acc=map("%l$_",(0..7)); +my ($t0,$t1,$t2,$t3,$t4,$t5,$t6,$t7)=(map("%o$_",(0..5)),"%g4","%g5"); +my ($bi,$a0,$mask,$carry)=(map("%i$_",(3..5)),"%g1"); +my ($rp_real,$ap_real)=("%g2","%g3"); + +$code.=<<___; +.type ecp_nistz256_precomputed,#object +.size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed +.align 64 +.LRR: ! 2^512 mod P precomputed for NIST P256 polynomial +.long 0x00000003, 0x00000000, 0xffffffff, 0xfffffffb +.long 0xfffffffe, 0xffffffff, 0xfffffffd, 0x00000004 +.Lone: +.long 1,0,0,0,0,0,0,0 +.asciz "ECP_NISTZ256 for SPARCv9, CRYPTOGAMS by <appro\@openssl.org>" + +! void ecp_nistz256_to_mont(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_to_mont +.align 64 +ecp_nistz256_to_mont: + save %sp,-STACK_FRAME,%sp + nop +1: call .+8 + add %o7,.LRR-1b,$bp + call __ecp_nistz256_mul_mont + nop + ret + restore +.type ecp_nistz256_to_mont,#function +.size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont + +! void ecp_nistz256_from_mont(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_from_mont +.align 32 +ecp_nistz256_from_mont: + save %sp,-STACK_FRAME,%sp + nop +1: call .+8 + add %o7,.Lone-1b,$bp + call __ecp_nistz256_mul_mont + nop + ret + restore +.type ecp_nistz256_from_mont,#function +.size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont + +! void ecp_nistz256_mul_mont(BN_ULONG %i0[8],const BN_ULONG %i1[8], +! const BN_ULONG %i2[8]); +.globl ecp_nistz256_mul_mont +.align 32 +ecp_nistz256_mul_mont: + save %sp,-STACK_FRAME,%sp + nop + call __ecp_nistz256_mul_mont + nop + ret + restore +.type ecp_nistz256_mul_mont,#function +.size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont + +! void ecp_nistz256_sqr_mont(BN_ULONG %i0[8],const BN_ULONG %i2[8]); +.globl ecp_nistz256_sqr_mont +.align 32 +ecp_nistz256_sqr_mont: + save %sp,-STACK_FRAME,%sp + mov $ap,$bp + call __ecp_nistz256_mul_mont + nop + ret + restore +.type ecp_nistz256_sqr_mont,#function +.size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont +___ + +######################################################################## +# Special thing to keep in mind is that $t0-$t7 hold 64-bit values, +# while all others are meant to keep 32. "Meant to" means that additions +# to @acc[0-7] do "contaminate" upper bits, but they are cleared before +# they can affect outcome (follow 'and' with $mask). Also keep in mind +# that addition with carry is addition with 32-bit carry, even though +# CPU is 64-bit. [Addition with 64-bit carry was introduced in T3, see +# below for VIS3 code paths.] + +$code.=<<___; +.align 32 +__ecp_nistz256_mul_mont: + ld [$bp+0],$bi ! b[0] + mov -1,$mask + ld [$ap+0],$a0 + srl $mask,0,$mask ! 0xffffffff + ld [$ap+4],$t1 + ld [$ap+8],$t2 + ld [$ap+12],$t3 + ld [$ap+16],$t4 + ld [$ap+20],$t5 + ld [$ap+24],$t6 + ld [$ap+28],$t7 + mulx $a0,$bi,$t0 ! a[0-7]*b[0], 64-bit results + mulx $t1,$bi,$t1 + mulx $t2,$bi,$t2 + mulx $t3,$bi,$t3 + mulx $t4,$bi,$t4 + mulx $t5,$bi,$t5 + mulx $t6,$bi,$t6 + mulx $t7,$bi,$t7 + srlx $t0,32,@acc[1] ! extract high parts + srlx $t1,32,@acc[2] + srlx $t2,32,@acc[3] + srlx $t3,32,@acc[4] + srlx $t4,32,@acc[5] + srlx $t5,32,@acc[6] + srlx $t6,32,@acc[7] + srlx $t7,32,@acc[0] ! "@acc[8]" + mov 0,$carry +___ +for($i=1;$i<8;$i++) { +$code.=<<___; + addcc @acc[1],$t1,@acc[1] ! accumulate high parts + ld [$bp+4*$i],$bi ! b[$i] + ld [$ap+4],$t1 ! re-load a[1-7] + addccc @acc[2],$t2,@acc[2] + addccc @acc[3],$t3,@acc[3] + ld [$ap+8],$t2 + ld [$ap+12],$t3 + addccc @acc[4],$t4,@acc[4] + addccc @acc[5],$t5,@acc[5] + ld [$ap+16],$t4 + ld [$ap+20],$t5 + addccc @acc[6],$t6,@acc[6] + addccc @acc[7],$t7,@acc[7] + ld [$ap+24],$t6 + ld [$ap+28],$t7 + addccc @acc[0],$carry,@acc[0] ! "@acc[8]" + addc %g0,%g0,$carry +___ + # Reduction iteration is normally performed by accumulating + # result of multiplication of modulus by "magic" digit [and + # omitting least significant word, which is guaranteed to + # be 0], but thanks to special form of modulus and "magic" + # digit being equal to least significant word, it can be + # performed with additions and subtractions alone. Indeed: + # + # ffff.0001.0000.0000.0000.ffff.ffff.ffff + # * abcd + # + xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we + # rewrite above as: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + abcd.0000.abcd.0000.0000.abcd.0000.0000.0000 + # - abcd.0000.0000.0000.0000.0000.0000.abcd + # + # or marking redundant operations: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.---- + # + abcd.0000.abcd.0000.0000.abcd.----.----.---- + # - abcd.----.----.----.----.----.----.---- + +$code.=<<___; + ! multiplication-less reduction + addcc @acc[3],$t0,@acc[3] ! r[3]+=r[0] + addccc @acc[4],%g0,@acc[4] ! r[4]+=0 + and @acc[1],$mask,@acc[1] + and @acc[2],$mask,@acc[2] + addccc @acc[5],%g0,@acc[5] ! r[5]+=0 + addccc @acc[6],$t0,@acc[6] ! r[6]+=r[0] + and @acc[3],$mask,@acc[3] + and @acc[4],$mask,@acc[4] + addccc @acc[7],%g0,@acc[7] ! r[7]+=0 + addccc @acc[0],$t0,@acc[0] ! r[8]+=r[0] "@acc[8]" + and @acc[5],$mask,@acc[5] + and @acc[6],$mask,@acc[6] + addc $carry,%g0,$carry ! top-most carry + subcc @acc[7],$t0,@acc[7] ! r[7]-=r[0] + subccc @acc[0],%g0,@acc[0] ! r[8]-=0 "@acc[8]" + subc $carry,%g0,$carry ! top-most carry + and @acc[7],$mask,@acc[7] + and @acc[0],$mask,@acc[0] ! "@acc[8]" +___ + push(@acc,shift(@acc)); # rotate registers to "omit" acc[0] +$code.=<<___; + mulx $a0,$bi,$t0 ! a[0-7]*b[$i], 64-bit results + mulx $t1,$bi,$t1 + mulx $t2,$bi,$t2 + mulx $t3,$bi,$t3 + mulx $t4,$bi,$t4 + mulx $t5,$bi,$t5 + mulx $t6,$bi,$t6 + mulx $t7,$bi,$t7 + add @acc[0],$t0,$t0 ! accumulate low parts, can't overflow + add @acc[1],$t1,$t1 + srlx $t0,32,@acc[1] ! extract high parts + add @acc[2],$t2,$t2 + srlx $t1,32,@acc[2] + add @acc[3],$t3,$t3 + srlx $t2,32,@acc[3] + add @acc[4],$t4,$t4 + srlx $t3,32,@acc[4] + add @acc[5],$t5,$t5 + srlx $t4,32,@acc[5] + add @acc[6],$t6,$t6 + srlx $t5,32,@acc[6] + add @acc[7],$t7,$t7 + srlx $t6,32,@acc[7] + srlx $t7,32,@acc[0] ! "@acc[8]" +___ +} +$code.=<<___; + addcc @acc[1],$t1,@acc[1] ! accumulate high parts + addccc @acc[2],$t2,@acc[2] + addccc @acc[3],$t3,@acc[3] + addccc @acc[4],$t4,@acc[4] + addccc @acc[5],$t5,@acc[5] + addccc @acc[6],$t6,@acc[6] + addccc @acc[7],$t7,@acc[7] + addccc @acc[0],$carry,@acc[0] ! "@acc[8]" + addc %g0,%g0,$carry + + addcc @acc[3],$t0,@acc[3] ! multiplication-less reduction + addccc @acc[4],%g0,@acc[4] + addccc @acc[5],%g0,@acc[5] + addccc @acc[6],$t0,@acc[6] + addccc @acc[7],%g0,@acc[7] + addccc @acc[0],$t0,@acc[0] ! "@acc[8]" + addc $carry,%g0,$carry + subcc @acc[7],$t0,@acc[7] + subccc @acc[0],%g0,@acc[0] ! "@acc[8]" + subc $carry,%g0,$carry ! top-most carry +___ + push(@acc,shift(@acc)); # rotate registers to omit acc[0] +$code.=<<___; + ! Final step is "if result > mod, subtract mod", but we do it + ! "other way around", namely subtract modulus from result + ! and if it borrowed, add modulus back. + + subcc @acc[0],-1,@acc[0] ! subtract modulus + subccc @acc[1],-1,@acc[1] + subccc @acc[2],-1,@acc[2] + subccc @acc[3],0,@acc[3] + subccc @acc[4],0,@acc[4] + subccc @acc[5],0,@acc[5] + subccc @acc[6],1,@acc[6] + subccc @acc[7],-1,@acc[7] + subc $carry,0,$carry ! broadcast borrow bit + + ! Note that because mod has special form, i.e. consists of + ! 0xffffffff, 1 and 0s, we can conditionally synthesize it by + ! using value of broadcasted borrow and the borrow bit itself. + ! To minimize dependency chain we first broadcast and then + ! extract the bit by negating (follow $bi). + + addcc @acc[0],$carry,@acc[0] ! add modulus or zero + addccc @acc[1],$carry,@acc[1] + neg $carry,$bi + st @acc[0],[$rp] + addccc @acc[2],$carry,@acc[2] + st @acc[1],[$rp+4] + addccc @acc[3],0,@acc[3] + st @acc[2],[$rp+8] + addccc @acc[4],0,@acc[4] + st @acc[3],[$rp+12] + addccc @acc[5],0,@acc[5] + st @acc[4],[$rp+16] + addccc @acc[6],$bi,@acc[6] + st @acc[5],[$rp+20] + addc @acc[7],$carry,@acc[7] + st @acc[6],[$rp+24] + retl + st @acc[7],[$rp+28] +.type __ecp_nistz256_mul_mont,#function +.size __ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont + +! void ecp_nistz256_add(BN_ULONG %i0[8],const BN_ULONG %i1[8], +! const BN_ULONG %i2[8]); +.globl ecp_nistz256_add +.align 32 +ecp_nistz256_add: + save %sp,-STACK_FRAME,%sp + ld [$ap],@acc[0] + ld [$ap+4],@acc[1] + ld [$ap+8],@acc[2] + ld [$ap+12],@acc[3] + ld [$ap+16],@acc[4] + ld [$ap+20],@acc[5] + ld [$ap+24],@acc[6] + call __ecp_nistz256_add + ld [$ap+28],@acc[7] + ret + restore +.type ecp_nistz256_add,#function +.size ecp_nistz256_add,.-ecp_nistz256_add + +.align 32 +__ecp_nistz256_add: + ld [$bp+0],$t0 ! b[0] + ld [$bp+4],$t1 + ld [$bp+8],$t2 + ld [$bp+12],$t3 + addcc @acc[0],$t0,@acc[0] + ld [$bp+16],$t4 + ld [$bp+20],$t5 + addccc @acc[1],$t1,@acc[1] + ld [$bp+24],$t6 + ld [$bp+28],$t7 + addccc @acc[2],$t2,@acc[2] + addccc @acc[3],$t3,@acc[3] + addccc @acc[4],$t4,@acc[4] + addccc @acc[5],$t5,@acc[5] + addccc @acc[6],$t6,@acc[6] + addccc @acc[7],$t7,@acc[7] + addc %g0,%g0,$carry + +.Lreduce_by_sub: + + ! if a+b >= modulus, subtract modulus. + ! + ! But since comparison implies subtraction, we subtract + ! modulus and then add it back if subraction borrowed. + + subcc @acc[0],-1,@acc[0] + subccc @acc[1],-1,@acc[1] + subccc @acc[2],-1,@acc[2] + subccc @acc[3], 0,@acc[3] + subccc @acc[4], 0,@acc[4] + subccc @acc[5], 0,@acc[5] + subccc @acc[6], 1,@acc[6] + subccc @acc[7],-1,@acc[7] + subc $carry,0,$carry + + ! Note that because mod has special form, i.e. consists of + ! 0xffffffff, 1 and 0s, we can conditionally synthesize it by + ! using value of borrow and its negative. + + addcc @acc[0],$carry,@acc[0] ! add synthesized modulus + addccc @acc[1],$carry,@acc[1] + neg $carry,$bi + st @acc[0],[$rp] + addccc @acc[2],$carry,@acc[2] + st @acc[1],[$rp+4] + addccc @acc[3],0,@acc[3] + st @acc[2],[$rp+8] + addccc @acc[4],0,@acc[4] + st @acc[3],[$rp+12] + addccc @acc[5],0,@acc[5] + st @acc[4],[$rp+16] + addccc @acc[6],$bi,@acc[6] + st @acc[5],[$rp+20] + addc @acc[7],$carry,@acc[7] + st @acc[6],[$rp+24] + retl + st @acc[7],[$rp+28] +.type __ecp_nistz256_add,#function +.size __ecp_nistz256_add,.-__ecp_nistz256_add + +! void ecp_nistz256_mul_by_2(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_mul_by_2 +.align 32 +ecp_nistz256_mul_by_2: + save %sp,-STACK_FRAME,%sp + ld [$ap],@acc[0] + ld [$ap+4],@acc[1] + ld [$ap+8],@acc[2] + ld [$ap+12],@acc[3] + ld [$ap+16],@acc[4] + ld [$ap+20],@acc[5] + ld [$ap+24],@acc[6] + call __ecp_nistz256_mul_by_2 + ld [$ap+28],@acc[7] + ret + restore +.type ecp_nistz256_mul_by_2,#function +.size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2 + +.align 32 +__ecp_nistz256_mul_by_2: + addcc @acc[0],@acc[0],@acc[0] ! a+a=2*a + addccc @acc[1],@acc[1],@acc[1] + addccc @acc[2],@acc[2],@acc[2] + addccc @acc[3],@acc[3],@acc[3] + addccc @acc[4],@acc[4],@acc[4] + addccc @acc[5],@acc[5],@acc[5] + addccc @acc[6],@acc[6],@acc[6] + addccc @acc[7],@acc[7],@acc[7] + b .Lreduce_by_sub + addc %g0,%g0,$carry +.type __ecp_nistz256_mul_by_2,#function +.size __ecp_nistz256_mul_by_2,.-__ecp_nistz256_mul_by_2 + +! void ecp_nistz256_mul_by_3(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_mul_by_3 +.align 32 +ecp_nistz256_mul_by_3: + save %sp,-STACK_FRAME,%sp + ld [$ap],@acc[0] + ld [$ap+4],@acc[1] + ld [$ap+8],@acc[2] + ld [$ap+12],@acc[3] + ld [$ap+16],@acc[4] + ld [$ap+20],@acc[5] + ld [$ap+24],@acc[6] + call __ecp_nistz256_mul_by_3 + ld [$ap+28],@acc[7] + ret + restore +.type ecp_nistz256_mul_by_3,#function +.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3 + +.align 32 +__ecp_nistz256_mul_by_3: + addcc @acc[0],@acc[0],$t0 ! a+a=2*a + addccc @acc[1],@acc[1],$t1 + addccc @acc[2],@acc[2],$t2 + addccc @acc[3],@acc[3],$t3 + addccc @acc[4],@acc[4],$t4 + addccc @acc[5],@acc[5],$t5 + addccc @acc[6],@acc[6],$t6 + addccc @acc[7],@acc[7],$t7 + addc %g0,%g0,$carry + + subcc $t0,-1,$t0 ! .Lreduce_by_sub but without stores + subccc $t1,-1,$t1 + subccc $t2,-1,$t2 + subccc $t3, 0,$t3 + subccc $t4, 0,$t4 + subccc $t5, 0,$t5 + subccc $t6, 1,$t6 + subccc $t7,-1,$t7 + subc $carry,0,$carry + + addcc $t0,$carry,$t0 ! add synthesized modulus + addccc $t1,$carry,$t1 + neg $carry,$bi + addccc $t2,$carry,$t2 + addccc $t3,0,$t3 + addccc $t4,0,$t4 + addccc $t5,0,$t5 + addccc $t6,$bi,$t6 + addc $t7,$carry,$t7 + + addcc $t0,@acc[0],@acc[0] ! 2*a+a=3*a + addccc $t1,@acc[1],@acc[1] + addccc $t2,@acc[2],@acc[2] + addccc $t3,@acc[3],@acc[3] + addccc $t4,@acc[4],@acc[4] + addccc $t5,@acc[5],@acc[5] + addccc $t6,@acc[6],@acc[6] + addccc $t7,@acc[7],@acc[7] + b .Lreduce_by_sub + addc %g0,%g0,$carry +.type __ecp_nistz256_mul_by_3,#function +.size __ecp_nistz256_mul_by_3,.-__ecp_nistz256_mul_by_3 + +! void ecp_nistz256_sub(BN_ULONG %i0[8],const BN_ULONG %i1[8], +! const BN_ULONG %i2[8]); +.globl ecp_nistz256_sub +.align 32 +ecp_nistz256_sub: + save %sp,-STACK_FRAME,%sp + ld [$ap],@acc[0] + ld [$ap+4],@acc[1] + ld [$ap+8],@acc[2] + ld [$ap+12],@acc[3] + ld [$ap+16],@acc[4] + ld [$ap+20],@acc[5] + ld [$ap+24],@acc[6] + call __ecp_nistz256_sub_from + ld [$ap+28],@acc[7] + ret + restore +.type ecp_nistz256_sub,#function +.size ecp_nistz256_sub,.-ecp_nistz256_sub + +! void ecp_nistz256_neg(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_neg +.align 32 +ecp_nistz256_neg: + save %sp,-STACK_FRAME,%sp + mov $ap,$bp + mov 0,@acc[0] + mov 0,@acc[1] + mov 0,@acc[2] + mov 0,@acc[3] + mov 0,@acc[4] + mov 0,@acc[5] + mov 0,@acc[6] + call __ecp_nistz256_sub_from + mov 0,@acc[7] + ret + restore +.type ecp_nistz256_neg,#function +.size ecp_nistz256_neg,.-ecp_nistz256_neg + +.align 32 +__ecp_nistz256_sub_from: + ld [$bp+0],$t0 ! b[0] + ld [$bp+4],$t1 + ld [$bp+8],$t2 + ld [$bp+12],$t3 + subcc @acc[0],$t0,@acc[0] + ld [$bp+16],$t4 + ld [$bp+20],$t5 + subccc @acc[1],$t1,@acc[1] + subccc @acc[2],$t2,@acc[2] + ld [$bp+24],$t6 + ld [$bp+28],$t7 + subccc @acc[3],$t3,@acc[3] + subccc @acc[4],$t4,@acc[4] + subccc @acc[5],$t5,@acc[5] + subccc @acc[6],$t6,@acc[6] + subccc @acc[7],$t7,@acc[7] + subc %g0,%g0,$carry ! broadcast borrow bit + +.Lreduce_by_add: + + ! if a-b borrows, add modulus. + ! + ! Note that because mod has special form, i.e. consists of + ! 0xffffffff, 1 and 0s, we can conditionally synthesize it by + ! using value of broadcasted borrow and the borrow bit itself. + ! To minimize dependency chain we first broadcast and then + ! extract the bit by negating (follow $bi). + + addcc @acc[0],$carry,@acc[0] ! add synthesized modulus + addccc @acc[1],$carry,@acc[1] + neg $carry,$bi + st @acc[0],[$rp] + addccc @acc[2],$carry,@acc[2] + st @acc[1],[$rp+4] + addccc @acc[3],0,@acc[3] + st @acc[2],[$rp+8] + addccc @acc[4],0,@acc[4] + st @acc[3],[$rp+12] + addccc @acc[5],0,@acc[5] + st @acc[4],[$rp+16] + addccc @acc[6],$bi,@acc[6] + st @acc[5],[$rp+20] + addc @acc[7],$carry,@acc[7] + st @acc[6],[$rp+24] + retl + st @acc[7],[$rp+28] +.type __ecp_nistz256_sub_from,#function +.size __ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from + +.align 32 +__ecp_nistz256_sub_morf: + ld [$bp+0],$t0 ! b[0] + ld [$bp+4],$t1 + ld [$bp+8],$t2 + ld [$bp+12],$t3 + subcc $t0,@acc[0],@acc[0] + ld [$bp+16],$t4 + ld [$bp+20],$t5 + subccc $t1,@acc[1],@acc[1] + subccc $t2,@acc[2],@acc[2] + ld [$bp+24],$t6 + ld [$bp+28],$t7 + subccc $t3,@acc[3],@acc[3] + subccc $t4,@acc[4],@acc[4] + subccc $t5,@acc[5],@acc[5] + subccc $t6,@acc[6],@acc[6] + subccc $t7,@acc[7],@acc[7] + b .Lreduce_by_add + subc %g0,%g0,$carry ! broadcast borrow bit +.type __ecp_nistz256_sub_morf,#function +.size __ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf + +! void ecp_nistz256_div_by_2(BN_ULONG %i0[8],const BN_ULONG %i1[8]); +.globl ecp_nistz256_div_by_2 +.align 32 +ecp_nistz256_div_by_2: + save %sp,-STACK_FRAME,%sp + ld [$ap],@acc[0] + ld [$ap+4],@acc[1] + ld [$ap+8],@acc[2] + ld [$ap+12],@acc[3] + ld [$ap+16],@acc[4] + ld [$ap+20],@acc[5] + ld [$ap+24],@acc[6] + call __ecp_nistz256_div_by_2 + ld [$ap+28],@acc[7] + ret + restore +.type ecp_nistz256_div_by_2,#function +.size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2 + +.align 32 +__ecp_nistz256_div_by_2: + ! ret = (a is odd ? a+mod : a) >> 1 + + and @acc[0],1,$bi + neg $bi,$carry + addcc @acc[0],$carry,@acc[0] + addccc @acc[1],$carry,@acc[1] + addccc @acc[2],$carry,@acc[2] + addccc @acc[3],0,@acc[3] + addccc @acc[4],0,@acc[4] + addccc @acc[5],0,@acc[5] + addccc @acc[6],$bi,@acc[6] + addccc @acc[7],$carry,@acc[7] + addc %g0,%g0,$carry + + ! ret >>= 1 + + srl @acc[0],1,@acc[0] + sll @acc[1],31,$t0 + srl @acc[1],1,@acc[1] + or @acc[0],$t0,@acc[0] + sll @acc[2],31,$t1 + srl @acc[2],1,@acc[2] + or @acc[1],$t1,@acc[1] + sll @acc[3],31,$t2 + st @acc[0],[$rp] + srl @acc[3],1,@acc[3] + or @acc[2],$t2,@acc[2] + sll @acc[4],31,$t3 + st @acc[1],[$rp+4] + srl @acc[4],1,@acc[4] + or @acc[3],$t3,@acc[3] + sll @acc[5],31,$t4 + st @acc[2],[$rp+8] + srl @acc[5],1,@acc[5] + or @acc[4],$t4,@acc[4] + sll @acc[6],31,$t5 + st @acc[3],[$rp+12] + srl @acc[6],1,@acc[6] + or @acc[5],$t5,@acc[5] + sll @acc[7],31,$t6 + st @acc[4],[$rp+16] + srl @acc[7],1,@acc[7] + or @acc[6],$t6,@acc[6] + sll $carry,31,$t7 + st @acc[5],[$rp+20] + or @acc[7],$t7,@acc[7] + st @acc[6],[$rp+24] + retl + st @acc[7],[$rp+28] +.type __ecp_nistz256_div_by_2,#function +.size __ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2 +___ + +######################################################################## +# following subroutines are "literal" implementation of those found in +# ecp_nistz256.c +# +######################################################################## +# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp); +# +{ +my ($S,$M,$Zsqr,$tmp0)=map(32*$_,(0..3)); +# above map() describes stack layout with 4 temporary +# 256-bit vectors on top. + +$code.=<<___; +#ifdef __PIC__ +SPARC_PIC_THUNK(%g1) +#endif + +.globl ecp_nistz256_point_double +.align 32 +ecp_nistz256_point_double: + SPARC_LOAD_ADDRESS_LEAF(OPENSSL_sparcv9cap_P,%g1,%g5) + ld [%g1],%g1 ! OPENSSL_sparcv9cap_P[0] + and %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK),%g1 + cmp %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK) + be ecp_nistz256_point_double_vis3 + nop + + save %sp,-STACK_FRAME-32*4,%sp + + mov $rp,$rp_real + mov $ap,$ap_real + +.Lpoint_double_shortcut: + ld [$ap+32],@acc[0] + ld [$ap+32+4],@acc[1] + ld [$ap+32+8],@acc[2] + ld [$ap+32+12],@acc[3] + ld [$ap+32+16],@acc[4] + ld [$ap+32+20],@acc[5] + ld [$ap+32+24],@acc[6] + ld [$ap+32+28],@acc[7] + call __ecp_nistz256_mul_by_2 ! p256_mul_by_2(S, in_y); + add %sp,LOCALS+$S,$rp + + add $ap_real,64,$bp + add $ap_real,64,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Zsqr, in_z); + add %sp,LOCALS+$Zsqr,$rp + + add $ap_real,0,$bp + call __ecp_nistz256_add ! p256_add(M, Zsqr, in_x); + add %sp,LOCALS+$M,$rp + + add %sp,LOCALS+$S,$bp + add %sp,LOCALS+$S,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(S, S); + add %sp,LOCALS+$S,$rp + + ld [$ap_real],@acc[0] + add %sp,LOCALS+$Zsqr,$bp + ld [$ap_real+4],@acc[1] + ld [$ap_real+8],@acc[2] + ld [$ap_real+12],@acc[3] + ld [$ap_real+16],@acc[4] + ld [$ap_real+20],@acc[5] + ld [$ap_real+24],@acc[6] + ld [$ap_real+28],@acc[7] + call __ecp_nistz256_sub_from ! p256_sub(Zsqr, in_x, Zsqr); + add %sp,LOCALS+$Zsqr,$rp + + add $ap_real,32,$bp + add $ap_real,64,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(tmp0, in_z, in_y); + add %sp,LOCALS+$tmp0,$rp + + call __ecp_nistz256_mul_by_2 ! p256_mul_by_2(res_z, tmp0); + add $rp_real,64,$rp + + add %sp,LOCALS+$Zsqr,$bp + add %sp,LOCALS+$M,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(M, M, Zsqr); + add %sp,LOCALS+$M,$rp + + call __ecp_nistz256_mul_by_3 ! p256_mul_by_3(M, M); + add %sp,LOCALS+$M,$rp + + add %sp,LOCALS+$S,$bp + add %sp,LOCALS+$S,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(tmp0, S); + add %sp,LOCALS+$tmp0,$rp + + call __ecp_nistz256_div_by_2 ! p256_div_by_2(res_y, tmp0); + add $rp_real,32,$rp + + add $ap_real,0,$bp + add %sp,LOCALS+$S,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S, S, in_x); + add %sp,LOCALS+$S,$rp + + call __ecp_nistz256_mul_by_2 ! p256_mul_by_2(tmp0, S); + add %sp,LOCALS+$tmp0,$rp + + add %sp,LOCALS+$M,$bp + add %sp,LOCALS+$M,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(res_x, M); + add $rp_real,0,$rp + + add %sp,LOCALS+$tmp0,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_x, res_x, tmp0); + add $rp_real,0,$rp + + add %sp,LOCALS+$S,$bp + call __ecp_nistz256_sub_morf ! p256_sub(S, S, res_x); + add %sp,LOCALS+$S,$rp + + add %sp,LOCALS+$M,$bp + add %sp,LOCALS+$S,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S, S, M); + add %sp,LOCALS+$S,$rp + + add $rp_real,32,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_y, S, res_y); + add $rp_real,32,$rp + + ret + restore +.type ecp_nistz256_point_double,#function +.size ecp_nistz256_point_double,.-ecp_nistz256_point_double +___ +} + +######################################################################## +# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT *in2); +{ +my ($res_x,$res_y,$res_z, + $H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2)=map(32*$_,(0..11)); +my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); + +# above map() describes stack layout with 12 temporary +# 256-bit vectors on top. Then we reserve some space for +# !in1infty, !in2infty, result of check for zero and return pointer. + +my $bp_real=$rp_real; + +$code.=<<___; +.globl ecp_nistz256_point_add +.align 32 +ecp_nistz256_point_add: + SPARC_LOAD_ADDRESS_LEAF(OPENSSL_sparcv9cap_P,%g1,%g5) + ld [%g1],%g1 ! OPENSSL_sparcv9cap_P[0] + and %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK),%g1 + cmp %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK) + be ecp_nistz256_point_add_vis3 + nop + + save %sp,-STACK_FRAME-32*12-32,%sp + + stx $rp,[%fp+STACK_BIAS-8] ! off-load $rp + mov $ap,$ap_real + mov $bp,$bp_real + + ld [$bp+64],$t0 ! in2_z + ld [$bp+64+4],$t1 + ld [$bp+64+8],$t2 + ld [$bp+64+12],$t3 + ld [$bp+64+16],$t4 + ld [$bp+64+20],$t5 + ld [$bp+64+24],$t6 + ld [$bp+64+28],$t7 + or $t1,$t0,$t0 + or $t3,$t2,$t2 + or $t5,$t4,$t4 + or $t7,$t6,$t6 + or $t2,$t0,$t0 + or $t6,$t4,$t4 + or $t4,$t0,$t0 ! !in2infty + movrnz $t0,-1,$t0 + st $t0,[%fp+STACK_BIAS-12] + + ld [$ap+64],$t0 ! in1_z + ld [$ap+64+4],$t1 + ld [$ap+64+8],$t2 + ld [$ap+64+12],$t3 + ld [$ap+64+16],$t4 + ld [$ap+64+20],$t5 + ld [$ap+64+24],$t6 + ld [$ap+64+28],$t7 + or $t1,$t0,$t0 + or $t3,$t2,$t2 + or $t5,$t4,$t4 + or $t7,$t6,$t6 + or $t2,$t0,$t0 + or $t6,$t4,$t4 + or $t4,$t0,$t0 ! !in1infty + movrnz $t0,-1,$t0 + st $t0,[%fp+STACK_BIAS-16] + + add $bp_real,64,$bp + add $bp_real,64,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Z2sqr, in2_z); + add %sp,LOCALS+$Z2sqr,$rp + + add $ap_real,64,$bp + add $ap_real,64,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Z1sqr, in1_z); + add %sp,LOCALS+$Z1sqr,$rp + + add $bp_real,64,$bp + add %sp,LOCALS+$Z2sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S1, Z2sqr, in2_z); + add %sp,LOCALS+$S1,$rp + + add $ap_real,64,$bp + add %sp,LOCALS+$Z1sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, Z1sqr, in1_z); + add %sp,LOCALS+$S2,$rp + + add $ap_real,32,$bp + add %sp,LOCALS+$S1,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S1, S1, in1_y); + add %sp,LOCALS+$S1,$rp + + add $bp_real,32,$bp + add %sp,LOCALS+$S2,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, S2, in2_y); + add %sp,LOCALS+$S2,$rp + + add %sp,LOCALS+$S1,$bp + call __ecp_nistz256_sub_from ! p256_sub(R, S2, S1); + add %sp,LOCALS+$R,$rp + + or @acc[1],@acc[0],@acc[0] ! see if result is zero + or @acc[3],@acc[2],@acc[2] + or @acc[5],@acc[4],@acc[4] + or @acc[7],@acc[6],@acc[6] + or @acc[2],@acc[0],@acc[0] + or @acc[6],@acc[4],@acc[4] + or @acc[4],@acc[0],@acc[0] + st @acc[0],[%fp+STACK_BIAS-20] + + add $ap_real,0,$bp + add %sp,LOCALS+$Z2sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(U1, in1_x, Z2sqr); + add %sp,LOCALS+$U1,$rp + + add $bp_real,0,$bp + add %sp,LOCALS+$Z1sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(U2, in2_x, Z1sqr); + add %sp,LOCALS+$U2,$rp + + add %sp,LOCALS+$U1,$bp + call __ecp_nistz256_sub_from ! p256_sub(H, U2, U1); + add %sp,LOCALS+$H,$rp + + or @acc[1],@acc[0],@acc[0] ! see if result is zero + or @acc[3],@acc[2],@acc[2] + or @acc[5],@acc[4],@acc[4] + or @acc[7],@acc[6],@acc[6] + or @acc[2],@acc[0],@acc[0] + or @acc[6],@acc[4],@acc[4] + orcc @acc[4],@acc[0],@acc[0] + + bne,pt %icc,.Ladd_proceed ! is_equal(U1,U2)? + nop + + ld [%fp+STACK_BIAS-12],$t0 + ld [%fp+STACK_BIAS-16],$t1 + ld [%fp+STACK_BIAS-20],$t2 + andcc $t0,$t1,%g0 + be,pt %icc,.Ladd_proceed ! (in1infty || in2infty)? + nop + andcc $t2,$t2,%g0 + be,pt %icc,.Ladd_double ! is_equal(S1,S2)? + nop + + ldx [%fp+STACK_BIAS-8],$rp + st %g0,[$rp] + st %g0,[$rp+4] + st %g0,[$rp+8] + st %g0,[$rp+12] + st %g0,[$rp+16] + st %g0,[$rp+20] + st %g0,[$rp+24] + st %g0,[$rp+28] + st %g0,[$rp+32] + st %g0,[$rp+32+4] + st %g0,[$rp+32+8] + st %g0,[$rp+32+12] + st %g0,[$rp+32+16] + st %g0,[$rp+32+20] + st %g0,[$rp+32+24] + st %g0,[$rp+32+28] + st %g0,[$rp+64] + st %g0,[$rp+64+4] + st %g0,[$rp+64+8] + st %g0,[$rp+64+12] + st %g0,[$rp+64+16] + st %g0,[$rp+64+20] + st %g0,[$rp+64+24] + st %g0,[$rp+64+28] + b .Ladd_done + nop + +.align 16 +.Ladd_double: + ldx [%fp+STACK_BIAS-8],$rp_real + mov $ap_real,$ap + b .Lpoint_double_shortcut + add %sp,32*(12-4)+32,%sp ! difference in frame sizes + +.align 16 +.Ladd_proceed: + add %sp,LOCALS+$R,$bp + add %sp,LOCALS+$R,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Rsqr, R); + add %sp,LOCALS+$Rsqr,$rp + + add $ap_real,64,$bp + add %sp,LOCALS+$H,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(res_z, H, in1_z); + add %sp,LOCALS+$res_z,$rp + + add %sp,LOCALS+$H,$bp + add %sp,LOCALS+$H,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Hsqr, H); + add %sp,LOCALS+$Hsqr,$rp + + add $bp_real,64,$bp + add %sp,LOCALS+$res_z,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(res_z, res_z, in2_z); + add %sp,LOCALS+$res_z,$rp + + add %sp,LOCALS+$H,$bp + add %sp,LOCALS+$Hsqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(Hcub, Hsqr, H); + add %sp,LOCALS+$Hcub,$rp + + add %sp,LOCALS+$U1,$bp + add %sp,LOCALS+$Hsqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(U2, U1, Hsqr); + add %sp,LOCALS+$U2,$rp + + call __ecp_nistz256_mul_by_2 ! p256_mul_by_2(Hsqr, U2); + add %sp,LOCALS+$Hsqr,$rp + + add %sp,LOCALS+$Rsqr,$bp + call __ecp_nistz256_sub_morf ! p256_sub(res_x, Rsqr, Hsqr); + add %sp,LOCALS+$res_x,$rp + + add %sp,LOCALS+$Hcub,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_x, res_x, Hcub); + add %sp,LOCALS+$res_x,$rp + + add %sp,LOCALS+$U2,$bp + call __ecp_nistz256_sub_morf ! p256_sub(res_y, U2, res_x); + add %sp,LOCALS+$res_y,$rp + + add %sp,LOCALS+$Hcub,$bp + add %sp,LOCALS+$S1,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, S1, Hcub); + add %sp,LOCALS+$S2,$rp + + add %sp,LOCALS+$R,$bp + add %sp,LOCALS+$res_y,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(res_y, res_y, R); + add %sp,LOCALS+$res_y,$rp + + add %sp,LOCALS+$S2,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_y, res_y, S2); + add %sp,LOCALS+$res_y,$rp + + ld [%fp+STACK_BIAS-16],$t1 ! !in1infty + ld [%fp+STACK_BIAS-12],$t2 ! !in2infty + ldx [%fp+STACK_BIAS-8],$rp +___ +for($i=0;$i<96;$i+=8) { # conditional moves +$code.=<<___; + ld [%sp+LOCALS+$i],@acc[0] ! res + ld [%sp+LOCALS+$i+4],@acc[1] + ld [$bp_real+$i],@acc[2] ! in2 + ld [$bp_real+$i+4],@acc[3] + ld [$ap_real+$i],@acc[4] ! in1 + ld [$ap_real+$i+4],@acc[5] + movrz $t1,@acc[2],@acc[0] + movrz $t1,@acc[3],@acc[1] + movrz $t2,@acc[4],@acc[0] + movrz $t2,@acc[5],@acc[1] + st @acc[0],[$rp+$i] + st @acc[1],[$rp+$i+4] +___ +} +$code.=<<___; +.Ladd_done: + ret + restore +.type ecp_nistz256_point_add,#function +.size ecp_nistz256_point_add,.-ecp_nistz256_point_add +___ +} + +######################################################################## +# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT_AFFINE *in2); +{ +my ($res_x,$res_y,$res_z, + $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..9)); +my $Z1sqr = $S2; +# above map() describes stack layout with 10 temporary +# 256-bit vectors on top. Then we reserve some space for +# !in1infty, !in2infty, result of check for zero and return pointer. + +my @ONE_mont=(1,0,0,-1,-1,-1,-2,0); +my $bp_real=$rp_real; + +$code.=<<___; +.globl ecp_nistz256_point_add_affine +.align 32 +ecp_nistz256_point_add_affine: + SPARC_LOAD_ADDRESS_LEAF(OPENSSL_sparcv9cap_P,%g1,%g5) + ld [%g1],%g1 ! OPENSSL_sparcv9cap_P[0] + and %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK),%g1 + cmp %g1,(SPARCV9_VIS3|SPARCV9_64BIT_STACK) + be ecp_nistz256_point_add_affine_vis3 + nop + + save %sp,-STACK_FRAME-32*10-32,%sp + + stx $rp,[%fp+STACK_BIAS-8] ! off-load $rp + mov $ap,$ap_real + mov $bp,$bp_real + + ld [$ap+64],$t0 ! in1_z + ld [$ap+64+4],$t1 + ld [$ap+64+8],$t2 + ld [$ap+64+12],$t3 + ld [$ap+64+16],$t4 + ld [$ap+64+20],$t5 + ld [$ap+64+24],$t6 + ld [$ap+64+28],$t7 + or $t1,$t0,$t0 + or $t3,$t2,$t2 + or $t5,$t4,$t4 + or $t7,$t6,$t6 + or $t2,$t0,$t0 + or $t6,$t4,$t4 + or $t4,$t0,$t0 ! !in1infty + movrnz $t0,-1,$t0 + st $t0,[%fp+STACK_BIAS-16] + + ld [$bp],@acc[0] ! in2_x + ld [$bp+4],@acc[1] + ld [$bp+8],@acc[2] + ld [$bp+12],@acc[3] + ld [$bp+16],@acc[4] + ld [$bp+20],@acc[5] + ld [$bp+24],@acc[6] + ld [$bp+28],@acc[7] + ld [$bp+32],$t0 ! in2_y + ld [$bp+32+4],$t1 + ld [$bp+32+8],$t2 + ld [$bp+32+12],$t3 + ld [$bp+32+16],$t4 + ld [$bp+32+20],$t5 + ld [$bp+32+24],$t6 + ld [$bp+32+28],$t7 + or @acc[1],@acc[0],@acc[0] + or @acc[3],@acc[2],@acc[2] + or @acc[5],@acc[4],@acc[4] + or @acc[7],@acc[6],@acc[6] + or @acc[2],@acc[0],@acc[0] + or @acc[6],@acc[4],@acc[4] + or @acc[4],@acc[0],@acc[0] + or $t1,$t0,$t0 + or $t3,$t2,$t2 + or $t5,$t4,$t4 + or $t7,$t6,$t6 + or $t2,$t0,$t0 + or $t6,$t4,$t4 + or $t4,$t0,$t0 + or @acc[0],$t0,$t0 ! !in2infty + movrnz $t0,-1,$t0 + st $t0,[%fp+STACK_BIAS-12] + + add $ap_real,64,$bp + add $ap_real,64,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Z1sqr, in1_z); + add %sp,LOCALS+$Z1sqr,$rp + + add $bp_real,0,$bp + add %sp,LOCALS+$Z1sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(U2, Z1sqr, in2_x); + add %sp,LOCALS+$U2,$rp + + add $ap_real,0,$bp + call __ecp_nistz256_sub_from ! p256_sub(H, U2, in1_x); + add %sp,LOCALS+$H,$rp + + add $ap_real,64,$bp + add %sp,LOCALS+$Z1sqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, Z1sqr, in1_z); + add %sp,LOCALS+$S2,$rp + + add $ap_real,64,$bp + add %sp,LOCALS+$H,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(res_z, H, in1_z); + add %sp,LOCALS+$res_z,$rp + + add $bp_real,32,$bp + add %sp,LOCALS+$S2,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, S2, in2_y); + add %sp,LOCALS+$S2,$rp + + add $ap_real,32,$bp + call __ecp_nistz256_sub_from ! p256_sub(R, S2, in1_y); + add %sp,LOCALS+$R,$rp + + add %sp,LOCALS+$H,$bp + add %sp,LOCALS+$H,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Hsqr, H); + add %sp,LOCALS+$Hsqr,$rp + + add %sp,LOCALS+$R,$bp + add %sp,LOCALS+$R,$ap + call __ecp_nistz256_mul_mont ! p256_sqr_mont(Rsqr, R); + add %sp,LOCALS+$Rsqr,$rp + + add %sp,LOCALS+$H,$bp + add %sp,LOCALS+$Hsqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(Hcub, Hsqr, H); + add %sp,LOCALS+$Hcub,$rp + + add $ap_real,0,$bp + add %sp,LOCALS+$Hsqr,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(U2, in1_x, Hsqr); + add %sp,LOCALS+$U2,$rp + + call __ecp_nistz256_mul_by_2 ! p256_mul_by_2(Hsqr, U2); + add %sp,LOCALS+$Hsqr,$rp + + add %sp,LOCALS+$Rsqr,$bp + call __ecp_nistz256_sub_morf ! p256_sub(res_x, Rsqr, Hsqr); + add %sp,LOCALS+$res_x,$rp + + add %sp,LOCALS+$Hcub,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_x, res_x, Hcub); + add %sp,LOCALS+$res_x,$rp + + add %sp,LOCALS+$U2,$bp + call __ecp_nistz256_sub_morf ! p256_sub(res_y, U2, res_x); + add %sp,LOCALS+$res_y,$rp + + add $ap_real,32,$bp + add %sp,LOCALS+$Hcub,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(S2, in1_y, Hcub); + add %sp,LOCALS+$S2,$rp + + add %sp,LOCALS+$R,$bp + add %sp,LOCALS+$res_y,$ap + call __ecp_nistz256_mul_mont ! p256_mul_mont(res_y, res_y, R); + add %sp,LOCALS+$res_y,$rp + + add %sp,LOCALS+$S2,$bp + call __ecp_nistz256_sub_from ! p256_sub(res_y, res_y, S2); + add %sp,LOCALS+$res_y,$rp + + ld [%fp+STACK_BIAS-16],$t1 ! !in1infty + ld [%fp+STACK_BIAS-12],$t2 ! !in2infty + ldx [%fp+STACK_BIAS-8],$rp +___ +for($i=0;$i<64;$i+=8) { # conditional moves +$code.=<<___; + ld [%sp+LOCALS+$i],@acc[0] ! res + ld [%sp+LOCALS+$i+4],@acc[1] + ld [$bp_real+$i],@acc[2] ! in2 + ld [$bp_real+$i+4],@acc[3] + ld [$ap_real+$i],@acc[4] ! in1 + ld [$ap_real+$i+4],@acc[5] + movrz $t1,@acc[2],@acc[0] + movrz $t1,@acc[3],@acc[1] + movrz $t2,@acc[4],@acc[0] + movrz $t2,@acc[5],@acc[1] + st @acc[0],[$rp+$i] + st @acc[1],[$rp+$i+4] +___ +} +for(;$i<96;$i+=8) { +my $j=($i-64)/4; +$code.=<<___; + ld [%sp+LOCALS+$i],@acc[0] ! res + ld [%sp+LOCALS+$i+4],@acc[1] + ld [$ap_real+$i],@acc[4] ! in1 + ld [$ap_real+$i+4],@acc[5] + movrz $t1,@ONE_mont[$j],@acc[0] + movrz $t1,@ONE_mont[$j+1],@acc[1] + movrz $t2,@acc[4],@acc[0] + movrz $t2,@acc[5],@acc[1] + st @acc[0],[$rp+$i] + st @acc[1],[$rp+$i+4] +___ +} +$code.=<<___; + ret + restore +.type ecp_nistz256_point_add_affine,#function +.size ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine +___ +} }}} +{{{ +my ($out,$inp,$index)=map("%i$_",(0..2)); +my $mask="%o0"; + +$code.=<<___; +! void ecp_nistz256_scatter_w5(void *%i0,const P256_POINT *%i1, +! int %i2); +.globl ecp_nistz256_scatter_w5 +.align 32 +ecp_nistz256_scatter_w5: + save %sp,-STACK_FRAME,%sp + + sll $index,2,$index + add $out,$index,$out + + ld [$inp],%l0 ! X + ld [$inp+4],%l1 + ld [$inp+8],%l2 + ld [$inp+12],%l3 + ld [$inp+16],%l4 + ld [$inp+20],%l5 + ld [$inp+24],%l6 + ld [$inp+28],%l7 + add $inp,32,$inp + st %l0,[$out+64*0-4] + st %l1,[$out+64*1-4] + st %l2,[$out+64*2-4] + st %l3,[$out+64*3-4] + st %l4,[$out+64*4-4] + st %l5,[$out+64*5-4] + st %l6,[$out+64*6-4] + st %l7,[$out+64*7-4] + add $out,64*8,$out + + ld [$inp],%l0 ! Y + ld [$inp+4],%l1 + ld [$inp+8],%l2 + ld [$inp+12],%l3 + ld [$inp+16],%l4 + ld [$inp+20],%l5 + ld [$inp+24],%l6 + ld [$inp+28],%l7 + add $inp,32,$inp + st %l0,[$out+64*0-4] + st %l1,[$out+64*1-4] + st %l2,[$out+64*2-4] + st %l3,[$out+64*3-4] + st %l4,[$out+64*4-4] + st %l5,[$out+64*5-4] + st %l6,[$out+64*6-4] + st %l7,[$out+64*7-4] + add $out,64*8,$out + + ld [$inp],%l0 ! Z + ld [$inp+4],%l1 + ld [$inp+8],%l2 + ld [$inp+12],%l3 + ld [$inp+16],%l4 + ld [$inp+20],%l5 + ld [$inp+24],%l6 + ld [$inp+28],%l7 + st %l0,[$out+64*0-4] + st %l1,[$out+64*1-4] + st %l2,[$out+64*2-4] + st %l3,[$out+64*3-4] + st %l4,[$out+64*4-4] + st %l5,[$out+64*5-4] + st %l6,[$out+64*6-4] + st %l7,[$out+64*7-4] + + ret + restore +.type ecp_nistz256_scatter_w5,#function +.size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5 + +! void ecp_nistz256_gather_w5(P256_POINT *%i0,const void *%i1, +! int %i2); +.globl ecp_nistz256_gather_w5 +.align 32 +ecp_nistz256_gather_w5: + save %sp,-STACK_FRAME,%sp + + neg $index,$mask + srax $mask,63,$mask + + add $index,$mask,$index + sll $index,2,$index + add $inp,$index,$inp + + ld [$inp+64*0],%l0 + ld [$inp+64*1],%l1 + ld [$inp+64*2],%l2 + ld [$inp+64*3],%l3 + ld [$inp+64*4],%l4 + ld [$inp+64*5],%l5 + ld [$inp+64*6],%l6 + ld [$inp+64*7],%l7 + add $inp,64*8,$inp + and %l0,$mask,%l0 + and %l1,$mask,%l1 + st %l0,[$out] ! X + and %l2,$mask,%l2 + st %l1,[$out+4] + and %l3,$mask,%l3 + st %l2,[$out+8] + and %l4,$mask,%l4 + st %l3,[$out+12] + and %l5,$mask,%l5 + st %l4,[$out+16] + and %l6,$mask,%l6 + st %l5,[$out+20] + and %l7,$mask,%l7 + st %l6,[$out+24] + st %l7,[$out+28] + add $out,32,$out + + ld [$inp+64*0],%l0 + ld [$inp+64*1],%l1 + ld [$inp+64*2],%l2 + ld [$inp+64*3],%l3 + ld [$inp+64*4],%l4 + ld [$inp+64*5],%l5 + ld [$inp+64*6],%l6 + ld [$inp+64*7],%l7 + add $inp,64*8,$inp + and %l0,$mask,%l0 + and %l1,$mask,%l1 + st %l0,[$out] ! Y + and %l2,$mask,%l2 + st %l1,[$out+4] + and %l3,$mask,%l3 + st %l2,[$out+8] + and %l4,$mask,%l4 + st %l3,[$out+12] + and %l5,$mask,%l5 + st %l4,[$out+16] + and %l6,$mask,%l6 + st %l5,[$out+20] + and %l7,$mask,%l7 + st %l6,[$out+24] + st %l7,[$out+28] + add $out,32,$out + + ld [$inp+64*0],%l0 + ld [$inp+64*1],%l1 + ld [$inp+64*2],%l2 + ld [$inp+64*3],%l3 + ld [$inp+64*4],%l4 + ld [$inp+64*5],%l5 + ld [$inp+64*6],%l6 + ld [$inp+64*7],%l7 + and %l0,$mask,%l0 + and %l1,$mask,%l1 + st %l0,[$out] ! Z + and %l2,$mask,%l2 + st %l1,[$out+4] + and %l3,$mask,%l3 + st %l2,[$out+8] + and %l4,$mask,%l4 + st %l3,[$out+12] + and %l5,$mask,%l5 + st %l4,[$out+16] + and %l6,$mask,%l6 + st %l5,[$out+20] + and %l7,$mask,%l7 + st %l6,[$out+24] + st %l7,[$out+28] + + ret + restore +.type ecp_nistz256_gather_w5,#function +.size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5 + +! void ecp_nistz256_scatter_w7(void *%i0,const P256_POINT_AFFINE *%i1, +! int %i2); +.globl ecp_nistz256_scatter_w7 +.align 32 +ecp_nistz256_scatter_w7: + save %sp,-STACK_FRAME,%sp + nop + add $out,$index,$out + mov 64/4,$index +.Loop_scatter_w7: + ld [$inp],%l0 + add $inp,4,$inp + subcc $index,1,$index + stb %l0,[$out+64*0-1] + srl %l0,8,%l1 + stb %l1,[$out+64*1-1] + srl %l0,16,%l2 + stb %l2,[$out+64*2-1] + srl %l0,24,%l3 + stb %l3,[$out+64*3-1] + bne .Loop_scatter_w7 + add $out,64*4,$out + + ret + restore +.type ecp_nistz256_scatter_w7,#function +.size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7 + +! void ecp_nistz256_gather_w7(P256_POINT_AFFINE *%i0,const void *%i1, +! int %i2); +.globl ecp_nistz256_gather_w7 +.align 32 +ecp_nistz256_gather_w7: + save %sp,-STACK_FRAME,%sp + + neg $index,$mask + srax $mask,63,$mask + + add $index,$mask,$index + add $inp,$index,$inp + mov 64/4,$index + +.Loop_gather_w7: + ldub [$inp+64*0],%l0 + prefetch [$inp+3840+64*0],1 + subcc $index,1,$index + ldub [$inp+64*1],%l1 + prefetch [$inp+3840+64*1],1 + ldub [$inp+64*2],%l2 + prefetch [$inp+3840+64*2],1 + ldub [$inp+64*3],%l3 + prefetch [$inp+3840+64*3],1 + add $inp,64*4,$inp + sll %l1,8,%l1 + sll %l2,16,%l2 + or %l0,%l1,%l0 + sll %l3,24,%l3 + or %l0,%l2,%l0 + or %l0,%l3,%l0 + and %l0,$mask,%l0 + st %l0,[$out] + bne .Loop_gather_w7 + add $out,4,$out + + ret + restore +.type ecp_nistz256_gather_w7,#function +.size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7 +___ +}}} +{{{ +######################################################################## +# Following subroutines are VIS3 counterparts of those above that +# implement ones found in ecp_nistz256.c. Key difference is that they +# use 128-bit muliplication and addition with 64-bit carry, and in order +# to do that they perform conversion from uin32_t[8] to uint64_t[4] upon +# entry and vice versa on return. +# +my ($rp,$ap,$bp)=map("%i$_",(0..2)); +my ($t0,$t1,$t2,$t3,$a0,$a1,$a2,$a3)=map("%l$_",(0..7)); +my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5)=map("%o$_",(0..5)); +my ($bi,$poly1,$poly3,$minus1)=(map("%i$_",(3..5)),"%g1"); +my ($rp_real,$ap_real)=("%g2","%g3"); +my ($acc6,$acc7)=($bp,$bi); # used in squaring + +$code.=<<___; +.align 32 +__ecp_nistz256_mul_by_2_vis3: + addcc $acc0,$acc0,$acc0 + addxccc $acc1,$acc1,$acc1 + addxccc $acc2,$acc2,$acc2 + addxccc $acc3,$acc3,$acc3 + b .Lreduce_by_sub_vis3 + addxc %g0,%g0,$acc4 ! did it carry? +.type __ecp_nistz256_mul_by_2_vis3,#function +.size __ecp_nistz256_mul_by_2_vis3,.-__ecp_nistz256_mul_by_2_vis3 + +.align 32 +__ecp_nistz256_add_vis3: + ldx [$bp+0],$t0 + ldx [$bp+8],$t1 + ldx [$bp+16],$t2 + ldx [$bp+24],$t3 + +__ecp_nistz256_add_noload_vis3: + + addcc $t0,$acc0,$acc0 + addxccc $t1,$acc1,$acc1 + addxccc $t2,$acc2,$acc2 + addxccc $t3,$acc3,$acc3 + addxc %g0,%g0,$acc4 ! did it carry? + +.Lreduce_by_sub_vis3: + + addcc $acc0,1,$t0 ! add -modulus, i.e. subtract + addxccc $acc1,$poly1,$t1 + addxccc $acc2,$minus1,$t2 + addxccc $acc3,$poly3,$t3 + addxc $acc4,$minus1,$acc4 + + movrz $acc4,$t0,$acc0 ! ret = borrow ? ret : ret-modulus + movrz $acc4,$t1,$acc1 + stx $acc0,[$rp] + movrz $acc4,$t2,$acc2 + stx $acc1,[$rp+8] + movrz $acc4,$t3,$acc3 + stx $acc2,[$rp+16] + retl + stx $acc3,[$rp+24] +.type __ecp_nistz256_add_vis3,#function +.size __ecp_nistz256_add_vis3,.-__ecp_nistz256_add_vis3 + +! Trouble with subtraction is that there is no subtraction with 64-bit +! borrow, only with 32-bit one. For this reason we "decompose" 64-bit +! $acc0-$acc3 to 32-bit values and pick b[4] in 32-bit pieces. But +! recall that SPARC is big-endian, which is why you'll observe that +! b[4] is accessed as 4-0-12-8-20-16-28-24. And prior reduction we +! "collect" result back to 64-bit $acc0-$acc3. +.align 32 +__ecp_nistz256_sub_from_vis3: + ld [$bp+4],$t0 + ld [$bp+0],$t1 + ld [$bp+12],$t2 + ld [$bp+8],$t3 + + srlx $acc0,32,$acc4 + not $poly1,$poly1 + srlx $acc1,32,$acc5 + subcc $acc0,$t0,$acc0 + ld [$bp+20],$t0 + subccc $acc4,$t1,$acc4 + ld [$bp+16],$t1 + subccc $acc1,$t2,$acc1 + ld [$bp+28],$t2 + and $acc0,$poly1,$acc0 + subccc $acc5,$t3,$acc5 + ld [$bp+24],$t3 + sllx $acc4,32,$acc4 + and $acc1,$poly1,$acc1 + sllx $acc5,32,$acc5 + or $acc0,$acc4,$acc0 + srlx $acc2,32,$acc4 + or $acc1,$acc5,$acc1 + srlx $acc3,32,$acc5 + subccc $acc2,$t0,$acc2 + subccc $acc4,$t1,$acc4 + subccc $acc3,$t2,$acc3 + and $acc2,$poly1,$acc2 + subccc $acc5,$t3,$acc5 + sllx $acc4,32,$acc4 + and $acc3,$poly1,$acc3 + sllx $acc5,32,$acc5 + or $acc2,$acc4,$acc2 + subc %g0,%g0,$acc4 ! did it borrow? + b .Lreduce_by_add_vis3 + or $acc3,$acc5,$acc3 +.type __ecp_nistz256_sub_from_vis3,#function +.size __ecp_nistz256_sub_from_vis3,.-__ecp_nistz256_sub_from_vis3 + +.align 32 +__ecp_nistz256_sub_morf_vis3: + ld [$bp+4],$t0 + ld [$bp+0],$t1 + ld [$bp+12],$t2 + ld [$bp+8],$t3 + + srlx $acc0,32,$acc4 + not $poly1,$poly1 + srlx $acc1,32,$acc5 + subcc $t0,$acc0,$acc0 + ld [$bp+20],$t0 + subccc $t1,$acc4,$acc4 + ld [$bp+16],$t1 + subccc $t2,$acc1,$acc1 + ld [$bp+28],$t2 + and $acc0,$poly1,$acc0 + subccc $t3,$acc5,$acc5 + ld [$bp+24],$t3 + sllx $acc4,32,$acc4 + and $acc1,$poly1,$acc1 + sllx $acc5,32,$acc5 + or $acc0,$acc4,$acc0 + srlx $acc2,32,$acc4 + or $acc1,$acc5,$acc1 + srlx $acc3,32,$acc5 + subccc $t0,$acc2,$acc2 + subccc $t1,$acc4,$acc4 + subccc $t2,$acc3,$acc3 + and $acc2,$poly1,$acc2 + subccc $t3,$acc5,$acc5 + sllx $acc4,32,$acc4 + and $acc3,$poly1,$acc3 + sllx $acc5,32,$acc5 + or $acc2,$acc4,$acc2 + subc %g0,%g0,$acc4 ! did it borrow? + or $acc3,$acc5,$acc3 + +.Lreduce_by_add_vis3: + + addcc $acc0,-1,$t0 ! add modulus + not $poly3,$t3 + addxccc $acc1,$poly1,$t1 + not $poly1,$poly1 ! restore $poly1 + addxccc $acc2,%g0,$t2 + addxc $acc3,$t3,$t3 + + movrnz $acc4,$t0,$acc0 ! if a-b borrowed, ret = ret+mod + movrnz $acc4,$t1,$acc1 + stx $acc0,[$rp] + movrnz $acc4,$t2,$acc2 + stx $acc1,[$rp+8] + movrnz $acc4,$t3,$acc3 + stx $acc2,[$rp+16] + retl + stx $acc3,[$rp+24] +.type __ecp_nistz256_sub_morf_vis3,#function +.size __ecp_nistz256_sub_morf_vis3,.-__ecp_nistz256_sub_morf_vis3 + +.align 32 +__ecp_nistz256_div_by_2_vis3: + ! ret = (a is odd ? a+mod : a) >> 1 + + not $poly1,$t1 + not $poly3,$t3 + and $acc0,1,$acc5 + addcc $acc0,-1,$t0 ! add modulus + addxccc $acc1,$t1,$t1 + addxccc $acc2,%g0,$t2 + addxccc $acc3,$t3,$t3 + addxc %g0,%g0,$acc4 ! carry bit + + movrnz $acc5,$t0,$acc0 + movrnz $acc5,$t1,$acc1 + movrnz $acc5,$t2,$acc2 + movrnz $acc5,$t3,$acc3 + movrz $acc5,%g0,$acc4 + + ! ret >>= 1 + + srlx $acc0,1,$acc0 + sllx $acc1,63,$t0 + srlx $acc1,1,$acc1 + or $acc0,$t0,$acc0 + sllx $acc2,63,$t1 + srlx $acc2,1,$acc2 + or $acc1,$t1,$acc1 + sllx $acc3,63,$t2 + stx $acc0,[$rp] + srlx $acc3,1,$acc3 + or $acc2,$t2,$acc2 + sllx $acc4,63,$t3 ! don't forget carry bit + stx $acc1,[$rp+8] + or $acc3,$t3,$acc3 + stx $acc2,[$rp+16] + retl + stx $acc3,[$rp+24] +.type __ecp_nistz256_div_by_2_vis3,#function +.size __ecp_nistz256_div_by_2_vis3,.-__ecp_nistz256_div_by_2_vis3 + +! compared to __ecp_nistz256_mul_mont it's almost 4x smaller and +! 4x faster [on T4]... +.align 32 +__ecp_nistz256_mul_mont_vis3: + mulx $a0,$bi,$acc0 + not $poly3,$poly3 ! 0xFFFFFFFF00000001 + umulxhi $a0,$bi,$t0 + mulx $a1,$bi,$acc1 + umulxhi $a1,$bi,$t1 + mulx $a2,$bi,$acc2 + umulxhi $a2,$bi,$t2 + mulx $a3,$bi,$acc3 + umulxhi $a3,$bi,$t3 + ldx [$bp+8],$bi ! b[1] + + addcc $acc1,$t0,$acc1 ! accumulate high parts of multiplication + sllx $acc0,32,$t0 + addxccc $acc2,$t1,$acc2 + srlx $acc0,32,$t1 + addxccc $acc3,$t2,$acc3 + addxc %g0,$t3,$acc4 + mov 0,$acc5 +___ +for($i=1;$i<4;$i++) { + # Reduction iteration is normally performed by accumulating + # result of multiplication of modulus by "magic" digit [and + # omitting least significant word, which is guaranteed to + # be 0], but thanks to special form of modulus and "magic" + # digit being equal to least significant word, it can be + # performed with additions and subtractions alone. Indeed: + # + # ffff0001.00000000.0000ffff.ffffffff + # * abcdefgh + # + xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh + # + # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we + # rewrite above as: + # + # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh + # + abcdefgh.abcdefgh.0000abcd.efgh0000.00000000 + # - 0000abcd.efgh0000.00000000.00000000.abcdefgh + # + # or marking redundant operations: + # + # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.-------- + # + abcdefgh.abcdefgh.0000abcd.efgh0000.-------- + # - 0000abcd.efgh0000.--------.--------.-------- + # ^^^^^^^^ but this word is calculated with umulxhi, because + # there is no subtract with 64-bit borrow:-( + +$code.=<<___; + sub $acc0,$t0,$t2 ! acc0*0xFFFFFFFF00000001, low part + umulxhi $acc0,$poly3,$t3 ! acc0*0xFFFFFFFF00000001, high part + addcc $acc1,$t0,$acc0 ! +=acc[0]<<96 and omit acc[0] + mulx $a0,$bi,$t0 + addxccc $acc2,$t1,$acc1 + mulx $a1,$bi,$t1 + addxccc $acc3,$t2,$acc2 ! +=acc[0]*0xFFFFFFFF00000001 + mulx $a2,$bi,$t2 + addxccc $acc4,$t3,$acc3 + mulx $a3,$bi,$t3 + addxc $acc5,%g0,$acc4 + + addcc $acc0,$t0,$acc0 ! accumulate low parts of multiplication + umulxhi $a0,$bi,$t0 + addxccc $acc1,$t1,$acc1 + umulxhi $a1,$bi,$t1 + addxccc $acc2,$t2,$acc2 + umulxhi $a2,$bi,$t2 + addxccc $acc3,$t3,$acc3 + umulxhi $a3,$bi,$t3 + addxc $acc4,%g0,$acc4 +___ +$code.=<<___ if ($i<3); + ldx [$bp+8*($i+1)],$bi ! bp[$i+1] +___ +$code.=<<___; + addcc $acc1,$t0,$acc1 ! accumulate high parts of multiplication + sllx $acc0,32,$t0 + addxccc $acc2,$t1,$acc2 + srlx $acc0,32,$t1 + addxccc $acc3,$t2,$acc3 + addxccc $acc4,$t3,$acc4 + addxc %g0,%g0,$acc5 +___ +} +$code.=<<___; + sub $acc0,$t0,$t2 ! acc0*0xFFFFFFFF00000001, low part + umulxhi $acc0,$poly3,$t3 ! acc0*0xFFFFFFFF00000001, high part + addcc $acc1,$t0,$acc0 ! +=acc[0]<<96 and omit acc[0] + addxccc $acc2,$t1,$acc1 + addxccc $acc3,$t2,$acc2 ! +=acc[0]*0xFFFFFFFF00000001 + addxccc $acc4,$t3,$acc3 + b .Lmul_final_vis3 ! see below + addxc $acc5,%g0,$acc4 +.type __ecp_nistz256_mul_mont_vis3,#function +.size __ecp_nistz256_mul_mont_vis3,.-__ecp_nistz256_mul_mont_vis3 + +! compared to above __ecp_nistz256_mul_mont_vis3 it's 21% less +! instructions, but only 14% faster [on T4]... +.align 32 +__ecp_nistz256_sqr_mont_vis3: + ! | | | | | |a1*a0| | + ! | | | | |a2*a0| | | + ! | |a3*a2|a3*a0| | | | + ! | | | |a2*a1| | | | + ! | | |a3*a1| | | | | + ! *| | | | | | | | 2| + ! +|a3*a3|a2*a2|a1*a1|a0*a0| + ! |--+--+--+--+--+--+--+--| + ! |A7|A6|A5|A4|A3|A2|A1|A0|, where Ax is $accx, i.e. follow $accx + ! + ! "can't overflow" below mark carrying into high part of + ! multiplication result, which can't overflow, because it + ! can never be all ones. + + mulx $a1,$a0,$acc1 ! a[1]*a[0] + umulxhi $a1,$a0,$t1 + mulx $a2,$a0,$acc2 ! a[2]*a[0] + umulxhi $a2,$a0,$t2 + mulx $a3,$a0,$acc3 ! a[3]*a[0] + umulxhi $a3,$a0,$acc4 + + addcc $acc2,$t1,$acc2 ! accumulate high parts of multiplication + mulx $a2,$a1,$t0 ! a[2]*a[1] + umulxhi $a2,$a1,$t1 + addxccc $acc3,$t2,$acc3 + mulx $a3,$a1,$t2 ! a[3]*a[1] + umulxhi $a3,$a1,$t3 + addxc $acc4,%g0,$acc4 ! can't overflow + + mulx $a3,$a2,$acc5 ! a[3]*a[2] + not $poly3,$poly3 ! 0xFFFFFFFF00000001 + umulxhi $a3,$a2,$acc6 + + addcc $t2,$t1,$t1 ! accumulate high parts of multiplication + mulx $a0,$a0,$acc0 ! a[0]*a[0] + addxc $t3,%g0,$t2 ! can't overflow + + addcc $acc3,$t0,$acc3 ! accumulate low parts of multiplication + umulxhi $a0,$a0,$a0 + addxccc $acc4,$t1,$acc4 + mulx $a1,$a1,$t1 ! a[1]*a[1] + addxccc $acc5,$t2,$acc5 + umulxhi $a1,$a1,$a1 + addxc $acc6,%g0,$acc6 ! can't overflow + + addcc $acc1,$acc1,$acc1 ! acc[1-6]*=2 + mulx $a2,$a2,$t2 ! a[2]*a[2] + addxccc $acc2,$acc2,$acc2 + umulxhi $a2,$a2,$a2 + addxccc $acc3,$acc3,$acc3 + mulx $a3,$a3,$t3 ! a[3]*a[3] + addxccc $acc4,$acc4,$acc4 + umulxhi $a3,$a3,$a3 + addxccc $acc5,$acc5,$acc5 + addxccc $acc6,$acc6,$acc6 + addxc %g0,%g0,$acc7 + + addcc $acc1,$a0,$acc1 ! +a[i]*a[i] + addxccc $acc2,$t1,$acc2 + addxccc $acc3,$a1,$acc3 + addxccc $acc4,$t2,$acc4 + sllx $acc0,32,$t0 + addxccc $acc5,$a2,$acc5 + srlx $acc0,32,$t1 + addxccc $acc6,$t3,$acc6 + sub $acc0,$t0,$t2 ! acc0*0xFFFFFFFF00000001, low part + addxc $acc7,$a3,$acc7 +___ +for($i=0;$i<3;$i++) { # reductions, see commentary + # in multiplication for details +$code.=<<___; + umulxhi $acc0,$poly3,$t3 ! acc0*0xFFFFFFFF00000001, high part + addcc $acc1,$t0,$acc0 ! +=acc[0]<<96 and omit acc[0] + sllx $acc0,32,$t0 + addxccc $acc2,$t1,$acc1 + srlx $acc0,32,$t1 + addxccc $acc3,$t2,$acc2 ! +=acc[0]*0xFFFFFFFF00000001 + sub $acc0,$t0,$t2 ! acc0*0xFFFFFFFF00000001, low part + addxc %g0,$t3,$acc3 ! cant't overflow +___ +} +$code.=<<___; + umulxhi $acc0,$poly3,$t3 ! acc0*0xFFFFFFFF00000001, high part + addcc $acc1,$t0,$acc0 ! +=acc[0]<<96 and omit acc[0] + addxccc $acc2,$t1,$acc1 + addxccc $acc3,$t2,$acc2 ! +=acc[0]*0xFFFFFFFF00000001 + addxc %g0,$t3,$acc3 ! can't overflow + + addcc $acc0,$acc4,$acc0 ! accumulate upper half + addxccc $acc1,$acc5,$acc1 + addxccc $acc2,$acc6,$acc2 + addxccc $acc3,$acc7,$acc3 + addxc %g0,%g0,$acc4 + +.Lmul_final_vis3: + + ! Final step is "if result > mod, subtract mod", but as comparison + ! means subtraction, we do the subtraction and then copy outcome + ! if it didn't borrow. But note that as we [have to] replace + ! subtraction with addition with negative, carry/borrow logic is + ! inverse. + + addcc $acc0,1,$t0 ! add -modulus, i.e. subtract + not $poly3,$poly3 ! restore 0x00000000FFFFFFFE + addxccc $acc1,$poly1,$t1 + addxccc $acc2,$minus1,$t2 + addxccc $acc3,$poly3,$t3 + addxccc $acc4,$minus1,%g0 ! did it carry? + + movcs %xcc,$t0,$acc0 + movcs %xcc,$t1,$acc1 + stx $acc0,[$rp] + movcs %xcc,$t2,$acc2 + stx $acc1,[$rp+8] + movcs %xcc,$t3,$acc3 + stx $acc2,[$rp+16] + retl + stx $acc3,[$rp+24] +.type __ecp_nistz256_sqr_mont_vis3,#function +.size __ecp_nistz256_sqr_mont_vis3,.-__ecp_nistz256_sqr_mont_vis3 +___ + +######################################################################## +# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp); +# +{ +my ($res_x,$res_y,$res_z, + $in_x,$in_y,$in_z, + $S,$M,$Zsqr,$tmp0)=map(32*$_,(0..9)); +# above map() describes stack layout with 10 temporary +# 256-bit vectors on top. + +$code.=<<___; +.align 32 +ecp_nistz256_point_double_vis3: + save %sp,-STACK64_FRAME-32*10,%sp + + mov $rp,$rp_real +.Ldouble_shortcut_vis3: + mov -1,$minus1 + mov -2,$poly3 + sllx $minus1,32,$poly1 ! 0xFFFFFFFF00000000 + srl $poly3,0,$poly3 ! 0x00000000FFFFFFFE + + ! convert input to uint64_t[4] + ld [$ap],$a0 ! in_x + ld [$ap+4],$t0 + ld [$ap+8],$a1 + ld [$ap+12],$t1 + ld [$ap+16],$a2 + ld [$ap+20],$t2 + ld [$ap+24],$a3 + ld [$ap+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + ld [$ap+32],$acc0 ! in_y + or $a0,$t0,$a0 + ld [$ap+32+4],$t0 + sllx $t2,32,$t2 + ld [$ap+32+8],$acc1 + or $a1,$t1,$a1 + ld [$ap+32+12],$t1 + sllx $t3,32,$t3 + ld [$ap+32+16],$acc2 + or $a2,$t2,$a2 + ld [$ap+32+20],$t2 + or $a3,$t3,$a3 + ld [$ap+32+24],$acc3 + sllx $t0,32,$t0 + ld [$ap+32+28],$t3 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in_x] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in_x+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in_x+16] + or $acc0,$t0,$acc0 + stx $a3,[%sp+LOCALS64+$in_x+24] + or $acc1,$t1,$acc1 + stx $acc0,[%sp+LOCALS64+$in_y] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in_y+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in_y+16] + stx $acc3,[%sp+LOCALS64+$in_y+24] + + ld [$ap+64],$a0 ! in_z + ld [$ap+64+4],$t0 + ld [$ap+64+8],$a1 + ld [$ap+64+12],$t1 + ld [$ap+64+16],$a2 + ld [$ap+64+20],$t2 + ld [$ap+64+24],$a3 + ld [$ap+64+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + or $a0,$t0,$a0 + sllx $t2,32,$t2 + or $a1,$t1,$a1 + sllx $t3,32,$t3 + or $a2,$t2,$a2 + or $a3,$t3,$a3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in_z] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in_z+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in_z+16] + stx $a3,[%sp+LOCALS64+$in_z+24] + + ! in_y is still in $acc0-$acc3 + call __ecp_nistz256_mul_by_2_vis3 ! p256_mul_by_2(S, in_y); + add %sp,LOCALS64+$S,$rp + + ! in_z is still in $a0-$a3 + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Zsqr, in_z); + add %sp,LOCALS64+$Zsqr,$rp + + mov $acc0,$a0 ! put Zsqr aside + mov $acc1,$a1 + mov $acc2,$a2 + mov $acc3,$a3 + + add %sp,LOCALS64+$in_x,$bp + call __ecp_nistz256_add_vis3 ! p256_add(M, Zsqr, in_x); + add %sp,LOCALS64+$M,$rp + + mov $a0,$acc0 ! restore Zsqr + ldx [%sp+LOCALS64+$S],$a0 ! forward load + mov $a1,$acc1 + ldx [%sp+LOCALS64+$S+8],$a1 + mov $a2,$acc2 + ldx [%sp+LOCALS64+$S+16],$a2 + mov $a3,$acc3 + ldx [%sp+LOCALS64+$S+24],$a3 + + add %sp,LOCALS64+$in_x,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(Zsqr, in_x, Zsqr); + add %sp,LOCALS64+$Zsqr,$rp + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(S, S); + add %sp,LOCALS64+$S,$rp + + ldx [%sp+LOCALS64+$in_z],$bi + ldx [%sp+LOCALS64+$in_y],$a0 + ldx [%sp+LOCALS64+$in_y+8],$a1 + ldx [%sp+LOCALS64+$in_y+16],$a2 + ldx [%sp+LOCALS64+$in_y+24],$a3 + add %sp,LOCALS64+$in_z,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(tmp0, in_z, in_y); + add %sp,LOCALS64+$tmp0,$rp + + ldx [%sp+LOCALS64+$M],$bi ! forward load + ldx [%sp+LOCALS64+$Zsqr],$a0 + ldx [%sp+LOCALS64+$Zsqr+8],$a1 + ldx [%sp+LOCALS64+$Zsqr+16],$a2 + ldx [%sp+LOCALS64+$Zsqr+24],$a3 + + call __ecp_nistz256_mul_by_2_vis3 ! p256_mul_by_2(res_z, tmp0); + add %sp,LOCALS64+$res_z,$rp + + add %sp,LOCALS64+$M,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(M, M, Zsqr); + add %sp,LOCALS64+$M,$rp + + mov $acc0,$a0 ! put aside M + mov $acc1,$a1 + mov $acc2,$a2 + mov $acc3,$a3 + call __ecp_nistz256_mul_by_2_vis3 + add %sp,LOCALS64+$M,$rp + mov $a0,$t0 ! copy M + ldx [%sp+LOCALS64+$S],$a0 ! forward load + mov $a1,$t1 + ldx [%sp+LOCALS64+$S+8],$a1 + mov $a2,$t2 + ldx [%sp+LOCALS64+$S+16],$a2 + mov $a3,$t3 + ldx [%sp+LOCALS64+$S+24],$a3 + call __ecp_nistz256_add_noload_vis3 ! p256_mul_by_3(M, M); + add %sp,LOCALS64+$M,$rp + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(tmp0, S); + add %sp,LOCALS64+$tmp0,$rp + + ldx [%sp+LOCALS64+$S],$bi ! forward load + ldx [%sp+LOCALS64+$in_x],$a0 + ldx [%sp+LOCALS64+$in_x+8],$a1 + ldx [%sp+LOCALS64+$in_x+16],$a2 + ldx [%sp+LOCALS64+$in_x+24],$a3 + + call __ecp_nistz256_div_by_2_vis3 ! p256_div_by_2(res_y, tmp0); + add %sp,LOCALS64+$res_y,$rp + + add %sp,LOCALS64+$S,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S, S, in_x); + add %sp,LOCALS64+$S,$rp + + ldx [%sp+LOCALS64+$M],$a0 ! forward load + ldx [%sp+LOCALS64+$M+8],$a1 + ldx [%sp+LOCALS64+$M+16],$a2 + ldx [%sp+LOCALS64+$M+24],$a3 + + call __ecp_nistz256_mul_by_2_vis3 ! p256_mul_by_2(tmp0, S); + add %sp,LOCALS64+$tmp0,$rp + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(res_x, M); + add %sp,LOCALS64+$res_x,$rp + + add %sp,LOCALS64+$tmp0,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_x, res_x, tmp0); + add %sp,LOCALS64+$res_x,$rp + + ldx [%sp+LOCALS64+$M],$a0 ! forward load + ldx [%sp+LOCALS64+$M+8],$a1 + ldx [%sp+LOCALS64+$M+16],$a2 + ldx [%sp+LOCALS64+$M+24],$a3 + + add %sp,LOCALS64+$S,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(S, S, res_x); + add %sp,LOCALS64+$S,$rp + + mov $acc0,$bi + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S, S, M); + add %sp,LOCALS64+$S,$rp + + ldx [%sp+LOCALS64+$res_x],$a0 ! forward load + ldx [%sp+LOCALS64+$res_x+8],$a1 + ldx [%sp+LOCALS64+$res_x+16],$a2 + ldx [%sp+LOCALS64+$res_x+24],$a3 + + add %sp,LOCALS64+$res_y,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_y, S, res_y); + add %sp,LOCALS64+$res_y,$bp + + ! convert output to uint_32[8] + srlx $a0,32,$t0 + srlx $a1,32,$t1 + st $a0,[$rp_real] ! res_x + srlx $a2,32,$t2 + st $t0,[$rp_real+4] + srlx $a3,32,$t3 + st $a1,[$rp_real+8] + st $t1,[$rp_real+12] + st $a2,[$rp_real+16] + st $t2,[$rp_real+20] + st $a3,[$rp_real+24] + st $t3,[$rp_real+28] + + ldx [%sp+LOCALS64+$res_z],$a0 ! forward load + srlx $acc0,32,$t0 + ldx [%sp+LOCALS64+$res_z+8],$a1 + srlx $acc1,32,$t1 + ldx [%sp+LOCALS64+$res_z+16],$a2 + srlx $acc2,32,$t2 + ldx [%sp+LOCALS64+$res_z+24],$a3 + srlx $acc3,32,$t3 + st $acc0,[$rp_real+32] ! res_y + st $t0, [$rp_real+32+4] + st $acc1,[$rp_real+32+8] + st $t1, [$rp_real+32+12] + st $acc2,[$rp_real+32+16] + st $t2, [$rp_real+32+20] + st $acc3,[$rp_real+32+24] + st $t3, [$rp_real+32+28] + + srlx $a0,32,$t0 + srlx $a1,32,$t1 + st $a0,[$rp_real+64] ! res_z + srlx $a2,32,$t2 + st $t0,[$rp_real+64+4] + srlx $a3,32,$t3 + st $a1,[$rp_real+64+8] + st $t1,[$rp_real+64+12] + st $a2,[$rp_real+64+16] + st $t2,[$rp_real+64+20] + st $a3,[$rp_real+64+24] + st $t3,[$rp_real+64+28] + + ret + restore +.type ecp_nistz256_point_double_vis3,#function +.size ecp_nistz256_point_double_vis3,.-ecp_nistz256_point_double_vis3 +___ +} +######################################################################## +# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT *in2); +{ +my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y,$in2_z, + $H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2)=map(32*$_,(0..17)); +my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); + +# above map() describes stack layout with 18 temporary +# 256-bit vectors on top. Then we reserve some space for +# !in1infty, !in2infty and result of check for zero. + +$code.=<<___; +.globl ecp_nistz256_point_add_vis3 +.align 32 +ecp_nistz256_point_add_vis3: + save %sp,-STACK64_FRAME-32*18-32,%sp + + mov $rp,$rp_real + mov -1,$minus1 + mov -2,$poly3 + sllx $minus1,32,$poly1 ! 0xFFFFFFFF00000000 + srl $poly3,0,$poly3 ! 0x00000000FFFFFFFE + + ! convert input to uint64_t[4] + ld [$bp],$a0 ! in2_x + ld [$bp+4],$t0 + ld [$bp+8],$a1 + ld [$bp+12],$t1 + ld [$bp+16],$a2 + ld [$bp+20],$t2 + ld [$bp+24],$a3 + ld [$bp+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + ld [$bp+32],$acc0 ! in2_y + or $a0,$t0,$a0 + ld [$bp+32+4],$t0 + sllx $t2,32,$t2 + ld [$bp+32+8],$acc1 + or $a1,$t1,$a1 + ld [$bp+32+12],$t1 + sllx $t3,32,$t3 + ld [$bp+32+16],$acc2 + or $a2,$t2,$a2 + ld [$bp+32+20],$t2 + or $a3,$t3,$a3 + ld [$bp+32+24],$acc3 + sllx $t0,32,$t0 + ld [$bp+32+28],$t3 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in2_x] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in2_x+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in2_x+16] + or $acc0,$t0,$acc0 + stx $a3,[%sp+LOCALS64+$in2_x+24] + or $acc1,$t1,$acc1 + stx $acc0,[%sp+LOCALS64+$in2_y] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in2_y+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in2_y+16] + stx $acc3,[%sp+LOCALS64+$in2_y+24] + + ld [$bp+64],$acc0 ! in2_z + ld [$bp+64+4],$t0 + ld [$bp+64+8],$acc1 + ld [$bp+64+12],$t1 + ld [$bp+64+16],$acc2 + ld [$bp+64+20],$t2 + ld [$bp+64+24],$acc3 + ld [$bp+64+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + ld [$ap],$a0 ! in1_x + or $acc0,$t0,$acc0 + ld [$ap+4],$t0 + sllx $t2,32,$t2 + ld [$ap+8],$a1 + or $acc1,$t1,$acc1 + ld [$ap+12],$t1 + sllx $t3,32,$t3 + ld [$ap+16],$a2 + or $acc2,$t2,$acc2 + ld [$ap+20],$t2 + or $acc3,$t3,$acc3 + ld [$ap+24],$a3 + sllx $t0,32,$t0 + ld [$ap+28],$t3 + sllx $t1,32,$t1 + stx $acc0,[%sp+LOCALS64+$in2_z] + sllx $t2,32,$t2 + stx $acc1,[%sp+LOCALS64+$in2_z+8] + sllx $t3,32,$t3 + stx $acc2,[%sp+LOCALS64+$in2_z+16] + stx $acc3,[%sp+LOCALS64+$in2_z+24] + + or $acc1,$acc0,$acc0 + or $acc3,$acc2,$acc2 + or $acc2,$acc0,$acc0 + movrnz $acc0,-1,$acc0 ! !in2infty + stx $acc0,[%fp+STACK_BIAS-8] + + or $a0,$t0,$a0 + ld [$ap+32],$acc0 ! in1_y + or $a1,$t1,$a1 + ld [$ap+32+4],$t0 + or $a2,$t2,$a2 + ld [$ap+32+8],$acc1 + or $a3,$t3,$a3 + ld [$ap+32+12],$t1 + ld [$ap+32+16],$acc2 + ld [$ap+32+20],$t2 + ld [$ap+32+24],$acc3 + sllx $t0,32,$t0 + ld [$ap+32+28],$t3 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in1_x] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in1_x+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in1_x+16] + or $acc0,$t0,$acc0 + stx $a3,[%sp+LOCALS64+$in1_x+24] + or $acc1,$t1,$acc1 + stx $acc0,[%sp+LOCALS64+$in1_y] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in1_y+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in1_y+16] + stx $acc3,[%sp+LOCALS64+$in1_y+24] + + ldx [%sp+LOCALS64+$in2_z],$a0 ! forward load + ldx [%sp+LOCALS64+$in2_z+8],$a1 + ldx [%sp+LOCALS64+$in2_z+16],$a2 + ldx [%sp+LOCALS64+$in2_z+24],$a3 + + ld [$ap+64],$acc0 ! in1_z + ld [$ap+64+4],$t0 + ld [$ap+64+8],$acc1 + ld [$ap+64+12],$t1 + ld [$ap+64+16],$acc2 + ld [$ap+64+20],$t2 + ld [$ap+64+24],$acc3 + ld [$ap+64+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + or $acc0,$t0,$acc0 + sllx $t2,32,$t2 + or $acc1,$t1,$acc1 + sllx $t3,32,$t3 + stx $acc0,[%sp+LOCALS64+$in1_z] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in1_z+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in1_z+16] + stx $acc3,[%sp+LOCALS64+$in1_z+24] + + or $acc1,$acc0,$acc0 + or $acc3,$acc2,$acc2 + or $acc2,$acc0,$acc0 + movrnz $acc0,-1,$acc0 ! !in1infty + stx $acc0,[%fp+STACK_BIAS-16] + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Z2sqr, in2_z); + add %sp,LOCALS64+$Z2sqr,$rp + + ldx [%sp+LOCALS64+$in1_z],$a0 + ldx [%sp+LOCALS64+$in1_z+8],$a1 + ldx [%sp+LOCALS64+$in1_z+16],$a2 + ldx [%sp+LOCALS64+$in1_z+24],$a3 + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Z1sqr, in1_z); + add %sp,LOCALS64+$Z1sqr,$rp + + ldx [%sp+LOCALS64+$Z2sqr],$bi + ldx [%sp+LOCALS64+$in2_z],$a0 + ldx [%sp+LOCALS64+$in2_z+8],$a1 + ldx [%sp+LOCALS64+$in2_z+16],$a2 + ldx [%sp+LOCALS64+$in2_z+24],$a3 + add %sp,LOCALS64+$Z2sqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S1, Z2sqr, in2_z); + add %sp,LOCALS64+$S1,$rp + + ldx [%sp+LOCALS64+$Z1sqr],$bi + ldx [%sp+LOCALS64+$in1_z],$a0 + ldx [%sp+LOCALS64+$in1_z+8],$a1 + ldx [%sp+LOCALS64+$in1_z+16],$a2 + ldx [%sp+LOCALS64+$in1_z+24],$a3 + add %sp,LOCALS64+$Z1sqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, Z1sqr, in1_z); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$S1],$bi + ldx [%sp+LOCALS64+$in1_y],$a0 + ldx [%sp+LOCALS64+$in1_y+8],$a1 + ldx [%sp+LOCALS64+$in1_y+16],$a2 + ldx [%sp+LOCALS64+$in1_y+24],$a3 + add %sp,LOCALS64+$S1,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S1, S1, in1_y); + add %sp,LOCALS64+$S1,$rp + + ldx [%sp+LOCALS64+$S2],$bi + ldx [%sp+LOCALS64+$in2_y],$a0 + ldx [%sp+LOCALS64+$in2_y+8],$a1 + ldx [%sp+LOCALS64+$in2_y+16],$a2 + ldx [%sp+LOCALS64+$in2_y+24],$a3 + add %sp,LOCALS64+$S2,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, S2, in2_y); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$Z2sqr],$bi ! forward load + ldx [%sp+LOCALS64+$in1_x],$a0 + ldx [%sp+LOCALS64+$in1_x+8],$a1 + ldx [%sp+LOCALS64+$in1_x+16],$a2 + ldx [%sp+LOCALS64+$in1_x+24],$a3 + + add %sp,LOCALS64+$S1,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(R, S2, S1); + add %sp,LOCALS64+$R,$rp + + or $acc1,$acc0,$acc0 ! see if result is zero + or $acc3,$acc2,$acc2 + or $acc2,$acc0,$acc0 + stx $acc0,[%fp+STACK_BIAS-24] + + add %sp,LOCALS64+$Z2sqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(U1, in1_x, Z2sqr); + add %sp,LOCALS64+$U1,$rp + + ldx [%sp+LOCALS64+$Z1sqr],$bi + ldx [%sp+LOCALS64+$in2_x],$a0 + ldx [%sp+LOCALS64+$in2_x+8],$a1 + ldx [%sp+LOCALS64+$in2_x+16],$a2 + ldx [%sp+LOCALS64+$in2_x+24],$a3 + add %sp,LOCALS64+$Z1sqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(U2, in2_x, Z1sqr); + add %sp,LOCALS64+$U2,$rp + + ldx [%sp+LOCALS64+$R],$a0 ! forward load + ldx [%sp+LOCALS64+$R+8],$a1 + ldx [%sp+LOCALS64+$R+16],$a2 + ldx [%sp+LOCALS64+$R+24],$a3 + + add %sp,LOCALS64+$U1,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(H, U2, U1); + add %sp,LOCALS64+$H,$rp + + or $acc1,$acc0,$acc0 ! see if result is zero + or $acc3,$acc2,$acc2 + orcc $acc2,$acc0,$acc0 + + bne,pt %xcc,.Ladd_proceed_vis3 ! is_equal(U1,U2)? + nop + + ldx [%fp+STACK_BIAS-8],$t0 + ldx [%fp+STACK_BIAS-16],$t1 + ldx [%fp+STACK_BIAS-24],$t2 + andcc $t0,$t1,%g0 + be,pt %xcc,.Ladd_proceed_vis3 ! (in1infty || in2infty)? + nop + andcc $t2,$t2,%g0 + be,a,pt %xcc,.Ldouble_shortcut_vis3 ! is_equal(S1,S2)? + add %sp,32*(12-10)+32,%sp ! difference in frame sizes + + st %g0,[$rp_real] + st %g0,[$rp_real+4] + st %g0,[$rp_real+8] + st %g0,[$rp_real+12] + st %g0,[$rp_real+16] + st %g0,[$rp_real+20] + st %g0,[$rp_real+24] + st %g0,[$rp_real+28] + st %g0,[$rp_real+32] + st %g0,[$rp_real+32+4] + st %g0,[$rp_real+32+8] + st %g0,[$rp_real+32+12] + st %g0,[$rp_real+32+16] + st %g0,[$rp_real+32+20] + st %g0,[$rp_real+32+24] + st %g0,[$rp_real+32+28] + st %g0,[$rp_real+64] + st %g0,[$rp_real+64+4] + st %g0,[$rp_real+64+8] + st %g0,[$rp_real+64+12] + st %g0,[$rp_real+64+16] + st %g0,[$rp_real+64+20] + st %g0,[$rp_real+64+24] + st %g0,[$rp_real+64+28] + b .Ladd_done_vis3 + nop + +.align 16 +.Ladd_proceed_vis3: + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Rsqr, R); + add %sp,LOCALS64+$Rsqr,$rp + + ldx [%sp+LOCALS64+$H],$bi + ldx [%sp+LOCALS64+$in1_z],$a0 + ldx [%sp+LOCALS64+$in1_z+8],$a1 + ldx [%sp+LOCALS64+$in1_z+16],$a2 + ldx [%sp+LOCALS64+$in1_z+24],$a3 + add %sp,LOCALS64+$H,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(res_z, H, in1_z); + add %sp,LOCALS64+$res_z,$rp + + ldx [%sp+LOCALS64+$H],$a0 + ldx [%sp+LOCALS64+$H+8],$a1 + ldx [%sp+LOCALS64+$H+16],$a2 + ldx [%sp+LOCALS64+$H+24],$a3 + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Hsqr, H); + add %sp,LOCALS64+$Hsqr,$rp + + ldx [%sp+LOCALS64+$res_z],$bi + ldx [%sp+LOCALS64+$in2_z],$a0 + ldx [%sp+LOCALS64+$in2_z+8],$a1 + ldx [%sp+LOCALS64+$in2_z+16],$a2 + ldx [%sp+LOCALS64+$in2_z+24],$a3 + add %sp,LOCALS64+$res_z,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(res_z, res_z, in2_z); + add %sp,LOCALS64+$res_z,$rp + + ldx [%sp+LOCALS64+$H],$bi + ldx [%sp+LOCALS64+$Hsqr],$a0 + ldx [%sp+LOCALS64+$Hsqr+8],$a1 + ldx [%sp+LOCALS64+$Hsqr+16],$a2 + ldx [%sp+LOCALS64+$Hsqr+24],$a3 + add %sp,LOCALS64+$H,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(Hcub, Hsqr, H); + add %sp,LOCALS64+$Hcub,$rp + + ldx [%sp+LOCALS64+$U1],$bi + ldx [%sp+LOCALS64+$Hsqr],$a0 + ldx [%sp+LOCALS64+$Hsqr+8],$a1 + ldx [%sp+LOCALS64+$Hsqr+16],$a2 + ldx [%sp+LOCALS64+$Hsqr+24],$a3 + add %sp,LOCALS64+$U1,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(U2, U1, Hsqr); + add %sp,LOCALS64+$U2,$rp + + call __ecp_nistz256_mul_by_2_vis3 ! p256_mul_by_2(Hsqr, U2); + add %sp,LOCALS64+$Hsqr,$rp + + add %sp,LOCALS64+$Rsqr,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(res_x, Rsqr, Hsqr); + add %sp,LOCALS64+$res_x,$rp + + add %sp,LOCALS64+$Hcub,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_x, res_x, Hcub); + add %sp,LOCALS64+$res_x,$rp + + ldx [%sp+LOCALS64+$S1],$bi ! forward load + ldx [%sp+LOCALS64+$Hcub],$a0 + ldx [%sp+LOCALS64+$Hcub+8],$a1 + ldx [%sp+LOCALS64+$Hcub+16],$a2 + ldx [%sp+LOCALS64+$Hcub+24],$a3 + + add %sp,LOCALS64+$U2,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(res_y, U2, res_x); + add %sp,LOCALS64+$res_y,$rp + + add %sp,LOCALS64+$S1,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, S1, Hcub); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$R],$bi + ldx [%sp+LOCALS64+$res_y],$a0 + ldx [%sp+LOCALS64+$res_y+8],$a1 + ldx [%sp+LOCALS64+$res_y+16],$a2 + ldx [%sp+LOCALS64+$res_y+24],$a3 + add %sp,LOCALS64+$R,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(res_y, res_y, R); + add %sp,LOCALS64+$res_y,$rp + + add %sp,LOCALS64+$S2,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_y, res_y, S2); + add %sp,LOCALS64+$res_y,$rp + + ldx [%fp+STACK_BIAS-16],$t1 ! !in1infty + ldx [%fp+STACK_BIAS-8],$t2 ! !in2infty +___ +for($i=0;$i<96;$i+=16) { # conditional moves +$code.=<<___; + ldx [%sp+LOCALS64+$res_x+$i],$acc0 ! res + ldx [%sp+LOCALS64+$res_x+$i+8],$acc1 + ldx [%sp+LOCALS64+$in2_x+$i],$acc2 ! in2 + ldx [%sp+LOCALS64+$in2_x+$i+8],$acc3 + ldx [%sp+LOCALS64+$in1_x+$i],$acc4 ! in1 + ldx [%sp+LOCALS64+$in1_x+$i+8],$acc5 + movrz $t1,$acc2,$acc0 + movrz $t1,$acc3,$acc1 + movrz $t2,$acc4,$acc0 + movrz $t2,$acc5,$acc1 + srlx $acc0,32,$acc2 + srlx $acc1,32,$acc3 + st $acc0,[$rp_real+$i] + st $acc2,[$rp_real+$i+4] + st $acc1,[$rp_real+$i+8] + st $acc3,[$rp_real+$i+12] +___ +} +$code.=<<___; +.Ladd_done_vis3: + ret + restore +.type ecp_nistz256_point_add_vis3,#function +.size ecp_nistz256_point_add_vis3,.-ecp_nistz256_point_add_vis3 +___ +} +######################################################################## +# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT_AFFINE *in2); +{ +my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y, + $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..14)); +my $Z1sqr = $S2; +# above map() describes stack layout with 15 temporary +# 256-bit vectors on top. Then we reserve some space for +# !in1infty and !in2infty. + +$code.=<<___; +.align 32 +ecp_nistz256_point_add_affine_vis3: + save %sp,-STACK64_FRAME-32*15-32,%sp + + mov $rp,$rp_real + mov -1,$minus1 + mov -2,$poly3 + sllx $minus1,32,$poly1 ! 0xFFFFFFFF00000000 + srl $poly3,0,$poly3 ! 0x00000000FFFFFFFE + + ! convert input to uint64_t[4] + ld [$bp],$a0 ! in2_x + ld [$bp+4],$t0 + ld [$bp+8],$a1 + ld [$bp+12],$t1 + ld [$bp+16],$a2 + ld [$bp+20],$t2 + ld [$bp+24],$a3 + ld [$bp+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + ld [$bp+32],$acc0 ! in2_y + or $a0,$t0,$a0 + ld [$bp+32+4],$t0 + sllx $t2,32,$t2 + ld [$bp+32+8],$acc1 + or $a1,$t1,$a1 + ld [$bp+32+12],$t1 + sllx $t3,32,$t3 + ld [$bp+32+16],$acc2 + or $a2,$t2,$a2 + ld [$bp+32+20],$t2 + or $a3,$t3,$a3 + ld [$bp+32+24],$acc3 + sllx $t0,32,$t0 + ld [$bp+32+28],$t3 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in2_x] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in2_x+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in2_x+16] + or $acc0,$t0,$acc0 + stx $a3,[%sp+LOCALS64+$in2_x+24] + or $acc1,$t1,$acc1 + stx $acc0,[%sp+LOCALS64+$in2_y] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in2_y+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in2_y+16] + stx $acc3,[%sp+LOCALS64+$in2_y+24] + + or $a1,$a0,$a0 + or $a3,$a2,$a2 + or $acc1,$acc0,$acc0 + or $acc3,$acc2,$acc2 + or $a2,$a0,$a0 + or $acc2,$acc0,$acc0 + or $acc0,$a0,$a0 + movrnz $a0,-1,$a0 ! !in2infty + stx $a0,[%fp+STACK_BIAS-8] + + ld [$ap],$a0 ! in1_x + ld [$ap+4],$t0 + ld [$ap+8],$a1 + ld [$ap+12],$t1 + ld [$ap+16],$a2 + ld [$ap+20],$t2 + ld [$ap+24],$a3 + ld [$ap+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + ld [$ap+32],$acc0 ! in1_y + or $a0,$t0,$a0 + ld [$ap+32+4],$t0 + sllx $t2,32,$t2 + ld [$ap+32+8],$acc1 + or $a1,$t1,$a1 + ld [$ap+32+12],$t1 + sllx $t3,32,$t3 + ld [$ap+32+16],$acc2 + or $a2,$t2,$a2 + ld [$ap+32+20],$t2 + or $a3,$t3,$a3 + ld [$ap+32+24],$acc3 + sllx $t0,32,$t0 + ld [$ap+32+28],$t3 + sllx $t1,32,$t1 + stx $a0,[%sp+LOCALS64+$in1_x] + sllx $t2,32,$t2 + stx $a1,[%sp+LOCALS64+$in1_x+8] + sllx $t3,32,$t3 + stx $a2,[%sp+LOCALS64+$in1_x+16] + or $acc0,$t0,$acc0 + stx $a3,[%sp+LOCALS64+$in1_x+24] + or $acc1,$t1,$acc1 + stx $acc0,[%sp+LOCALS64+$in1_y] + or $acc2,$t2,$acc2 + stx $acc1,[%sp+LOCALS64+$in1_y+8] + or $acc3,$t3,$acc3 + stx $acc2,[%sp+LOCALS64+$in1_y+16] + stx $acc3,[%sp+LOCALS64+$in1_y+24] + + ld [$ap+64],$a0 ! in1_z + ld [$ap+64+4],$t0 + ld [$ap+64+8],$a1 + ld [$ap+64+12],$t1 + ld [$ap+64+16],$a2 + ld [$ap+64+20],$t2 + ld [$ap+64+24],$a3 + ld [$ap+64+28],$t3 + sllx $t0,32,$t0 + sllx $t1,32,$t1 + or $a0,$t0,$a0 + sllx $t2,32,$t2 + or $a1,$t1,$a1 + sllx $t3,32,$t3 + stx $a0,[%sp+LOCALS64+$in1_z] + or $a2,$t2,$a2 + stx $a1,[%sp+LOCALS64+$in1_z+8] + or $a3,$t3,$a3 + stx $a2,[%sp+LOCALS64+$in1_z+16] + stx $a3,[%sp+LOCALS64+$in1_z+24] + + or $a1,$a0,$t0 + or $a3,$a2,$t2 + or $t2,$t0,$t0 + movrnz $t0,-1,$t0 ! !in1infty + stx $t0,[%fp+STACK_BIAS-16] + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Z1sqr, in1_z); + add %sp,LOCALS64+$Z1sqr,$rp + + ldx [%sp+LOCALS64+$in2_x],$bi + mov $acc0,$a0 + mov $acc1,$a1 + mov $acc2,$a2 + mov $acc3,$a3 + add %sp,LOCALS64+$in2_x,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(U2, Z1sqr, in2_x); + add %sp,LOCALS64+$U2,$rp + + ldx [%sp+LOCALS64+$Z1sqr],$bi ! forward load + ldx [%sp+LOCALS64+$in1_z],$a0 + ldx [%sp+LOCALS64+$in1_z+8],$a1 + ldx [%sp+LOCALS64+$in1_z+16],$a2 + ldx [%sp+LOCALS64+$in1_z+24],$a3 + + add %sp,LOCALS64+$in1_x,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(H, U2, in1_x); + add %sp,LOCALS64+$H,$rp + + add %sp,LOCALS64+$Z1sqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, Z1sqr, in1_z); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$H],$bi + ldx [%sp+LOCALS64+$in1_z],$a0 + ldx [%sp+LOCALS64+$in1_z+8],$a1 + ldx [%sp+LOCALS64+$in1_z+16],$a2 + ldx [%sp+LOCALS64+$in1_z+24],$a3 + add %sp,LOCALS64+$H,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(res_z, H, in1_z); + add %sp,LOCALS64+$res_z,$rp + + ldx [%sp+LOCALS64+$S2],$bi + ldx [%sp+LOCALS64+$in2_y],$a0 + ldx [%sp+LOCALS64+$in2_y+8],$a1 + ldx [%sp+LOCALS64+$in2_y+16],$a2 + ldx [%sp+LOCALS64+$in2_y+24],$a3 + add %sp,LOCALS64+$S2,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, S2, in2_y); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$H],$a0 ! forward load + ldx [%sp+LOCALS64+$H+8],$a1 + ldx [%sp+LOCALS64+$H+16],$a2 + ldx [%sp+LOCALS64+$H+24],$a3 + + add %sp,LOCALS64+$in1_y,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(R, S2, in1_y); + add %sp,LOCALS64+$R,$rp + + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Hsqr, H); + add %sp,LOCALS64+$Hsqr,$rp + + ldx [%sp+LOCALS64+$R],$a0 + ldx [%sp+LOCALS64+$R+8],$a1 + ldx [%sp+LOCALS64+$R+16],$a2 + ldx [%sp+LOCALS64+$R+24],$a3 + call __ecp_nistz256_sqr_mont_vis3 ! p256_sqr_mont(Rsqr, R); + add %sp,LOCALS64+$Rsqr,$rp + + ldx [%sp+LOCALS64+$H],$bi + ldx [%sp+LOCALS64+$Hsqr],$a0 + ldx [%sp+LOCALS64+$Hsqr+8],$a1 + ldx [%sp+LOCALS64+$Hsqr+16],$a2 + ldx [%sp+LOCALS64+$Hsqr+24],$a3 + add %sp,LOCALS64+$H,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(Hcub, Hsqr, H); + add %sp,LOCALS64+$Hcub,$rp + + ldx [%sp+LOCALS64+$Hsqr],$bi + ldx [%sp+LOCALS64+$in1_x],$a0 + ldx [%sp+LOCALS64+$in1_x+8],$a1 + ldx [%sp+LOCALS64+$in1_x+16],$a2 + ldx [%sp+LOCALS64+$in1_x+24],$a3 + add %sp,LOCALS64+$Hsqr,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(U2, in1_x, Hsqr); + add %sp,LOCALS64+$U2,$rp + + call __ecp_nistz256_mul_by_2_vis3 ! p256_mul_by_2(Hsqr, U2); + add %sp,LOCALS64+$Hsqr,$rp + + add %sp,LOCALS64+$Rsqr,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(res_x, Rsqr, Hsqr); + add %sp,LOCALS64+$res_x,$rp + + add %sp,LOCALS64+$Hcub,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_x, res_x, Hcub); + add %sp,LOCALS64+$res_x,$rp + + ldx [%sp+LOCALS64+$Hcub],$bi ! forward load + ldx [%sp+LOCALS64+$in1_y],$a0 + ldx [%sp+LOCALS64+$in1_y+8],$a1 + ldx [%sp+LOCALS64+$in1_y+16],$a2 + ldx [%sp+LOCALS64+$in1_y+24],$a3 + + add %sp,LOCALS64+$U2,$bp + call __ecp_nistz256_sub_morf_vis3 ! p256_sub(res_y, U2, res_x); + add %sp,LOCALS64+$res_y,$rp + + add %sp,LOCALS64+$Hcub,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(S2, in1_y, Hcub); + add %sp,LOCALS64+$S2,$rp + + ldx [%sp+LOCALS64+$R],$bi + ldx [%sp+LOCALS64+$res_y],$a0 + ldx [%sp+LOCALS64+$res_y+8],$a1 + ldx [%sp+LOCALS64+$res_y+16],$a2 + ldx [%sp+LOCALS64+$res_y+24],$a3 + add %sp,LOCALS64+$R,$bp + call __ecp_nistz256_mul_mont_vis3 ! p256_mul_mont(res_y, res_y, R); + add %sp,LOCALS64+$res_y,$rp + + add %sp,LOCALS64+$S2,$bp + call __ecp_nistz256_sub_from_vis3 ! p256_sub(res_y, res_y, S2); + add %sp,LOCALS64+$res_y,$rp + + ldx [%fp+STACK_BIAS-16],$t1 ! !in1infty + ldx [%fp+STACK_BIAS-8],$t2 ! !in2infty +1: call .+8 + add %o7,.Lone_mont_vis3-1b,$bp +___ +for($i=0;$i<64;$i+=16) { # conditional moves +$code.=<<___; + ldx [%sp+LOCALS64+$res_x+$i],$acc0 ! res + ldx [%sp+LOCALS64+$res_x+$i+8],$acc1 + ldx [%sp+LOCALS64+$in2_x+$i],$acc2 ! in2 + ldx [%sp+LOCALS64+$in2_x+$i+8],$acc3 + ldx [%sp+LOCALS64+$in1_x+$i],$acc4 ! in1 + ldx [%sp+LOCALS64+$in1_x+$i+8],$acc5 + movrz $t1,$acc2,$acc0 + movrz $t1,$acc3,$acc1 + movrz $t2,$acc4,$acc0 + movrz $t2,$acc5,$acc1 + srlx $acc0,32,$acc2 + srlx $acc1,32,$acc3 + st $acc0,[$rp_real+$i] + st $acc2,[$rp_real+$i+4] + st $acc1,[$rp_real+$i+8] + st $acc3,[$rp_real+$i+12] +___ +} +for(;$i<96;$i+=16) { +$code.=<<___; + ldx [%sp+LOCALS64+$res_x+$i],$acc0 ! res + ldx [%sp+LOCALS64+$res_x+$i+8],$acc1 + ldx [$bp+$i-64],$acc2 ! "in2" + ldx [$bp+$i-64+8],$acc3 + ldx [%sp+LOCALS64+$in1_x+$i],$acc4 ! in1 + ldx [%sp+LOCALS64+$in1_x+$i+8],$acc5 + movrz $t1,$acc2,$acc0 + movrz $t1,$acc3,$acc1 + movrz $t2,$acc4,$acc0 + movrz $t2,$acc5,$acc1 + srlx $acc0,32,$acc2 + srlx $acc1,32,$acc3 + st $acc0,[$rp_real+$i] + st $acc2,[$rp_real+$i+4] + st $acc1,[$rp_real+$i+8] + st $acc3,[$rp_real+$i+12] +___ +} +$code.=<<___; + ret + restore +.type ecp_nistz256_point_add_affine_vis3,#function +.size ecp_nistz256_point_add_affine_vis3,.-ecp_nistz256_point_add_affine_vis3 +.align 64 +.Lone_mont_vis3: +.long 0x00000000,0x00000001, 0xffffffff,0x00000000 +.long 0xffffffff,0xffffffff, 0x00000000,0xfffffffe +.align 64 +___ +} }}} + +# Purpose of these subroutines is to explicitly encode VIS instructions, +# so that one can compile the module without having to specify VIS +# extensions on compiler command line, e.g. -xarch=v9 vs. -xarch=v9a. +# Idea is to reserve for option to produce "universal" binary and let +# programmer detect if current CPU is VIS capable at run-time. +sub unvis3 { +my ($mnemonic,$rs1,$rs2,$rd)=@_; +my %bias = ( "g" => 0, "o" => 8, "l" => 16, "i" => 24 ); +my ($ref,$opf); +my %visopf = ( "addxc" => 0x011, + "addxccc" => 0x013, + "umulxhi" => 0x016 ); + + $ref = "$mnemonic\t$rs1,$rs2,$rd"; + + if ($opf=$visopf{$mnemonic}) { + foreach ($rs1,$rs2,$rd) { + return $ref if (!/%([goli])([0-9])/); + $_=$bias{$1}+$2; + } + + return sprintf ".word\t0x%08x !%s", + 0x81b00000|$rd<<25|$rs1<<14|$opf<<5|$rs2, + $ref; + } else { + return $ref; + } +} + +foreach (split("\n",$code)) { + s/\`([^\`]*)\`/eval $1/ge; + + s/\b(umulxhi|addxc[c]{0,2})\s+(%[goli][0-7]),\s*(%[goli][0-7]),\s*(%[goli][0-7])/ + &unvis3($1,$2,$3,$4) + /ge; + + print $_,"\n"; +} + +close STDOUT; diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86.pl new file mode 100755 index 0000000..1d9e006 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86.pl @@ -0,0 +1,1866 @@ +#! /usr/bin/env perl +# Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +# ==================================================================== +# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL +# project. The module is, however, dual licensed under OpenSSL and +# CRYPTOGAMS licenses depending on where you obtain it. For further +# details see http://www.openssl.org/~appro/cryptogams/. +# ==================================================================== +# +# ECP_NISTZ256 module for x86/SSE2. +# +# October 2014. +# +# Original ECP_NISTZ256 submission targeting x86_64 is detailed in +# http://eprint.iacr.org/2013/816. In the process of adaptation +# original .c module was made 32-bit savvy in order to make this +# implementation possible. +# +# with/without -DECP_NISTZ256_ASM +# Pentium +66-163% +# PIII +72-172% +# P4 +65-132% +# Core2 +90-215% +# Sandy Bridge +105-265% (contemporary i[57]-* are all close to this) +# Atom +65-155% +# Opteron +54-110% +# Bulldozer +99-240% +# VIA Nano +93-290% +# +# Ranges denote minimum and maximum improvement coefficients depending +# on benchmark. Lower coefficients are for ECDSA sign, server-side +# operation. Keep in mind that +200% means 3x improvement. + +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +push(@INC,"${dir}","${dir}../../perlasm"); +require "x86asm.pl"; + +$output=pop; +open STDOUT,">$output"; + +&asm_init($ARGV[0],"ecp_nistz256-x86.pl",$ARGV[$#ARGV] eq "386"); + +$sse2=0; +for (@ARGV) { $sse2=1 if (/-DOPENSSL_IA32_SSE2/); } + +&external_label("OPENSSL_ia32cap_P") if ($sse2); + + +######################################################################## +# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7 +# +open TABLE,"<ecp_nistz256_table.c" or +open TABLE,"<${dir}../ecp_nistz256_table.c" or +die "failed to open ecp_nistz256_table.c:",$!; + +use integer; + +foreach(<TABLE>) { + s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo; +} +close TABLE; + +# See ecp_nistz256_table.c for explanation for why it's 64*16*37. +# 64*16*37-1 is because $#arr returns last valid index or @arr, not +# amount of elements. +die "insane number of elements" if ($#arr != 64*16*37-1); + +&public_label("ecp_nistz256_precomputed"); +&align(4096); +&set_label("ecp_nistz256_precomputed"); + +######################################################################## +# this conversion smashes P256_POINT_AFFINE by individual bytes with +# 64 byte interval, similar to +# 1111222233334444 +# 1234123412341234 +for(1..37) { + @tbl = splice(@arr,0,64*16); + for($i=0;$i<64;$i++) { + undef @line; + for($j=0;$j<64;$j++) { + push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff; + } + &data_byte(join(',',map { sprintf "0x%02x",$_} @line)); + } +} + +######################################################################## +# Keep in mind that constants are stored least to most significant word +&static_label("RR"); +&set_label("RR",64); +&data_word(3,0,-1,-5,-2,-1,-3,4); # 2^512 mod P-256 + +&static_label("ONE_mont"); +&set_label("ONE_mont"); +&data_word(1,0,0,-1,-1,-1,-2,0); + +&static_label("ONE"); +&set_label("ONE"); +&data_word(1,0,0,0,0,0,0,0); +&asciz("ECP_NISZ256 for x86/SSE2, CRYPTOGAMS by <appro\@openssl.org>"); +&align(64); + +######################################################################## +# void ecp_nistz256_mul_by_2(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_mul_by_2"); + &mov ("esi",&wparam(1)); + &mov ("edi",&wparam(0)); + &mov ("ebp","esi"); +######################################################################## +# common pattern for internal functions is that %edi is result pointer, +# %esi and %ebp are input ones, %ebp being optional. %edi is preserved. + &call ("_ecp_nistz256_add"); +&function_end("ecp_nistz256_mul_by_2"); + +######################################################################## +# void ecp_nistz256_mul_by_3(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_mul_by_3"); + &mov ("esi",&wparam(1)); + # multiplication by 3 is performed + # as 2*n+n, but we can't use output + # to store 2*n, because if output + # pointer equals to input, then + # we'll get 2*n+2*n. + &stack_push(8); # therefore we need to allocate + # 256-bit intermediate buffer. + &mov ("edi","esp"); + &mov ("ebp","esi"); + &call ("_ecp_nistz256_add"); + &lea ("esi",&DWP(0,"edi")); + &mov ("ebp",&wparam(1)); + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_add"); + &stack_pop(8); +&function_end("ecp_nistz256_mul_by_3"); + +######################################################################## +# void ecp_nistz256_div_by_2(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_div_by_2"); + &mov ("esi",&wparam(1)); + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_div_by_2"); +&function_end("ecp_nistz256_div_by_2"); + +&function_begin_B("_ecp_nistz256_div_by_2"); + # tmp = a is odd ? a+mod : a + # + # note that because mod has special form, i.e. consists of + # 0xffffffff, 1 and 0s, we can conditionally synthesize it by + # assigning least significant bit of input to one register, + # %ebp, and its negative to another, %edx. + + &mov ("ebp",&DWP(0,"esi")); + &xor ("edx","edx"); + &mov ("ebx",&DWP(4,"esi")); + &mov ("eax","ebp"); + &and ("ebp",1); + &mov ("ecx",&DWP(8,"esi")); + &sub ("edx","ebp"); + + &add ("eax","edx"); + &adc ("ebx","edx"); + &mov (&DWP(0,"edi"),"eax"); + &adc ("ecx","edx"); + &mov (&DWP(4,"edi"),"ebx"); + &mov (&DWP(8,"edi"),"ecx"); + + &mov ("eax",&DWP(12,"esi")); + &mov ("ebx",&DWP(16,"esi")); + &adc ("eax",0); + &mov ("ecx",&DWP(20,"esi")); + &adc ("ebx",0); + &mov (&DWP(12,"edi"),"eax"); + &adc ("ecx",0); + &mov (&DWP(16,"edi"),"ebx"); + &mov (&DWP(20,"edi"),"ecx"); + + &mov ("eax",&DWP(24,"esi")); + &mov ("ebx",&DWP(28,"esi")); + &adc ("eax","ebp"); + &adc ("ebx","edx"); + &mov (&DWP(24,"edi"),"eax"); + &sbb ("esi","esi"); # broadcast carry bit + &mov (&DWP(28,"edi"),"ebx"); + + # ret = tmp >> 1 + + &mov ("eax",&DWP(0,"edi")); + &mov ("ebx",&DWP(4,"edi")); + &mov ("ecx",&DWP(8,"edi")); + &mov ("edx",&DWP(12,"edi")); + + &shr ("eax",1); + &mov ("ebp","ebx"); + &shl ("ebx",31); + &or ("eax","ebx"); + + &shr ("ebp",1); + &mov ("ebx","ecx"); + &shl ("ecx",31); + &mov (&DWP(0,"edi"),"eax"); + &or ("ebp","ecx"); + &mov ("eax",&DWP(16,"edi")); + + &shr ("ebx",1); + &mov ("ecx","edx"); + &shl ("edx",31); + &mov (&DWP(4,"edi"),"ebp"); + &or ("ebx","edx"); + &mov ("ebp",&DWP(20,"edi")); + + &shr ("ecx",1); + &mov ("edx","eax"); + &shl ("eax",31); + &mov (&DWP(8,"edi"),"ebx"); + &or ("ecx","eax"); + &mov ("ebx",&DWP(24,"edi")); + + &shr ("edx",1); + &mov ("eax","ebp"); + &shl ("ebp",31); + &mov (&DWP(12,"edi"),"ecx"); + &or ("edx","ebp"); + &mov ("ecx",&DWP(28,"edi")); + + &shr ("eax",1); + &mov ("ebp","ebx"); + &shl ("ebx",31); + &mov (&DWP(16,"edi"),"edx"); + &or ("eax","ebx"); + + &shr ("ebp",1); + &mov ("ebx","ecx"); + &shl ("ecx",31); + &mov (&DWP(20,"edi"),"eax"); + &or ("ebp","ecx"); + + &shr ("ebx",1); + &shl ("esi",31); + &mov (&DWP(24,"edi"),"ebp"); + &or ("ebx","esi"); # handle top-most carry bit + &mov (&DWP(28,"edi"),"ebx"); + + &ret (); +&function_end_B("_ecp_nistz256_div_by_2"); + +######################################################################## +# void ecp_nistz256_add(BN_ULONG edi[8],const BN_ULONG esi[8], +# const BN_ULONG ebp[8]); +&function_begin("ecp_nistz256_add"); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_add"); +&function_end("ecp_nistz256_add"); + +&function_begin_B("_ecp_nistz256_add"); + &mov ("eax",&DWP(0,"esi")); + &mov ("ebx",&DWP(4,"esi")); + &mov ("ecx",&DWP(8,"esi")); + &add ("eax",&DWP(0,"ebp")); + &mov ("edx",&DWP(12,"esi")); + &adc ("ebx",&DWP(4,"ebp")); + &mov (&DWP(0,"edi"),"eax"); + &adc ("ecx",&DWP(8,"ebp")); + &mov (&DWP(4,"edi"),"ebx"); + &adc ("edx",&DWP(12,"ebp")); + &mov (&DWP(8,"edi"),"ecx"); + &mov (&DWP(12,"edi"),"edx"); + + &mov ("eax",&DWP(16,"esi")); + &mov ("ebx",&DWP(20,"esi")); + &mov ("ecx",&DWP(24,"esi")); + &adc ("eax",&DWP(16,"ebp")); + &mov ("edx",&DWP(28,"esi")); + &adc ("ebx",&DWP(20,"ebp")); + &mov (&DWP(16,"edi"),"eax"); + &adc ("ecx",&DWP(24,"ebp")); + &mov (&DWP(20,"edi"),"ebx"); + &mov ("esi",0); + &adc ("edx",&DWP(28,"ebp")); + &mov (&DWP(24,"edi"),"ecx"); + &adc ("esi",0); + &mov (&DWP(28,"edi"),"edx"); + + # if a+b >= modulus, subtract modulus. + # + # But since comparison implies subtraction, we subtract modulus + # to see if it borrows, and then subtract it for real if + # subtraction didn't borrow. + + &mov ("eax",&DWP(0,"edi")); + &mov ("ebx",&DWP(4,"edi")); + &mov ("ecx",&DWP(8,"edi")); + &sub ("eax",-1); + &mov ("edx",&DWP(12,"edi")); + &sbb ("ebx",-1); + &mov ("eax",&DWP(16,"edi")); + &sbb ("ecx",-1); + &mov ("ebx",&DWP(20,"edi")); + &sbb ("edx",0); + &mov ("ecx",&DWP(24,"edi")); + &sbb ("eax",0); + &mov ("edx",&DWP(28,"edi")); + &sbb ("ebx",0); + &sbb ("ecx",1); + &sbb ("edx",-1); + &sbb ("esi",0); + + # Note that because mod has special form, i.e. consists of + # 0xffffffff, 1 and 0s, we can conditionally synthesize it by + # by using borrow. + + ¬ ("esi"); + &mov ("eax",&DWP(0,"edi")); + &mov ("ebp","esi"); + &mov ("ebx",&DWP(4,"edi")); + &shr ("ebp",31); + &mov ("ecx",&DWP(8,"edi")); + &sub ("eax","esi"); + &mov ("edx",&DWP(12,"edi")); + &sbb ("ebx","esi"); + &mov (&DWP(0,"edi"),"eax"); + &sbb ("ecx","esi"); + &mov (&DWP(4,"edi"),"ebx"); + &sbb ("edx",0); + &mov (&DWP(8,"edi"),"ecx"); + &mov (&DWP(12,"edi"),"edx"); + + &mov ("eax",&DWP(16,"edi")); + &mov ("ebx",&DWP(20,"edi")); + &mov ("ecx",&DWP(24,"edi")); + &sbb ("eax",0); + &mov ("edx",&DWP(28,"edi")); + &sbb ("ebx",0); + &mov (&DWP(16,"edi"),"eax"); + &sbb ("ecx","ebp"); + &mov (&DWP(20,"edi"),"ebx"); + &sbb ("edx","esi"); + &mov (&DWP(24,"edi"),"ecx"); + &mov (&DWP(28,"edi"),"edx"); + + &ret (); +&function_end_B("_ecp_nistz256_add"); + +######################################################################## +# void ecp_nistz256_sub(BN_ULONG edi[8],const BN_ULONG esi[8], +# const BN_ULONG ebp[8]); +&function_begin("ecp_nistz256_sub"); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_sub"); +&function_end("ecp_nistz256_sub"); + +&function_begin_B("_ecp_nistz256_sub"); + &mov ("eax",&DWP(0,"esi")); + &mov ("ebx",&DWP(4,"esi")); + &mov ("ecx",&DWP(8,"esi")); + &sub ("eax",&DWP(0,"ebp")); + &mov ("edx",&DWP(12,"esi")); + &sbb ("ebx",&DWP(4,"ebp")); + &mov (&DWP(0,"edi"),"eax"); + &sbb ("ecx",&DWP(8,"ebp")); + &mov (&DWP(4,"edi"),"ebx"); + &sbb ("edx",&DWP(12,"ebp")); + &mov (&DWP(8,"edi"),"ecx"); + &mov (&DWP(12,"edi"),"edx"); + + &mov ("eax",&DWP(16,"esi")); + &mov ("ebx",&DWP(20,"esi")); + &mov ("ecx",&DWP(24,"esi")); + &sbb ("eax",&DWP(16,"ebp")); + &mov ("edx",&DWP(28,"esi")); + &sbb ("ebx",&DWP(20,"ebp")); + &sbb ("ecx",&DWP(24,"ebp")); + &mov (&DWP(16,"edi"),"eax"); + &sbb ("edx",&DWP(28,"ebp")); + &mov (&DWP(20,"edi"),"ebx"); + &sbb ("esi","esi"); # broadcast borrow bit + &mov (&DWP(24,"edi"),"ecx"); + &mov (&DWP(28,"edi"),"edx"); + + # if a-b borrows, add modulus. + # + # Note that because mod has special form, i.e. consists of + # 0xffffffff, 1 and 0s, we can conditionally synthesize it by + # assigning borrow bit to one register, %ebp, and its negative + # to another, %esi. But we started by calculating %esi... + + &mov ("eax",&DWP(0,"edi")); + &mov ("ebp","esi"); + &mov ("ebx",&DWP(4,"edi")); + &shr ("ebp",31); + &mov ("ecx",&DWP(8,"edi")); + &add ("eax","esi"); + &mov ("edx",&DWP(12,"edi")); + &adc ("ebx","esi"); + &mov (&DWP(0,"edi"),"eax"); + &adc ("ecx","esi"); + &mov (&DWP(4,"edi"),"ebx"); + &adc ("edx",0); + &mov (&DWP(8,"edi"),"ecx"); + &mov (&DWP(12,"edi"),"edx"); + + &mov ("eax",&DWP(16,"edi")); + &mov ("ebx",&DWP(20,"edi")); + &mov ("ecx",&DWP(24,"edi")); + &adc ("eax",0); + &mov ("edx",&DWP(28,"edi")); + &adc ("ebx",0); + &mov (&DWP(16,"edi"),"eax"); + &adc ("ecx","ebp"); + &mov (&DWP(20,"edi"),"ebx"); + &adc ("edx","esi"); + &mov (&DWP(24,"edi"),"ecx"); + &mov (&DWP(28,"edi"),"edx"); + + &ret (); +&function_end_B("_ecp_nistz256_sub"); + +######################################################################## +# void ecp_nistz256_neg(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_neg"); + &mov ("ebp",&wparam(1)); + &mov ("edi",&wparam(0)); + + &xor ("eax","eax"); + &stack_push(8); + &mov (&DWP(0,"esp"),"eax"); + &mov ("esi","esp"); + &mov (&DWP(4,"esp"),"eax"); + &mov (&DWP(8,"esp"),"eax"); + &mov (&DWP(12,"esp"),"eax"); + &mov (&DWP(16,"esp"),"eax"); + &mov (&DWP(20,"esp"),"eax"); + &mov (&DWP(24,"esp"),"eax"); + &mov (&DWP(28,"esp"),"eax"); + + &call ("_ecp_nistz256_sub"); + + &stack_pop(8); +&function_end("ecp_nistz256_neg"); + +&function_begin_B("_picup_eax"); + &mov ("eax",&DWP(0,"esp")); + &ret (); +&function_end_B("_picup_eax"); + +######################################################################## +# void ecp_nistz256_to_mont(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_to_mont"); + &mov ("esi",&wparam(1)); + &call ("_picup_eax"); + &set_label("pic"); + &lea ("ebp",&DWP(&label("RR")."-".&label("pic"),"eax")); + if ($sse2) { + &picmeup("eax","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("eax",&DWP(0,"eax")); } + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_mul_mont"); +&function_end("ecp_nistz256_to_mont"); + +######################################################################## +# void ecp_nistz256_from_mont(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_from_mont"); + &mov ("esi",&wparam(1)); + &call ("_picup_eax"); + &set_label("pic"); + &lea ("ebp",&DWP(&label("ONE")."-".&label("pic"),"eax")); + if ($sse2) { + &picmeup("eax","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("eax",&DWP(0,"eax")); } + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_mul_mont"); +&function_end("ecp_nistz256_from_mont"); + +######################################################################## +# void ecp_nistz256_mul_mont(BN_ULONG edi[8],const BN_ULONG esi[8], +# const BN_ULONG ebp[8]); +&function_begin("ecp_nistz256_mul_mont"); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + if ($sse2) { + &call ("_picup_eax"); + &set_label("pic"); + &picmeup("eax","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("eax",&DWP(0,"eax")); } + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_mul_mont"); +&function_end("ecp_nistz256_mul_mont"); + +######################################################################## +# void ecp_nistz256_sqr_mont(BN_ULONG edi[8],const BN_ULONG esi[8]); +&function_begin("ecp_nistz256_sqr_mont"); + &mov ("esi",&wparam(1)); + if ($sse2) { + &call ("_picup_eax"); + &set_label("pic"); + &picmeup("eax","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("eax",&DWP(0,"eax")); } + &mov ("edi",&wparam(0)); + &mov ("ebp","esi"); + &call ("_ecp_nistz256_mul_mont"); +&function_end("ecp_nistz256_sqr_mont"); + +&function_begin_B("_ecp_nistz256_mul_mont"); + if ($sse2) { + &and ("eax",1<<24|1<<26); + &cmp ("eax",1<<24|1<<26); # see if XMM+SSE2 is on + &jne (&label("mul_mont_ialu")); + + ######################################## + # SSE2 code path featuring 32x16-bit + # multiplications is ~2x faster than + # IALU counterpart (except on Atom)... + ######################################## + # stack layout: + # +------------------------------------+< %esp + # | 7 16-byte temporary XMM words, | + # | "sliding" toward lower address | + # . . + # +------------------------------------+ + # | unused XMM word | + # +------------------------------------+< +128,%ebx + # | 8 16-byte XMM words holding copies | + # | of a[i]<<64|a[i] | + # . . + # . . + # +------------------------------------+< +256 + &mov ("edx","esp"); + &sub ("esp",0x100); + + &movd ("xmm7",&DWP(0,"ebp")); # b[0] -> 0000.00xy + &lea ("ebp",&DWP(4,"ebp")); + &pcmpeqd("xmm6","xmm6"); + &psrlq ("xmm6",48); # compose 0xffff<<64|0xffff + + &pshuflw("xmm7","xmm7",0b11011100); # 0000.00xy -> 0000.0x0y + &and ("esp",-64); + &pshufd ("xmm7","xmm7",0b11011100); # 0000.0x0y -> 000x.000y + &lea ("ebx",&DWP(0x80,"esp")); + + &movd ("xmm0",&DWP(4*0,"esi")); # a[0] -> 0000.00xy + &pshufd ("xmm0","xmm0",0b11001100); # 0000.00xy -> 00xy.00xy + &movd ("xmm1",&DWP(4*1,"esi")); # a[1] -> ... + &movdqa (&QWP(0x00,"ebx"),"xmm0"); # offload converted a[0] + &pmuludq("xmm0","xmm7"); # a[0]*b[0] + + &movd ("xmm2",&DWP(4*2,"esi")); + &pshufd ("xmm1","xmm1",0b11001100); + &movdqa (&QWP(0x10,"ebx"),"xmm1"); + &pmuludq("xmm1","xmm7"); # a[1]*b[0] + + &movq ("xmm4","xmm0"); # clear upper 64 bits + &pslldq("xmm4",6); + &paddq ("xmm4","xmm0"); + &movdqa("xmm5","xmm4"); + &psrldq("xmm4",10); # upper 32 bits of a[0]*b[0] + &pand ("xmm5","xmm6"); # lower 32 bits of a[0]*b[0] + + # Upper half of a[0]*b[i] is carried into next multiplication + # iteration, while lower one "participates" in actual reduction. + # Normally latter is done by accumulating result of multiplication + # of modulus by "magic" digit, but thanks to special form of modulus + # and "magic" digit it can be performed only with additions and + # subtractions (see note in IALU section below). Note that we are + # not bothered with carry bits, they are accumulated in "flatten" + # phase after all multiplications and reductions. + + &movd ("xmm3",&DWP(4*3,"esi")); + &pshufd ("xmm2","xmm2",0b11001100); + &movdqa (&QWP(0x20,"ebx"),"xmm2"); + &pmuludq("xmm2","xmm7"); # a[2]*b[0] + &paddq ("xmm1","xmm4"); # a[1]*b[0]+hw(a[0]*b[0]), carry + &movdqa (&QWP(0x00,"esp"),"xmm1"); # t[0] + + &movd ("xmm0",&DWP(4*4,"esi")); + &pshufd ("xmm3","xmm3",0b11001100); + &movdqa (&QWP(0x30,"ebx"),"xmm3"); + &pmuludq("xmm3","xmm7"); # a[3]*b[0] + &movdqa (&QWP(0x10,"esp"),"xmm2"); + + &movd ("xmm1",&DWP(4*5,"esi")); + &pshufd ("xmm0","xmm0",0b11001100); + &movdqa (&QWP(0x40,"ebx"),"xmm0"); + &pmuludq("xmm0","xmm7"); # a[4]*b[0] + &paddq ("xmm3","xmm5"); # a[3]*b[0]+lw(a[0]*b[0]), reduction step + &movdqa (&QWP(0x20,"esp"),"xmm3"); + + &movd ("xmm2",&DWP(4*6,"esi")); + &pshufd ("xmm1","xmm1",0b11001100); + &movdqa (&QWP(0x50,"ebx"),"xmm1"); + &pmuludq("xmm1","xmm7"); # a[5]*b[0] + &movdqa (&QWP(0x30,"esp"),"xmm0"); + &pshufd("xmm4","xmm5",0b10110001); # xmm4 = xmm5<<32, reduction step + + &movd ("xmm3",&DWP(4*7,"esi")); + &pshufd ("xmm2","xmm2",0b11001100); + &movdqa (&QWP(0x60,"ebx"),"xmm2"); + &pmuludq("xmm2","xmm7"); # a[6]*b[0] + &movdqa (&QWP(0x40,"esp"),"xmm1"); + &psubq ("xmm4","xmm5"); # xmm4 = xmm5*0xffffffff, reduction step + + &movd ("xmm0",&DWP(0,"ebp")); # b[1] -> 0000.00xy + &pshufd ("xmm3","xmm3",0b11001100); + &movdqa (&QWP(0x70,"ebx"),"xmm3"); + &pmuludq("xmm3","xmm7"); # a[7]*b[0] + + &pshuflw("xmm7","xmm0",0b11011100); # 0000.00xy -> 0000.0x0y + &movdqa ("xmm0",&QWP(0x00,"ebx")); # pre-load converted a[0] + &pshufd ("xmm7","xmm7",0b11011100); # 0000.0x0y -> 000x.000y + + &mov ("ecx",6); + &lea ("ebp",&DWP(4,"ebp")); + &jmp (&label("madd_sse2")); + +&set_label("madd_sse2",16); + &paddq ("xmm2","xmm5"); # a[6]*b[i-1]+lw(a[0]*b[i-1]), reduction step [modulo-scheduled] + &paddq ("xmm3","xmm4"); # a[7]*b[i-1]+lw(a[0]*b[i-1])*0xffffffff, reduction step [modulo-scheduled] + &movdqa ("xmm1",&QWP(0x10,"ebx")); + &pmuludq("xmm0","xmm7"); # a[0]*b[i] + &movdqa(&QWP(0x50,"esp"),"xmm2"); + + &movdqa ("xmm2",&QWP(0x20,"ebx")); + &pmuludq("xmm1","xmm7"); # a[1]*b[i] + &movdqa(&QWP(0x60,"esp"),"xmm3"); + &paddq ("xmm0",&QWP(0x00,"esp")); + + &movdqa ("xmm3",&QWP(0x30,"ebx")); + &pmuludq("xmm2","xmm7"); # a[2]*b[i] + &movq ("xmm4","xmm0"); # clear upper 64 bits + &pslldq("xmm4",6); + &paddq ("xmm1",&QWP(0x10,"esp")); + &paddq ("xmm4","xmm0"); + &movdqa("xmm5","xmm4"); + &psrldq("xmm4",10); # upper 33 bits of a[0]*b[i]+t[0] + + &movdqa ("xmm0",&QWP(0x40,"ebx")); + &pmuludq("xmm3","xmm7"); # a[3]*b[i] + &paddq ("xmm1","xmm4"); # a[1]*b[i]+hw(a[0]*b[i]), carry + &paddq ("xmm2",&QWP(0x20,"esp")); + &movdqa (&QWP(0x00,"esp"),"xmm1"); + + &movdqa ("xmm1",&QWP(0x50,"ebx")); + &pmuludq("xmm0","xmm7"); # a[4]*b[i] + &paddq ("xmm3",&QWP(0x30,"esp")); + &movdqa (&QWP(0x10,"esp"),"xmm2"); + &pand ("xmm5","xmm6"); # lower 32 bits of a[0]*b[i] + + &movdqa ("xmm2",&QWP(0x60,"ebx")); + &pmuludq("xmm1","xmm7"); # a[5]*b[i] + &paddq ("xmm3","xmm5"); # a[3]*b[i]+lw(a[0]*b[i]), reduction step + &paddq ("xmm0",&QWP(0x40,"esp")); + &movdqa (&QWP(0x20,"esp"),"xmm3"); + &pshufd("xmm4","xmm5",0b10110001); # xmm4 = xmm5<<32, reduction step + + &movdqa ("xmm3","xmm7"); + &pmuludq("xmm2","xmm7"); # a[6]*b[i] + &movd ("xmm7",&DWP(0,"ebp")); # b[i++] -> 0000.00xy + &lea ("ebp",&DWP(4,"ebp")); + &paddq ("xmm1",&QWP(0x50,"esp")); + &psubq ("xmm4","xmm5"); # xmm4 = xmm5*0xffffffff, reduction step + &movdqa (&QWP(0x30,"esp"),"xmm0"); + &pshuflw("xmm7","xmm7",0b11011100); # 0000.00xy -> 0000.0x0y + + &pmuludq("xmm3",&QWP(0x70,"ebx")); # a[7]*b[i] + &pshufd("xmm7","xmm7",0b11011100); # 0000.0x0y -> 000x.000y + &movdqa("xmm0",&QWP(0x00,"ebx")); # pre-load converted a[0] + &movdqa (&QWP(0x40,"esp"),"xmm1"); + &paddq ("xmm2",&QWP(0x60,"esp")); + + &dec ("ecx"); + &jnz (&label("madd_sse2")); + + &paddq ("xmm2","xmm5"); # a[6]*b[6]+lw(a[0]*b[6]), reduction step [modulo-scheduled] + &paddq ("xmm3","xmm4"); # a[7]*b[6]+lw(a[0]*b[6])*0xffffffff, reduction step [modulo-scheduled] + &movdqa ("xmm1",&QWP(0x10,"ebx")); + &pmuludq("xmm0","xmm7"); # a[0]*b[7] + &movdqa(&QWP(0x50,"esp"),"xmm2"); + + &movdqa ("xmm2",&QWP(0x20,"ebx")); + &pmuludq("xmm1","xmm7"); # a[1]*b[7] + &movdqa(&QWP(0x60,"esp"),"xmm3"); + &paddq ("xmm0",&QWP(0x00,"esp")); + + &movdqa ("xmm3",&QWP(0x30,"ebx")); + &pmuludq("xmm2","xmm7"); # a[2]*b[7] + &movq ("xmm4","xmm0"); # clear upper 64 bits + &pslldq("xmm4",6); + &paddq ("xmm1",&QWP(0x10,"esp")); + &paddq ("xmm4","xmm0"); + &movdqa("xmm5","xmm4"); + &psrldq("xmm4",10); # upper 33 bits of a[0]*b[i]+t[0] + + &movdqa ("xmm0",&QWP(0x40,"ebx")); + &pmuludq("xmm3","xmm7"); # a[3]*b[7] + &paddq ("xmm1","xmm4"); # a[1]*b[7]+hw(a[0]*b[7]), carry + &paddq ("xmm2",&QWP(0x20,"esp")); + &movdqa (&QWP(0x00,"esp"),"xmm1"); + + &movdqa ("xmm1",&QWP(0x50,"ebx")); + &pmuludq("xmm0","xmm7"); # a[4]*b[7] + &paddq ("xmm3",&QWP(0x30,"esp")); + &movdqa (&QWP(0x10,"esp"),"xmm2"); + &pand ("xmm5","xmm6"); # lower 32 bits of a[0]*b[i] + + &movdqa ("xmm2",&QWP(0x60,"ebx")); + &pmuludq("xmm1","xmm7"); # a[5]*b[7] + &paddq ("xmm3","xmm5"); # reduction step + &paddq ("xmm0",&QWP(0x40,"esp")); + &movdqa (&QWP(0x20,"esp"),"xmm3"); + &pshufd("xmm4","xmm5",0b10110001); # xmm4 = xmm5<<32, reduction step + + &movdqa ("xmm3",&QWP(0x70,"ebx")); + &pmuludq("xmm2","xmm7"); # a[6]*b[7] + &paddq ("xmm1",&QWP(0x50,"esp")); + &psubq ("xmm4","xmm5"); # xmm4 = xmm5*0xffffffff, reduction step + &movdqa (&QWP(0x30,"esp"),"xmm0"); + + &pmuludq("xmm3","xmm7"); # a[7]*b[7] + &pcmpeqd("xmm7","xmm7"); + &movdqa ("xmm0",&QWP(0x00,"esp")); + &pslldq ("xmm7",8); + &movdqa (&QWP(0x40,"esp"),"xmm1"); + &paddq ("xmm2",&QWP(0x60,"esp")); + + &paddq ("xmm2","xmm5"); # a[6]*b[7]+lw(a[0]*b[7]), reduction step + &paddq ("xmm3","xmm4"); # a[6]*b[7]+lw(a[0]*b[7])*0xffffffff, reduction step + &movdqa(&QWP(0x50,"esp"),"xmm2"); + &movdqa(&QWP(0x60,"esp"),"xmm3"); + + &movdqa ("xmm1",&QWP(0x10,"esp")); + &movdqa ("xmm2",&QWP(0x20,"esp")); + &movdqa ("xmm3",&QWP(0x30,"esp")); + + &movq ("xmm4","xmm0"); # "flatten" + &pand ("xmm0","xmm7"); + &xor ("ebp","ebp"); + &pslldq ("xmm4",6); + &movq ("xmm5","xmm1"); + &paddq ("xmm0","xmm4"); + &pand ("xmm1","xmm7"); + &psrldq ("xmm0",6); + &movd ("eax","xmm0"); + &psrldq ("xmm0",4); + + &paddq ("xmm5","xmm0"); + &movdqa ("xmm0",&QWP(0x40,"esp")); + &sub ("eax",-1); # start subtracting modulus, + # this is used to determine + # if result is larger/smaller + # than modulus (see below) + &pslldq ("xmm5",6); + &movq ("xmm4","xmm2"); + &paddq ("xmm1","xmm5"); + &pand ("xmm2","xmm7"); + &psrldq ("xmm1",6); + &mov (&DWP(4*0,"edi"),"eax"); + &movd ("eax","xmm1"); + &psrldq ("xmm1",4); + + &paddq ("xmm4","xmm1"); + &movdqa ("xmm1",&QWP(0x50,"esp")); + &sbb ("eax",-1); + &pslldq ("xmm4",6); + &movq ("xmm5","xmm3"); + &paddq ("xmm2","xmm4"); + &pand ("xmm3","xmm7"); + &psrldq ("xmm2",6); + &mov (&DWP(4*1,"edi"),"eax"); + &movd ("eax","xmm2"); + &psrldq ("xmm2",4); + + &paddq ("xmm5","xmm2"); + &movdqa ("xmm2",&QWP(0x60,"esp")); + &sbb ("eax",-1); + &pslldq ("xmm5",6); + &movq ("xmm4","xmm0"); + &paddq ("xmm3","xmm5"); + &pand ("xmm0","xmm7"); + &psrldq ("xmm3",6); + &mov (&DWP(4*2,"edi"),"eax"); + &movd ("eax","xmm3"); + &psrldq ("xmm3",4); + + &paddq ("xmm4","xmm3"); + &sbb ("eax",0); + &pslldq ("xmm4",6); + &movq ("xmm5","xmm1"); + &paddq ("xmm0","xmm4"); + &pand ("xmm1","xmm7"); + &psrldq ("xmm0",6); + &mov (&DWP(4*3,"edi"),"eax"); + &movd ("eax","xmm0"); + &psrldq ("xmm0",4); + + &paddq ("xmm5","xmm0"); + &sbb ("eax",0); + &pslldq ("xmm5",6); + &movq ("xmm4","xmm2"); + &paddq ("xmm1","xmm5"); + &pand ("xmm2","xmm7"); + &psrldq ("xmm1",6); + &movd ("ebx","xmm1"); + &psrldq ("xmm1",4); + &mov ("esp","edx"); + + &paddq ("xmm4","xmm1"); + &pslldq ("xmm4",6); + &paddq ("xmm2","xmm4"); + &psrldq ("xmm2",6); + &movd ("ecx","xmm2"); + &psrldq ("xmm2",4); + &sbb ("ebx",0); + &movd ("edx","xmm2"); + &pextrw ("esi","xmm2",2); # top-most overflow bit + &sbb ("ecx",1); + &sbb ("edx",-1); + &sbb ("esi",0); # borrow from subtraction + + # Final step is "if result > mod, subtract mod", and at this point + # we have result - mod written to output buffer, as well as borrow + # bit from this subtraction, and if borrow bit is set, we add + # modulus back. + # + # Note that because mod has special form, i.e. consists of + # 0xffffffff, 1 and 0s, we can conditionally synthesize it by + # assigning borrow bit to one register, %ebp, and its negative + # to another, %esi. But we started by calculating %esi... + + &sub ("ebp","esi"); + &add (&DWP(4*0,"edi"),"esi"); # add modulus or zero + &adc (&DWP(4*1,"edi"),"esi"); + &adc (&DWP(4*2,"edi"),"esi"); + &adc (&DWP(4*3,"edi"),0); + &adc ("eax",0); + &adc ("ebx",0); + &mov (&DWP(4*4,"edi"),"eax"); + &adc ("ecx","ebp"); + &mov (&DWP(4*5,"edi"),"ebx"); + &adc ("edx","esi"); + &mov (&DWP(4*6,"edi"),"ecx"); + &mov (&DWP(4*7,"edi"),"edx"); + + &ret (); + +&set_label("mul_mont_ialu",16); } + + ######################################## + # IALU code path suitable for all CPUs. + ######################################## + # stack layout: + # +------------------------------------+< %esp + # | 8 32-bit temporary words, accessed | + # | as circular buffer | + # . . + # . . + # +------------------------------------+< +32 + # | offloaded destination pointer | + # +------------------------------------+ + # | unused | + # +------------------------------------+< +40 + &sub ("esp",10*4); + + &mov ("eax",&DWP(0*4,"esi")); # a[0] + &mov ("ebx",&DWP(0*4,"ebp")); # b[0] + &mov (&DWP(8*4,"esp"),"edi"); # off-load dst ptr + + &mul ("ebx"); # a[0]*b[0] + &mov (&DWP(0*4,"esp"),"eax"); # t[0] + &mov ("eax",&DWP(1*4,"esi")); + &mov ("ecx","edx") + + &mul ("ebx"); # a[1]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(2*4,"esi")); + &adc ("edx",0); + &mov (&DWP(1*4,"esp"),"ecx"); # t[1] + &mov ("ecx","edx"); + + &mul ("ebx"); # a[2]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(3*4,"esi")); + &adc ("edx",0); + &mov (&DWP(2*4,"esp"),"ecx"); # t[2] + &mov ("ecx","edx"); + + &mul ("ebx"); # a[3]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(4*4,"esi")); + &adc ("edx",0); + &mov (&DWP(3*4,"esp"),"ecx"); # t[3] + &mov ("ecx","edx"); + + &mul ("ebx"); # a[4]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(5*4,"esi")); + &adc ("edx",0); + &mov (&DWP(4*4,"esp"),"ecx"); # t[4] + &mov ("ecx","edx"); + + &mul ("ebx"); # a[5]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(6*4,"esi")); + &adc ("edx",0); + &mov (&DWP(5*4,"esp"),"ecx"); # t[5] + &mov ("ecx","edx"); + + &mul ("ebx"); # a[6]*b[0] + &add ("ecx","eax"); + &mov ("eax",&DWP(7*4,"esi")); + &adc ("edx",0); + &mov (&DWP(6*4,"esp"),"ecx"); # t[6] + &mov ("ecx","edx"); + + &xor ("edi","edi"); # initial top-most carry + &mul ("ebx"); # a[7]*b[0] + &add ("ecx","eax"); # t[7] + &mov ("eax",&DWP(0*4,"esp")); # t[0] + &adc ("edx",0); # t[8] + +for ($i=0;$i<7;$i++) { + my $j=$i+1; + + # Reduction iteration is normally performed by accumulating + # result of multiplication of modulus by "magic" digit [and + # omitting least significant word, which is guaranteed to + # be 0], but thanks to special form of modulus and "magic" + # digit being equal to least significant word, it can be + # performed with additions and subtractions alone. Indeed: + # + # ffff.0001.0000.0000.0000.ffff.ffff.ffff + # * abcd + # + xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we + # rewrite above as: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.abcd + # + abcd.0000.abcd.0000.0000.abcd.0000.0000.0000 + # - abcd.0000.0000.0000.0000.0000.0000.abcd + # + # or marking redundant operations: + # + # xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.---- + # + abcd.0000.abcd.0000.0000.abcd.----.----.---- + # - abcd.----.----.----.----.----.----.---- + + &add (&DWP((($i+3)%8)*4,"esp"),"eax"); # t[3]+=t[0] + &adc (&DWP((($i+4)%8)*4,"esp"),0); # t[4]+=0 + &adc (&DWP((($i+5)%8)*4,"esp"),0); # t[5]+=0 + &adc (&DWP((($i+6)%8)*4,"esp"),"eax"); # t[6]+=t[0] + &adc ("ecx",0); # t[7]+=0 + &adc ("edx","eax"); # t[8]+=t[0] + &adc ("edi",0); # top-most carry + &mov ("ebx",&DWP($j*4,"ebp")); # b[i] + &sub ("ecx","eax"); # t[7]-=t[0] + &mov ("eax",&DWP(0*4,"esi")); # a[0] + &sbb ("edx",0); # t[8]-=0 + &mov (&DWP((($i+7)%8)*4,"esp"),"ecx"); + &sbb ("edi",0); # top-most carry, + # keep in mind that + # netto result is + # *addition* of value + # with (abcd<<32)-abcd + # on top, so that + # underflow is + # impossible, because + # (abcd<<32)-abcd + # doesn't underflow + &mov (&DWP((($i+8)%8)*4,"esp"),"edx"); + + &mul ("ebx"); # a[0]*b[i] + &add ("eax",&DWP((($j+0)%8)*4,"esp")); + &adc ("edx",0); + &mov (&DWP((($j+0)%8)*4,"esp"),"eax"); + &mov ("eax",&DWP(1*4,"esi")); + &mov ("ecx","edx") + + &mul ("ebx"); # a[1]*b[i] + &add ("ecx",&DWP((($j+1)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(2*4,"esi")); + &mov (&DWP((($j+1)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[2]*b[i] + &add ("ecx",&DWP((($j+2)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(3*4,"esi")); + &mov (&DWP((($j+2)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[3]*b[i] + &add ("ecx",&DWP((($j+3)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(4*4,"esi")); + &mov (&DWP((($j+3)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[4]*b[i] + &add ("ecx",&DWP((($j+4)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(5*4,"esi")); + &mov (&DWP((($j+4)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[5]*b[i] + &add ("ecx",&DWP((($j+5)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(6*4,"esi")); + &mov (&DWP((($j+5)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[6]*b[i] + &add ("ecx",&DWP((($j+6)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); + &adc ("edx",0); + &mov ("eax",&DWP(7*4,"esi")); + &mov (&DWP((($j+6)%8)*4,"esp"),"ecx"); + &mov ("ecx","edx"); + + &mul ("ebx"); # a[7]*b[i] + &add ("ecx",&DWP((($j+7)%8)*4,"esp")); + &adc ("edx",0); + &add ("ecx","eax"); # t[7] + &mov ("eax",&DWP((($j+0)%8)*4,"esp")); # t[0] + &adc ("edx","edi"); # t[8] + &mov ("edi",0); + &adc ("edi",0); # top-most carry +} + &mov ("ebp",&DWP(8*4,"esp")); # restore dst ptr + &xor ("esi","esi"); + my $j=$i+1; + + # last multiplication-less reduction + &add (&DWP((($i+3)%8)*4,"esp"),"eax"); # t[3]+=t[0] + &adc (&DWP((($i+4)%8)*4,"esp"),0); # t[4]+=0 + &adc (&DWP((($i+5)%8)*4,"esp"),0); # t[5]+=0 + &adc (&DWP((($i+6)%8)*4,"esp"),"eax"); # t[6]+=t[0] + &adc ("ecx",0); # t[7]+=0 + &adc ("edx","eax"); # t[8]+=t[0] + &adc ("edi",0); # top-most carry + &mov ("ebx",&DWP((($j+1)%8)*4,"esp")); + &sub ("ecx","eax"); # t[7]-=t[0] + &mov ("eax",&DWP((($j+0)%8)*4,"esp")); + &sbb ("edx",0); # t[8]-=0 + &mov (&DWP((($i+7)%8)*4,"esp"),"ecx"); + &sbb ("edi",0); # top-most carry + &mov (&DWP((($i+8)%8)*4,"esp"),"edx"); + + # Final step is "if result > mod, subtract mod", but we do it + # "other way around", namely write result - mod to output buffer + # and if subtraction borrowed, add modulus back. + + &mov ("ecx",&DWP((($j+2)%8)*4,"esp")); + &sub ("eax",-1); + &mov ("edx",&DWP((($j+3)%8)*4,"esp")); + &sbb ("ebx",-1); + &mov (&DWP(0*4,"ebp"),"eax"); + &sbb ("ecx",-1); + &mov (&DWP(1*4,"ebp"),"ebx"); + &sbb ("edx",0); + &mov (&DWP(2*4,"ebp"),"ecx"); + &mov (&DWP(3*4,"ebp"),"edx"); + + &mov ("eax",&DWP((($j+4)%8)*4,"esp")); + &mov ("ebx",&DWP((($j+5)%8)*4,"esp")); + &mov ("ecx",&DWP((($j+6)%8)*4,"esp")); + &sbb ("eax",0); + &mov ("edx",&DWP((($j+7)%8)*4,"esp")); + &sbb ("ebx",0); + &sbb ("ecx",1); + &sbb ("edx",-1); + &sbb ("edi",0); + + # Note that because mod has special form, i.e. consists of + # 0xffffffff, 1 and 0s, we can conditionally synthesize it by + # assigning borrow bit to one register, %ebp, and its negative + # to another, %esi. But we started by calculating %esi... + + &sub ("esi","edi"); + &add (&DWP(0*4,"ebp"),"edi"); # add modulus or zero + &adc (&DWP(1*4,"ebp"),"edi"); + &adc (&DWP(2*4,"ebp"),"edi"); + &adc (&DWP(3*4,"ebp"),0); + &adc ("eax",0); + &adc ("ebx",0); + &mov (&DWP(4*4,"ebp"),"eax"); + &adc ("ecx","esi"); + &mov (&DWP(5*4,"ebp"),"ebx"); + &adc ("edx","edi"); + &mov (&DWP(6*4,"ebp"),"ecx"); + &mov ("edi","ebp"); # fulfill contract + &mov (&DWP(7*4,"ebp"),"edx"); + + &add ("esp",10*4); + &ret (); +&function_end_B("_ecp_nistz256_mul_mont"); + +######################################################################## +# void ecp_nistz256_scatter_w5(void *edi,const P256_POINT *esi, +# int ebp); +&function_begin("ecp_nistz256_scatter_w5"); + &mov ("edi",&wparam(0)); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + + &lea ("edi",&DWP(128-4,"edi","ebp",4)); + &mov ("ebp",96/16); +&set_label("scatter_w5_loop"); + &mov ("eax",&DWP(0,"esi")); + &mov ("ebx",&DWP(4,"esi")); + &mov ("ecx",&DWP(8,"esi")); + &mov ("edx",&DWP(12,"esi")); + &lea ("esi",&DWP(16,"esi")); + &mov (&DWP(64*0-128,"edi"),"eax"); + &mov (&DWP(64*1-128,"edi"),"ebx"); + &mov (&DWP(64*2-128,"edi"),"ecx"); + &mov (&DWP(64*3-128,"edi"),"edx"); + &lea ("edi",&DWP(64*4,"edi")); + &dec ("ebp"); + &jnz (&label("scatter_w5_loop")); +&function_end("ecp_nistz256_scatter_w5"); + +######################################################################## +# void ecp_nistz256_gather_w5(P256_POINT *edi,const void *esi, +# int ebp); +&function_begin("ecp_nistz256_gather_w5"); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + + &lea ("esi",&DWP(0,"esi","ebp",4)); + &neg ("ebp"); + &sar ("ebp",31); + &mov ("edi",&wparam(0)); + &lea ("esi",&DWP(0,"esi","ebp",4)); + + for($i=0;$i<24;$i+=4) { + &mov ("eax",&DWP(64*($i+0),"esi")); + &mov ("ebx",&DWP(64*($i+1),"esi")); + &mov ("ecx",&DWP(64*($i+2),"esi")); + &mov ("edx",&DWP(64*($i+3),"esi")); + &and ("eax","ebp"); + &and ("ebx","ebp"); + &and ("ecx","ebp"); + &and ("edx","ebp"); + &mov (&DWP(4*($i+0),"edi"),"eax"); + &mov (&DWP(4*($i+1),"edi"),"ebx"); + &mov (&DWP(4*($i+2),"edi"),"ecx"); + &mov (&DWP(4*($i+3),"edi"),"edx"); + } +&function_end("ecp_nistz256_gather_w5"); + +######################################################################## +# void ecp_nistz256_scatter_w7(void *edi,const P256_POINT_AFFINE *esi, +# int ebp); +&function_begin("ecp_nistz256_scatter_w7"); + &mov ("edi",&wparam(0)); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + + &lea ("edi",&DWP(-1,"edi","ebp")); + &mov ("ebp",64/4); +&set_label("scatter_w7_loop"); + &mov ("eax",&DWP(0,"esi")); + &lea ("esi",&DWP(4,"esi")); + &mov (&BP(64*0,"edi"),"al"); + &mov (&BP(64*1,"edi"),"ah"); + &shr ("eax",16); + &mov (&BP(64*2,"edi"),"al"); + &mov (&BP(64*3,"edi"),"ah"); + &lea ("edi",&DWP(64*4,"edi")); + &dec ("ebp"); + &jnz (&label("scatter_w7_loop")); +&function_end("ecp_nistz256_scatter_w7"); + +######################################################################## +# void ecp_nistz256_gather_w7(P256_POINT_AFFINE *edi,const void *esi, +# int ebp); +&function_begin("ecp_nistz256_gather_w7"); + &mov ("esi",&wparam(1)); + &mov ("ebp",&wparam(2)); + + &add ("esi","ebp"); + &neg ("ebp"), + &sar ("ebp",31); + &mov ("edi",&wparam(0)); + &lea ("esi",&DWP(0,"esi","ebp")); + + for($i=0;$i<64;$i+=4) { + &movz ("eax",&BP(64*($i+0),"esi")); + &movz ("ebx",&BP(64*($i+1),"esi")); + &movz ("ecx",&BP(64*($i+2),"esi")); + &and ("eax","ebp"); + &movz ("edx",&BP(64*($i+3),"esi")); + &and ("ebx","ebp"); + &mov (&BP($i+0,"edi"),"al"); + &and ("ecx","ebp"); + &mov (&BP($i+1,"edi"),"bl"); + &and ("edx","ebp"); + &mov (&BP($i+2,"edi"),"cl"); + &mov (&BP($i+3,"edi"),"dl"); + } +&function_end("ecp_nistz256_gather_w7"); + +######################################################################## +# following subroutines are "literal" implementation of those found in +# ecp_nistz256.c +# +######################################################################## +# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp); +# +&static_label("point_double_shortcut"); +&function_begin("ecp_nistz256_point_double"); +{ my ($S,$M,$Zsqr,$in_x,$tmp0)=map(32*$_,(0..4)); + + &mov ("esi",&wparam(1)); + + # above map() describes stack layout with 5 temporary + # 256-bit vectors on top, then we take extra word for + # OPENSSL_ia32cap_P copy. + &stack_push(8*5+1); + if ($sse2) { + &call ("_picup_eax"); + &set_label("pic"); + &picmeup("edx","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("ebp",&DWP(0,"edx")); } + +&set_label("point_double_shortcut"); + &mov ("eax",&DWP(0,"esi")); # copy in_x + &mov ("ebx",&DWP(4,"esi")); + &mov ("ecx",&DWP(8,"esi")); + &mov ("edx",&DWP(12,"esi")); + &mov (&DWP($in_x+0,"esp"),"eax"); + &mov (&DWP($in_x+4,"esp"),"ebx"); + &mov (&DWP($in_x+8,"esp"),"ecx"); + &mov (&DWP($in_x+12,"esp"),"edx"); + &mov ("eax",&DWP(16,"esi")); + &mov ("ebx",&DWP(20,"esi")); + &mov ("ecx",&DWP(24,"esi")); + &mov ("edx",&DWP(28,"esi")); + &mov (&DWP($in_x+16,"esp"),"eax"); + &mov (&DWP($in_x+20,"esp"),"ebx"); + &mov (&DWP($in_x+24,"esp"),"ecx"); + &mov (&DWP($in_x+28,"esp"),"edx"); + &mov (&DWP(32*5,"esp"),"ebp"); # OPENSSL_ia32cap_P copy + + &lea ("ebp",&DWP(32,"esi")); + &lea ("esi",&DWP(32,"esi")); + &lea ("edi",&DWP($S,"esp")); + &call ("_ecp_nistz256_add"); # p256_mul_by_2(S, in_y); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &mov ("esi",64); + &add ("esi",&wparam(1)); + &lea ("edi",&DWP($Zsqr,"esp")); + &mov ("ebp","esi"); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Zsqr, in_z); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($S,"esp")); + &lea ("ebp",&DWP($S,"esp")); + &lea ("edi",&DWP($S,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(S, S); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &mov ("ebp",&wparam(1)); + &lea ("esi",&DWP(32,"ebp")); + &lea ("ebp",&DWP(64,"ebp")); + &lea ("edi",&DWP($tmp0,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(tmp0, in_z, in_y); + + &lea ("esi",&DWP($in_x,"esp")); + &lea ("ebp",&DWP($Zsqr,"esp")); + &lea ("edi",&DWP($M,"esp")); + &call ("_ecp_nistz256_add"); # p256_add(M, in_x, Zsqr); + + &mov ("edi",64); + &lea ("esi",&DWP($tmp0,"esp")); + &lea ("ebp",&DWP($tmp0,"esp")); + &add ("edi",&wparam(0)); + &call ("_ecp_nistz256_add"); # p256_mul_by_2(res_z, tmp0); + + &lea ("esi",&DWP($in_x,"esp")); + &lea ("ebp",&DWP($Zsqr,"esp")); + &lea ("edi",&DWP($Zsqr,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(Zsqr, in_x, Zsqr); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($S,"esp")); + &lea ("ebp",&DWP($S,"esp")); + &lea ("edi",&DWP($tmp0,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(tmp0, S); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($M,"esp")); + &lea ("ebp",&DWP($Zsqr,"esp")); + &lea ("edi",&DWP($M,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(M, M, Zsqr); + + &mov ("edi",32); + &lea ("esi",&DWP($tmp0,"esp")); + &add ("edi",&wparam(0)); + &call ("_ecp_nistz256_div_by_2"); # p256_div_by_2(res_y, tmp0); + + &lea ("esi",&DWP($M,"esp")); + &lea ("ebp",&DWP($M,"esp")); + &lea ("edi",&DWP($tmp0,"esp")); + &call ("_ecp_nistz256_add"); # 1/2 p256_mul_by_3(M, M); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in_x,"esp")); + &lea ("ebp",&DWP($S,"esp")); + &lea ("edi",&DWP($S,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S, S, in_x); + + &lea ("esi",&DWP($tmp0,"esp")); + &lea ("ebp",&DWP($M,"esp")); + &lea ("edi",&DWP($M,"esp")); + &call ("_ecp_nistz256_add"); # 2/2 p256_mul_by_3(M, M); + + &lea ("esi",&DWP($S,"esp")); + &lea ("ebp",&DWP($S,"esp")); + &lea ("edi",&DWP($tmp0,"esp")); + &call ("_ecp_nistz256_add"); # p256_mul_by_2(tmp0, S); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($M,"esp")); + &lea ("ebp",&DWP($M,"esp")); + &mov ("edi",&wparam(0)); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(res_x, M); + + &mov ("esi","edi"); # %edi is still res_x here + &lea ("ebp",&DWP($tmp0,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_x, res_x, tmp0); + + &lea ("esi",&DWP($S,"esp")); + &mov ("ebp","edi"); # %edi is still res_x + &lea ("edi",&DWP($S,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(S, S, res_x); + + &mov ("eax",&DWP(32*5,"esp")); # OPENSSL_ia32cap_P copy + &mov ("esi","edi"); # %edi is still &S + &lea ("ebp",&DWP($M,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S, S, M); + + &mov ("ebp",32); + &lea ("esi",&DWP($S,"esp")); + &add ("ebp",&wparam(0)); + &mov ("edi","ebp"); + &call ("_ecp_nistz256_sub"); # p256_sub(res_y, S, res_y); + + &stack_pop(8*5+1); +} &function_end("ecp_nistz256_point_double"); + +######################################################################## +# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1, +# const P256_POINT *in2); +&function_begin("ecp_nistz256_point_add"); +{ my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y,$in2_z, + $H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2)=map(32*$_,(0..17)); + my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); + + &mov ("esi",&wparam(2)); + + # above map() describes stack layout with 18 temporary + # 256-bit vectors on top, then we take extra words for + # !in1infty, !in2infty, result of check for zero and + # OPENSSL_ia32cap_P copy. [one unused word for padding] + &stack_push(8*18+5); + if ($sse2) { + &call ("_picup_eax"); + &set_label("pic"); + &picmeup("edx","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("ebp",&DWP(0,"edx")); } + + &lea ("edi",&DWP($in2_x,"esp")); + for($i=0;$i<96;$i+=16) { + &mov ("eax",&DWP($i+0,"esi")); # copy in2 + &mov ("ebx",&DWP($i+4,"esi")); + &mov ("ecx",&DWP($i+8,"esi")); + &mov ("edx",&DWP($i+12,"esi")); + &mov (&DWP($i+0,"edi"),"eax"); + &mov (&DWP(32*18+12,"esp"),"ebp") if ($i==0); + &mov ("ebp","eax") if ($i==64); + &or ("ebp","eax") if ($i>64); + &mov (&DWP($i+4,"edi"),"ebx"); + &or ("ebp","ebx") if ($i>=64); + &mov (&DWP($i+8,"edi"),"ecx"); + &or ("ebp","ecx") if ($i>=64); + &mov (&DWP($i+12,"edi"),"edx"); + &or ("ebp","edx") if ($i>=64); + } + &xor ("eax","eax"); + &mov ("esi",&wparam(1)); + &sub ("eax","ebp"); + &or ("ebp","eax"); + &sar ("ebp",31); + &mov (&DWP(32*18+4,"esp"),"ebp"); # !in2infty + + &lea ("edi",&DWP($in1_x,"esp")); + for($i=0;$i<96;$i+=16) { + &mov ("eax",&DWP($i+0,"esi")); # copy in1 + &mov ("ebx",&DWP($i+4,"esi")); + &mov ("ecx",&DWP($i+8,"esi")); + &mov ("edx",&DWP($i+12,"esi")); + &mov (&DWP($i+0,"edi"),"eax"); + &mov ("ebp","eax") if ($i==64); + &or ("ebp","eax") if ($i>64); + &mov (&DWP($i+4,"edi"),"ebx"); + &or ("ebp","ebx") if ($i>=64); + &mov (&DWP($i+8,"edi"),"ecx"); + &or ("ebp","ecx") if ($i>=64); + &mov (&DWP($i+12,"edi"),"edx"); + &or ("ebp","edx") if ($i>=64); + } + &xor ("eax","eax"); + &sub ("eax","ebp"); + &or ("ebp","eax"); + &sar ("ebp",31); + &mov (&DWP(32*18+0,"esp"),"ebp"); # !in1infty + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_z,"esp")); + &lea ("ebp",&DWP($in2_z,"esp")); + &lea ("edi",&DWP($Z2sqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Z2sqr, in2_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in1_z,"esp")); + &lea ("ebp",&DWP($in1_z,"esp")); + &lea ("edi",&DWP($Z1sqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Z1sqr, in1_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($Z2sqr,"esp")); + &lea ("ebp",&DWP($in2_z,"esp")); + &lea ("edi",&DWP($S1,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S1, Z2sqr, in2_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($Z1sqr,"esp")); + &lea ("ebp",&DWP($in1_z,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, Z1sqr, in1_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in1_y,"esp")); + &lea ("ebp",&DWP($S1,"esp")); + &lea ("edi",&DWP($S1,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S1, S1, in1_y); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_y,"esp")); + &lea ("ebp",&DWP($S2,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, S2, in2_y); + + &lea ("esi",&DWP($S2,"esp")); + &lea ("ebp",&DWP($S1,"esp")); + &lea ("edi",&DWP($R,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(R, S2, S1); + + &or ("ebx","eax"); # see if result is zero + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &or ("ebx","ecx"); + &or ("ebx","edx"); + &or ("ebx",&DWP(0,"edi")); + &or ("ebx",&DWP(4,"edi")); + &lea ("esi",&DWP($in1_x,"esp")); + &or ("ebx",&DWP(8,"edi")); + &lea ("ebp",&DWP($Z2sqr,"esp")); + &or ("ebx",&DWP(12,"edi")); + &lea ("edi",&DWP($U1,"esp")); + &mov (&DWP(32*18+8,"esp"),"ebx"); + + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(U1, in1_x, Z2sqr); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_x,"esp")); + &lea ("ebp",&DWP($Z1sqr,"esp")); + &lea ("edi",&DWP($U2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(U2, in2_x, Z1sqr); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($U1,"esp")); + &lea ("edi",&DWP($H,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(H, U2, U1); + + &or ("eax","ebx"); # see if result is zero + &or ("eax","ecx"); + &or ("eax","edx"); + &or ("eax",&DWP(0,"edi")); + &or ("eax",&DWP(4,"edi")); + &or ("eax",&DWP(8,"edi")); + &or ("eax",&DWP(12,"edi")); + + &data_byte(0x3e); # predict taken + &jnz (&label("add_proceed")); # is_equal(U1,U2)? + + &mov ("eax",&DWP(32*18+0,"esp")); + &and ("eax",&DWP(32*18+4,"esp")); + &mov ("ebx",&DWP(32*18+8,"esp")); + &jz (&label("add_proceed")); # (in1infty || in2infty)? + &test ("ebx","ebx"); + &jz (&label("add_double")); # is_equal(S1,S2)? + + &mov ("edi",&wparam(0)); + &xor ("eax","eax"); + &mov ("ecx",96/4); + &data_byte(0xfc,0xf3,0xab); # cld; stosd + &jmp (&label("add_done")); + +&set_label("add_double",16); + &mov ("esi",&wparam(1)); + &mov ("ebp",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &add ("esp",4*((8*18+5)-(8*5+1))); # difference in frame sizes + &jmp (&label("point_double_shortcut")); + +&set_label("add_proceed",16); + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($R,"esp")); + &lea ("ebp",&DWP($R,"esp")); + &lea ("edi",&DWP($Rsqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Rsqr, R); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($H,"esp")); + &lea ("ebp",&DWP($in1_z,"esp")); + &lea ("edi",&DWP($res_z,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(res_z, H, in1_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($H,"esp")); + &lea ("ebp",&DWP($H,"esp")); + &lea ("edi",&DWP($Hsqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Hsqr, H); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_z,"esp")); + &lea ("ebp",&DWP($res_z,"esp")); + &lea ("edi",&DWP($res_z,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(res_z, res_z, in2_z); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($Hsqr,"esp")); + &lea ("ebp",&DWP($U1,"esp")); + &lea ("edi",&DWP($U2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(U2, U1, Hsqr); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($H,"esp")); + &lea ("ebp",&DWP($Hsqr,"esp")); + &lea ("edi",&DWP($Hcub,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(Hcub, Hsqr, H); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($U2,"esp")); + &lea ("edi",&DWP($Hsqr,"esp")); + &call ("_ecp_nistz256_add"); # p256_mul_by_2(Hsqr, U2); + + &lea ("esi",&DWP($Rsqr,"esp")); + &lea ("ebp",&DWP($Hsqr,"esp")); + &lea ("edi",&DWP($res_x,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_x, Rsqr, Hsqr); + + &lea ("esi",&DWP($res_x,"esp")); + &lea ("ebp",&DWP($Hcub,"esp")); + &lea ("edi",&DWP($res_x,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_x, res_x, Hcub); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($res_x,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_y, U2, res_x); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($Hcub,"esp")); + &lea ("ebp",&DWP($S1,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, S1, Hcub); + + &mov ("eax",&DWP(32*18+12,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($R,"esp")); + &lea ("ebp",&DWP($res_y,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(res_y, R, res_y); + + &lea ("esi",&DWP($res_y,"esp")); + &lea ("ebp",&DWP($S2,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_y, res_y, S2); + + &mov ("ebp",&DWP(32*18+0,"esp")); # !in1infty + &mov ("esi",&DWP(32*18+4,"esp")); # !in2infty + &mov ("edi",&wparam(0)); + &mov ("edx","ebp"); + ¬ ("ebp"); + &and ("edx","esi"); + &and ("ebp","esi"); + ¬ ("esi"); + + ######################################## + # conditional moves + for($i=64;$i<96;$i+=4) { + &mov ("eax","edx"); + &and ("eax",&DWP($res_x+$i,"esp")); + &mov ("ebx","ebp"); + &and ("ebx",&DWP($in2_x+$i,"esp")); + &mov ("ecx","esi"); + &and ("ecx",&DWP($in1_x+$i,"esp")); + &or ("eax","ebx"); + &or ("eax","ecx"); + &mov (&DWP($i,"edi"),"eax"); + } + for($i=0;$i<64;$i+=4) { + &mov ("eax","edx"); + &and ("eax",&DWP($res_x+$i,"esp")); + &mov ("ebx","ebp"); + &and ("ebx",&DWP($in2_x+$i,"esp")); + &mov ("ecx","esi"); + &and ("ecx",&DWP($in1_x+$i,"esp")); + &or ("eax","ebx"); + &or ("eax","ecx"); + &mov (&DWP($i,"edi"),"eax"); + } + &set_label("add_done"); + &stack_pop(8*18+5); +} &function_end("ecp_nistz256_point_add"); + +######################################################################## +# void ecp_nistz256_point_add_affine(P256_POINT *out, +# const P256_POINT *in1, +# const P256_POINT_AFFINE *in2); +&function_begin("ecp_nistz256_point_add_affine"); +{ + my ($res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y, + $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..14)); + my $Z1sqr = $S2; + my @ONE_mont=(1,0,0,-1,-1,-1,-2,0); + + &mov ("esi",&wparam(1)); + + # above map() describes stack layout with 15 temporary + # 256-bit vectors on top, then we take extra words for + # !in1infty, !in2infty, and OPENSSL_ia32cap_P copy. + &stack_push(8*15+3); + if ($sse2) { + &call ("_picup_eax"); + &set_label("pic"); + &picmeup("edx","OPENSSL_ia32cap_P","eax",&label("pic")); + &mov ("ebp",&DWP(0,"edx")); } + + &lea ("edi",&DWP($in1_x,"esp")); + for($i=0;$i<96;$i+=16) { + &mov ("eax",&DWP($i+0,"esi")); # copy in1 + &mov ("ebx",&DWP($i+4,"esi")); + &mov ("ecx",&DWP($i+8,"esi")); + &mov ("edx",&DWP($i+12,"esi")); + &mov (&DWP($i+0,"edi"),"eax"); + &mov (&DWP(32*15+8,"esp"),"ebp") if ($i==0); + &mov ("ebp","eax") if ($i==64); + &or ("ebp","eax") if ($i>64); + &mov (&DWP($i+4,"edi"),"ebx"); + &or ("ebp","ebx") if ($i>=64); + &mov (&DWP($i+8,"edi"),"ecx"); + &or ("ebp","ecx") if ($i>=64); + &mov (&DWP($i+12,"edi"),"edx"); + &or ("ebp","edx") if ($i>=64); + } + &xor ("eax","eax"); + &mov ("esi",&wparam(2)); + &sub ("eax","ebp"); + &or ("ebp","eax"); + &sar ("ebp",31); + &mov (&DWP(32*15+0,"esp"),"ebp"); # !in1infty + + &lea ("edi",&DWP($in2_x,"esp")); + for($i=0;$i<64;$i+=16) { + &mov ("eax",&DWP($i+0,"esi")); # copy in2 + &mov ("ebx",&DWP($i+4,"esi")); + &mov ("ecx",&DWP($i+8,"esi")); + &mov ("edx",&DWP($i+12,"esi")); + &mov (&DWP($i+0,"edi"),"eax"); + &mov ("ebp","eax") if ($i==0); + &or ("ebp","eax") if ($i!=0); + &mov (&DWP($i+4,"edi"),"ebx"); + &or ("ebp","ebx"); + &mov (&DWP($i+8,"edi"),"ecx"); + &or ("ebp","ecx"); + &mov (&DWP($i+12,"edi"),"edx"); + &or ("ebp","edx"); + } + &xor ("ebx","ebx"); + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &sub ("ebx","ebp"); + &lea ("esi",&DWP($in1_z,"esp")); + &or ("ebx","ebp"); + &lea ("ebp",&DWP($in1_z,"esp")); + &sar ("ebx",31); + &lea ("edi",&DWP($Z1sqr,"esp")); + &mov (&DWP(32*15+4,"esp"),"ebx"); # !in2infty + + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Z1sqr, in1_z); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_x,"esp")); + &mov ("ebp","edi"); # %esi is stull &Z1sqr + &lea ("edi",&DWP($U2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(U2, Z1sqr, in2_x); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in1_z,"esp")); + &lea ("ebp",&DWP($Z1sqr,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, Z1sqr, in1_z); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($in1_x,"esp")); + &lea ("edi",&DWP($H,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(H, U2, in1_x); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in2_y,"esp")); + &lea ("ebp",&DWP($S2,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, S2, in2_y); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in1_z,"esp")); + &lea ("ebp",&DWP($H,"esp")); + &lea ("edi",&DWP($res_z,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(res_z, H, in1_z); + + &lea ("esi",&DWP($S2,"esp")); + &lea ("ebp",&DWP($in1_y,"esp")); + &lea ("edi",&DWP($R,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(R, S2, in1_y); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($H,"esp")); + &lea ("ebp",&DWP($H,"esp")); + &lea ("edi",&DWP($Hsqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Hsqr, H); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($R,"esp")); + &lea ("ebp",&DWP($R,"esp")); + &lea ("edi",&DWP($Rsqr,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_sqr_mont(Rsqr, R); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($in1_x,"esp")); + &lea ("ebp",&DWP($Hsqr,"esp")); + &lea ("edi",&DWP($U2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(U2, in1_x, Hsqr); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($H,"esp")); + &lea ("ebp",&DWP($Hsqr,"esp")); + &lea ("edi",&DWP($Hcub,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(Hcub, Hsqr, H); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($U2,"esp")); + &lea ("edi",&DWP($Hsqr,"esp")); + &call ("_ecp_nistz256_add"); # p256_mul_by_2(Hsqr, U2); + + &lea ("esi",&DWP($Rsqr,"esp")); + &lea ("ebp",&DWP($Hsqr,"esp")); + &lea ("edi",&DWP($res_x,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_x, Rsqr, Hsqr); + + &lea ("esi",&DWP($res_x,"esp")); + &lea ("ebp",&DWP($Hcub,"esp")); + &lea ("edi",&DWP($res_x,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_x, res_x, Hcub); + + &lea ("esi",&DWP($U2,"esp")); + &lea ("ebp",&DWP($res_x,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_y, U2, res_x); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($Hcub,"esp")); + &lea ("ebp",&DWP($in1_y,"esp")); + &lea ("edi",&DWP($S2,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(S2, Hcub, in1_y); + + &mov ("eax",&DWP(32*15+8,"esp")); # OPENSSL_ia32cap_P copy + &lea ("esi",&DWP($R,"esp")); + &lea ("ebp",&DWP($res_y,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_mul_mont"); # p256_mul_mont(res_y, res_y, R); + + &lea ("esi",&DWP($res_y,"esp")); + &lea ("ebp",&DWP($S2,"esp")); + &lea ("edi",&DWP($res_y,"esp")); + &call ("_ecp_nistz256_sub"); # p256_sub(res_y, res_y, S2); + + &mov ("ebp",&DWP(32*15+0,"esp")); # !in1infty + &mov ("esi",&DWP(32*15+4,"esp")); # !in2infty + &mov ("edi",&wparam(0)); + &mov ("edx","ebp"); + ¬ ("ebp"); + &and ("edx","esi"); + &and ("ebp","esi"); + ¬ ("esi"); + + ######################################## + # conditional moves + for($i=64;$i<96;$i+=4) { + my $one=@ONE_mont[($i-64)/4]; + + &mov ("eax","edx"); + &and ("eax",&DWP($res_x+$i,"esp")); + &mov ("ebx","ebp") if ($one && $one!=-1); + &and ("ebx",$one) if ($one && $one!=-1); + &mov ("ecx","esi"); + &and ("ecx",&DWP($in1_x+$i,"esp")); + &or ("eax",$one==-1?"ebp":"ebx") if ($one); + &or ("eax","ecx"); + &mov (&DWP($i,"edi"),"eax"); + } + for($i=0;$i<64;$i+=4) { + &mov ("eax","edx"); + &and ("eax",&DWP($res_x+$i,"esp")); + &mov ("ebx","ebp"); + &and ("ebx",&DWP($in2_x+$i,"esp")); + &mov ("ecx","esi"); + &and ("ecx",&DWP($in1_x+$i,"esp")); + &or ("eax","ebx"); + &or ("eax","ecx"); + &mov (&DWP($i,"edi"),"eax"); + } + &stack_pop(8*15+3); +} &function_end("ecp_nistz256_point_add_affine"); + +&asm_finish(); + +close STDOUT; diff --git a/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86_64.pl b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86_64.pl new file mode 100755 index 0000000..714e852 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/asm/ecp_nistz256-x86_64.pl @@ -0,0 +1,3083 @@ +#! /usr/bin/env perl +# Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. +# +# Licensed under the OpenSSL license (the "License"). You may not use +# this file except in compliance with the License. You can obtain a copy +# in the file LICENSE in the source distribution or at +# https://www.openssl.org/source/license.html + + +############################################################################## +# # +# Copyright 2014 Intel Corporation # +# # +# Licensed under the Apache License, Version 2.0 (the "License"); # +# you may not use this file except in compliance with the License. # +# You may obtain a copy of the License at # +# # +# http://www.apache.org/licenses/LICENSE-2.0 # +# # +# Unless required by applicable law or agreed to in writing, software # +# distributed under the License is distributed on an "AS IS" BASIS, # +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # +# See the License for the specific language governing permissions and # +# limitations under the License. # +# # +############################################################################## +# # +# Developers and authors: # +# Shay Gueron (1, 2), and Vlad Krasnov (1) # +# (1) Intel Corporation, Israel Development Center # +# (2) University of Haifa # +# Reference: # +# S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with# +# 256 Bit Primes" # +# # +############################################################################## + +# Further optimization by <appro@openssl.org>: +# +# this/original with/without -DECP_NISTZ256_ASM(*) +# Opteron +12-49% +110-150% +# Bulldozer +14-45% +175-210% +# P4 +18-46% n/a :-( +# Westmere +12-34% +80-87% +# Sandy Bridge +9-35% +110-120% +# Ivy Bridge +9-35% +110-125% +# Haswell +8-37% +140-160% +# Broadwell +18-58% +145-210% +# Atom +15-50% +130-180% +# VIA Nano +43-160% +300-480% +# +# (*) "without -DECP_NISTZ256_ASM" refers to build with +# "enable-ec_nistp_64_gcc_128"; +# +# Ranges denote minimum and maximum improvement coefficients depending +# on benchmark. Lower coefficients are for ECDSA sign, relatively fastest +# server-side operation. Keep in mind that +100% means 2x improvement. + +$flavour = shift; +$output = shift; +if ($flavour =~ /\./) { $output = $flavour; undef $flavour; } + +$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/); + +$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; +( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or +( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or +die "can't locate x86_64-xlate.pl"; + +open OUT,"| \"$^X\" \"$xlate\" $flavour \"$output\""; +*STDOUT=*OUT; + +if (`$ENV{CC} -Wa,-v -c -o /dev/null -x assembler /dev/null 2>&1` + =~ /GNU assembler version ([2-9]\.[0-9]+)/) { + $avx = ($1>=2.19) + ($1>=2.22); + $addx = ($1>=2.23); +} + +if (!$addx && $win64 && ($flavour =~ /nasm/ || $ENV{ASM} =~ /nasm/) && + `nasm -v 2>&1` =~ /NASM version ([2-9]\.[0-9]+)/) { + $avx = ($1>=2.09) + ($1>=2.10); + $addx = ($1>=2.10); +} + +if (!$addx && $win64 && ($flavour =~ /masm/ || $ENV{ASM} =~ /ml64/) && + `ml64 2>&1` =~ /Version ([0-9]+)\./) { + $avx = ($1>=10) + ($1>=11); + $addx = ($1>=12); +} + +if (!$addx && `$ENV{CC} -v 2>&1` =~ /((?:^clang|LLVM) version|.*based on LLVM) ([3-9])\.([0-9]+)/) { + my $ver = $2 + $3/100.0; # 3.1->3.01, 3.10->3.10 + $avx = ($ver>=3.0) + ($ver>=3.01); + $addx = ($ver>=3.03); +} + +$code.=<<___; +.text +.extern OPENSSL_ia32cap_P + +# The polynomial +.align 64 +.Lpoly: +.quad 0xffffffffffffffff, 0x00000000ffffffff, 0x0000000000000000, 0xffffffff00000001 + +# 2^512 mod P precomputed for NIST P256 polynomial +.LRR: +.quad 0x0000000000000003, 0xfffffffbffffffff, 0xfffffffffffffffe, 0x00000004fffffffd + +.LOne: +.long 1,1,1,1,1,1,1,1 +.LTwo: +.long 2,2,2,2,2,2,2,2 +.LThree: +.long 3,3,3,3,3,3,3,3 +.LONE_mont: +.quad 0x0000000000000001, 0xffffffff00000000, 0xffffffffffffffff, 0x00000000fffffffe +___ + +{ +################################################################################ +# void ecp_nistz256_mul_by_2(uint64_t res[4], uint64_t a[4]); + +my ($a0,$a1,$a2,$a3)=map("%r$_",(8..11)); +my ($t0,$t1,$t2,$t3,$t4)=("%rax","%rdx","%rcx","%r12","%r13"); +my ($r_ptr,$a_ptr,$b_ptr)=("%rdi","%rsi","%rdx"); + +$code.=<<___; + +.globl ecp_nistz256_mul_by_2 +.type ecp_nistz256_mul_by_2,\@function,2 +.align 64 +ecp_nistz256_mul_by_2: + push %r12 + push %r13 + + mov 8*0($a_ptr), $a0 + xor $t4,$t4 + mov 8*1($a_ptr), $a1 + add $a0, $a0 # a0:a3+a0:a3 + mov 8*2($a_ptr), $a2 + adc $a1, $a1 + mov 8*3($a_ptr), $a3 + lea .Lpoly(%rip), $a_ptr + mov $a0, $t0 + adc $a2, $a2 + adc $a3, $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub 8*0($a_ptr), $a0 + mov $a2, $t2 + sbb 8*1($a_ptr), $a1 + sbb 8*2($a_ptr), $a2 + mov $a3, $t3 + sbb 8*3($a_ptr), $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2 + +################################################################################ +# void ecp_nistz256_div_by_2(uint64_t res[4], uint64_t a[4]); +.globl ecp_nistz256_div_by_2 +.type ecp_nistz256_div_by_2,\@function,2 +.align 32 +ecp_nistz256_div_by_2: + push %r12 + push %r13 + + mov 8*0($a_ptr), $a0 + mov 8*1($a_ptr), $a1 + mov 8*2($a_ptr), $a2 + mov $a0, $t0 + mov 8*3($a_ptr), $a3 + lea .Lpoly(%rip), $a_ptr + + mov $a1, $t1 + xor $t4, $t4 + add 8*0($a_ptr), $a0 + mov $a2, $t2 + adc 8*1($a_ptr), $a1 + adc 8*2($a_ptr), $a2 + mov $a3, $t3 + adc 8*3($a_ptr), $a3 + adc \$0, $t4 + xor $a_ptr, $a_ptr # borrow $a_ptr + test \$1, $t0 + + cmovz $t0, $a0 + cmovz $t1, $a1 + cmovz $t2, $a2 + cmovz $t3, $a3 + cmovz $a_ptr, $t4 + + mov $a1, $t0 # a0:a3>>1 + shr \$1, $a0 + shl \$63, $t0 + mov $a2, $t1 + shr \$1, $a1 + or $t0, $a0 + shl \$63, $t1 + mov $a3, $t2 + shr \$1, $a2 + or $t1, $a1 + shl \$63, $t2 + shr \$1, $a3 + shl \$63, $t4 + or $t2, $a2 + or $t4, $a3 + + mov $a0, 8*0($r_ptr) + mov $a1, 8*1($r_ptr) + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2 + +################################################################################ +# void ecp_nistz256_mul_by_3(uint64_t res[4], uint64_t a[4]); +.globl ecp_nistz256_mul_by_3 +.type ecp_nistz256_mul_by_3,\@function,2 +.align 32 +ecp_nistz256_mul_by_3: + push %r12 + push %r13 + + mov 8*0($a_ptr), $a0 + xor $t4, $t4 + mov 8*1($a_ptr), $a1 + add $a0, $a0 # a0:a3+a0:a3 + mov 8*2($a_ptr), $a2 + adc $a1, $a1 + mov 8*3($a_ptr), $a3 + mov $a0, $t0 + adc $a2, $a2 + adc $a3, $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub \$-1, $a0 + mov $a2, $t2 + sbb .Lpoly+8*1(%rip), $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb .Lpoly+8*3(%rip), $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + cmovc $t2, $a2 + cmovc $t3, $a3 + + xor $t4, $t4 + add 8*0($a_ptr), $a0 # a0:a3+=a_ptr[0:3] + adc 8*1($a_ptr), $a1 + mov $a0, $t0 + adc 8*2($a_ptr), $a2 + adc 8*3($a_ptr), $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub \$-1, $a0 + mov $a2, $t2 + sbb .Lpoly+8*1(%rip), $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb .Lpoly+8*3(%rip), $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3 + +################################################################################ +# void ecp_nistz256_add(uint64_t res[4], uint64_t a[4], uint64_t b[4]); +.globl ecp_nistz256_add +.type ecp_nistz256_add,\@function,3 +.align 32 +ecp_nistz256_add: + push %r12 + push %r13 + + mov 8*0($a_ptr), $a0 + xor $t4, $t4 + mov 8*1($a_ptr), $a1 + mov 8*2($a_ptr), $a2 + mov 8*3($a_ptr), $a3 + lea .Lpoly(%rip), $a_ptr + + add 8*0($b_ptr), $a0 + adc 8*1($b_ptr), $a1 + mov $a0, $t0 + adc 8*2($b_ptr), $a2 + adc 8*3($b_ptr), $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub 8*0($a_ptr), $a0 + mov $a2, $t2 + sbb 8*1($a_ptr), $a1 + sbb 8*2($a_ptr), $a2 + mov $a3, $t3 + sbb 8*3($a_ptr), $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_add,.-ecp_nistz256_add + +################################################################################ +# void ecp_nistz256_sub(uint64_t res[4], uint64_t a[4], uint64_t b[4]); +.globl ecp_nistz256_sub +.type ecp_nistz256_sub,\@function,3 +.align 32 +ecp_nistz256_sub: + push %r12 + push %r13 + + mov 8*0($a_ptr), $a0 + xor $t4, $t4 + mov 8*1($a_ptr), $a1 + mov 8*2($a_ptr), $a2 + mov 8*3($a_ptr), $a3 + lea .Lpoly(%rip), $a_ptr + + sub 8*0($b_ptr), $a0 + sbb 8*1($b_ptr), $a1 + mov $a0, $t0 + sbb 8*2($b_ptr), $a2 + sbb 8*3($b_ptr), $a3 + mov $a1, $t1 + sbb \$0, $t4 + + add 8*0($a_ptr), $a0 + mov $a2, $t2 + adc 8*1($a_ptr), $a1 + adc 8*2($a_ptr), $a2 + mov $a3, $t3 + adc 8*3($a_ptr), $a3 + test $t4, $t4 + + cmovz $t0, $a0 + cmovz $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovz $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovz $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_sub,.-ecp_nistz256_sub + +################################################################################ +# void ecp_nistz256_neg(uint64_t res[4], uint64_t a[4]); +.globl ecp_nistz256_neg +.type ecp_nistz256_neg,\@function,2 +.align 32 +ecp_nistz256_neg: + push %r12 + push %r13 + + xor $a0, $a0 + xor $a1, $a1 + xor $a2, $a2 + xor $a3, $a3 + xor $t4, $t4 + + sub 8*0($a_ptr), $a0 + sbb 8*1($a_ptr), $a1 + sbb 8*2($a_ptr), $a2 + mov $a0, $t0 + sbb 8*3($a_ptr), $a3 + lea .Lpoly(%rip), $a_ptr + mov $a1, $t1 + sbb \$0, $t4 + + add 8*0($a_ptr), $a0 + mov $a2, $t2 + adc 8*1($a_ptr), $a1 + adc 8*2($a_ptr), $a2 + mov $a3, $t3 + adc 8*3($a_ptr), $a3 + test $t4, $t4 + + cmovz $t0, $a0 + cmovz $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovz $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovz $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_neg,.-ecp_nistz256_neg +___ +} +{ +my ($r_ptr,$a_ptr,$b_org,$b_ptr)=("%rdi","%rsi","%rdx","%rbx"); +my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5,$acc6,$acc7)=map("%r$_",(8..15)); +my ($t0,$t1,$t2,$t3,$t4)=("%rcx","%rbp","%rbx","%rdx","%rax"); +my ($poly1,$poly3)=($acc6,$acc7); + +$code.=<<___; +################################################################################ +# void ecp_nistz256_to_mont( +# uint64_t res[4], +# uint64_t in[4]); +.globl ecp_nistz256_to_mont +.type ecp_nistz256_to_mont,\@function,2 +.align 32 +ecp_nistz256_to_mont: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx +___ +$code.=<<___; + lea .LRR(%rip), $b_org + jmp .Lmul_mont +.size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont + +################################################################################ +# void ecp_nistz256_mul_mont( +# uint64_t res[4], +# uint64_t a[4], +# uint64_t b[4]); + +.globl ecp_nistz256_mul_mont +.type ecp_nistz256_mul_mont,\@function,3 +.align 32 +ecp_nistz256_mul_mont: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx +___ +$code.=<<___; +.Lmul_mont: + push %rbp + push %rbx + push %r12 + push %r13 + push %r14 + push %r15 +___ +$code.=<<___ if ($addx); + cmp \$0x80100, %ecx + je .Lmul_montx +___ +$code.=<<___; + mov $b_org, $b_ptr + mov 8*0($b_org), %rax + mov 8*0($a_ptr), $acc1 + mov 8*1($a_ptr), $acc2 + mov 8*2($a_ptr), $acc3 + mov 8*3($a_ptr), $acc4 + + call __ecp_nistz256_mul_montq +___ +$code.=<<___ if ($addx); + jmp .Lmul_mont_done + +.align 32 +.Lmul_montx: + mov $b_org, $b_ptr + mov 8*0($b_org), %rdx + mov 8*0($a_ptr), $acc1 + mov 8*1($a_ptr), $acc2 + mov 8*2($a_ptr), $acc3 + mov 8*3($a_ptr), $acc4 + lea -128($a_ptr), $a_ptr # control u-op density + + call __ecp_nistz256_mul_montx +___ +$code.=<<___; +.Lmul_mont_done: + pop %r15 + pop %r14 + pop %r13 + pop %r12 + pop %rbx + pop %rbp + ret +.size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont + +.type __ecp_nistz256_mul_montq,\@abi-omnipotent +.align 32 +__ecp_nistz256_mul_montq: + ######################################################################## + # Multiply a by b[0] + mov %rax, $t1 + mulq $acc1 + mov .Lpoly+8*1(%rip),$poly1 + mov %rax, $acc0 + mov $t1, %rax + mov %rdx, $acc1 + + mulq $acc2 + mov .Lpoly+8*3(%rip),$poly3 + add %rax, $acc1 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $acc2 + + mulq $acc3 + add %rax, $acc2 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $acc3 + + mulq $acc4 + add %rax, $acc3 + mov $acc0, %rax + adc \$0, %rdx + xor $acc5, $acc5 + mov %rdx, $acc4 + + ######################################################################## + # First reduction step + # Basically now we want to multiply acc[0] by p256, + # and add the result to the acc. + # Due to the special form of p256 we do some optimizations + # + # acc[0] x p256[0..1] = acc[0] x 2^96 - acc[0] + # then we add acc[0] and get acc[0] x 2^96 + + mov $acc0, $t1 + shl \$32, $acc0 + mulq $poly3 + shr \$32, $t1 + add $acc0, $acc1 # +=acc[0]<<96 + adc $t1, $acc2 + adc %rax, $acc3 + mov 8*1($b_ptr), %rax + adc %rdx, $acc4 + adc \$0, $acc5 + xor $acc0, $acc0 + + ######################################################################## + # Multiply by b[1] + mov %rax, $t1 + mulq 8*0($a_ptr) + add %rax, $acc1 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*1($a_ptr) + add $t0, $acc2 + adc \$0, %rdx + add %rax, $acc2 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*2($a_ptr) + add $t0, $acc3 + adc \$0, %rdx + add %rax, $acc3 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*3($a_ptr) + add $t0, $acc4 + adc \$0, %rdx + add %rax, $acc4 + mov $acc1, %rax + adc %rdx, $acc5 + adc \$0, $acc0 + + ######################################################################## + # Second reduction step + mov $acc1, $t1 + shl \$32, $acc1 + mulq $poly3 + shr \$32, $t1 + add $acc1, $acc2 + adc $t1, $acc3 + adc %rax, $acc4 + mov 8*2($b_ptr), %rax + adc %rdx, $acc5 + adc \$0, $acc0 + xor $acc1, $acc1 + + ######################################################################## + # Multiply by b[2] + mov %rax, $t1 + mulq 8*0($a_ptr) + add %rax, $acc2 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*1($a_ptr) + add $t0, $acc3 + adc \$0, %rdx + add %rax, $acc3 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*2($a_ptr) + add $t0, $acc4 + adc \$0, %rdx + add %rax, $acc4 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*3($a_ptr) + add $t0, $acc5 + adc \$0, %rdx + add %rax, $acc5 + mov $acc2, %rax + adc %rdx, $acc0 + adc \$0, $acc1 + + ######################################################################## + # Third reduction step + mov $acc2, $t1 + shl \$32, $acc2 + mulq $poly3 + shr \$32, $t1 + add $acc2, $acc3 + adc $t1, $acc4 + adc %rax, $acc5 + mov 8*3($b_ptr), %rax + adc %rdx, $acc0 + adc \$0, $acc1 + xor $acc2, $acc2 + + ######################################################################## + # Multiply by b[3] + mov %rax, $t1 + mulq 8*0($a_ptr) + add %rax, $acc3 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*1($a_ptr) + add $t0, $acc4 + adc \$0, %rdx + add %rax, $acc4 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*2($a_ptr) + add $t0, $acc5 + adc \$0, %rdx + add %rax, $acc5 + mov $t1, %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq 8*3($a_ptr) + add $t0, $acc0 + adc \$0, %rdx + add %rax, $acc0 + mov $acc3, %rax + adc %rdx, $acc1 + adc \$0, $acc2 + + ######################################################################## + # Final reduction step + mov $acc3, $t1 + shl \$32, $acc3 + mulq $poly3 + shr \$32, $t1 + add $acc3, $acc4 + adc $t1, $acc5 + mov $acc4, $t0 + adc %rax, $acc0 + adc %rdx, $acc1 + mov $acc5, $t1 + adc \$0, $acc2 + + ######################################################################## + # Branch-less conditional subtraction of P + sub \$-1, $acc4 # .Lpoly[0] + mov $acc0, $t2 + sbb $poly1, $acc5 # .Lpoly[1] + sbb \$0, $acc0 # .Lpoly[2] + mov $acc1, $t3 + sbb $poly3, $acc1 # .Lpoly[3] + sbb \$0, $acc2 + + cmovc $t0, $acc4 + cmovc $t1, $acc5 + mov $acc4, 8*0($r_ptr) + cmovc $t2, $acc0 + mov $acc5, 8*1($r_ptr) + cmovc $t3, $acc1 + mov $acc0, 8*2($r_ptr) + mov $acc1, 8*3($r_ptr) + + ret +.size __ecp_nistz256_mul_montq,.-__ecp_nistz256_mul_montq + +################################################################################ +# void ecp_nistz256_sqr_mont( +# uint64_t res[4], +# uint64_t a[4]); + +# we optimize the square according to S.Gueron and V.Krasnov, +# "Speeding up Big-Number Squaring" +.globl ecp_nistz256_sqr_mont +.type ecp_nistz256_sqr_mont,\@function,2 +.align 32 +ecp_nistz256_sqr_mont: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx +___ +$code.=<<___; + push %rbp + push %rbx + push %r12 + push %r13 + push %r14 + push %r15 +___ +$code.=<<___ if ($addx); + cmp \$0x80100, %ecx + je .Lsqr_montx +___ +$code.=<<___; + mov 8*0($a_ptr), %rax + mov 8*1($a_ptr), $acc6 + mov 8*2($a_ptr), $acc7 + mov 8*3($a_ptr), $acc0 + + call __ecp_nistz256_sqr_montq +___ +$code.=<<___ if ($addx); + jmp .Lsqr_mont_done + +.align 32 +.Lsqr_montx: + mov 8*0($a_ptr), %rdx + mov 8*1($a_ptr), $acc6 + mov 8*2($a_ptr), $acc7 + mov 8*3($a_ptr), $acc0 + lea -128($a_ptr), $a_ptr # control u-op density + + call __ecp_nistz256_sqr_montx +___ +$code.=<<___; +.Lsqr_mont_done: + pop %r15 + pop %r14 + pop %r13 + pop %r12 + pop %rbx + pop %rbp + ret +.size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont + +.type __ecp_nistz256_sqr_montq,\@abi-omnipotent +.align 32 +__ecp_nistz256_sqr_montq: + mov %rax, $acc5 + mulq $acc6 # a[1]*a[0] + mov %rax, $acc1 + mov $acc7, %rax + mov %rdx, $acc2 + + mulq $acc5 # a[0]*a[2] + add %rax, $acc2 + mov $acc0, %rax + adc \$0, %rdx + mov %rdx, $acc3 + + mulq $acc5 # a[0]*a[3] + add %rax, $acc3 + mov $acc7, %rax + adc \$0, %rdx + mov %rdx, $acc4 + + ################################# + mulq $acc6 # a[1]*a[2] + add %rax, $acc3 + mov $acc0, %rax + adc \$0, %rdx + mov %rdx, $t1 + + mulq $acc6 # a[1]*a[3] + add %rax, $acc4 + mov $acc0, %rax + adc \$0, %rdx + add $t1, $acc4 + mov %rdx, $acc5 + adc \$0, $acc5 + + ################################# + mulq $acc7 # a[2]*a[3] + xor $acc7, $acc7 + add %rax, $acc5 + mov 8*0($a_ptr), %rax + mov %rdx, $acc6 + adc \$0, $acc6 + + add $acc1, $acc1 # acc1:6<<1 + adc $acc2, $acc2 + adc $acc3, $acc3 + adc $acc4, $acc4 + adc $acc5, $acc5 + adc $acc6, $acc6 + adc \$0, $acc7 + + mulq %rax + mov %rax, $acc0 + mov 8*1($a_ptr), %rax + mov %rdx, $t0 + + mulq %rax + add $t0, $acc1 + adc %rax, $acc2 + mov 8*2($a_ptr), %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq %rax + add $t0, $acc3 + adc %rax, $acc4 + mov 8*3($a_ptr), %rax + adc \$0, %rdx + mov %rdx, $t0 + + mulq %rax + add $t0, $acc5 + adc %rax, $acc6 + mov $acc0, %rax + adc %rdx, $acc7 + + mov .Lpoly+8*1(%rip), $a_ptr + mov .Lpoly+8*3(%rip), $t1 + + ########################################## + # Now the reduction + # First iteration + mov $acc0, $t0 + shl \$32, $acc0 + mulq $t1 + shr \$32, $t0 + add $acc0, $acc1 # +=acc[0]<<96 + adc $t0, $acc2 + adc %rax, $acc3 + mov $acc1, %rax + adc \$0, %rdx + + ########################################## + # Second iteration + mov $acc1, $t0 + shl \$32, $acc1 + mov %rdx, $acc0 + mulq $t1 + shr \$32, $t0 + add $acc1, $acc2 + adc $t0, $acc3 + adc %rax, $acc0 + mov $acc2, %rax + adc \$0, %rdx + + ########################################## + # Third iteration + mov $acc2, $t0 + shl \$32, $acc2 + mov %rdx, $acc1 + mulq $t1 + shr \$32, $t0 + add $acc2, $acc3 + adc $t0, $acc0 + adc %rax, $acc1 + mov $acc3, %rax + adc \$0, %rdx + + ########################################### + # Last iteration + mov $acc3, $t0 + shl \$32, $acc3 + mov %rdx, $acc2 + mulq $t1 + shr \$32, $t0 + add $acc3, $acc0 + adc $t0, $acc1 + adc %rax, $acc2 + adc \$0, %rdx + xor $acc3, $acc3 + + ############################################ + # Add the rest of the acc + add $acc0, $acc4 + adc $acc1, $acc5 + mov $acc4, $acc0 + adc $acc2, $acc6 + adc %rdx, $acc7 + mov $acc5, $acc1 + adc \$0, $acc3 + + sub \$-1, $acc4 # .Lpoly[0] + mov $acc6, $acc2 + sbb $a_ptr, $acc5 # .Lpoly[1] + sbb \$0, $acc6 # .Lpoly[2] + mov $acc7, $t0 + sbb $t1, $acc7 # .Lpoly[3] + sbb \$0, $acc3 + + cmovc $acc0, $acc4 + cmovc $acc1, $acc5 + mov $acc4, 8*0($r_ptr) + cmovc $acc2, $acc6 + mov $acc5, 8*1($r_ptr) + cmovc $t0, $acc7 + mov $acc6, 8*2($r_ptr) + mov $acc7, 8*3($r_ptr) + + ret +.size __ecp_nistz256_sqr_montq,.-__ecp_nistz256_sqr_montq +___ + +if ($addx) { +$code.=<<___; +.type __ecp_nistz256_mul_montx,\@abi-omnipotent +.align 32 +__ecp_nistz256_mul_montx: + ######################################################################## + # Multiply by b[0] + mulx $acc1, $acc0, $acc1 + mulx $acc2, $t0, $acc2 + mov \$32, $poly1 + xor $acc5, $acc5 # cf=0 + mulx $acc3, $t1, $acc3 + mov .Lpoly+8*3(%rip), $poly3 + adc $t0, $acc1 + mulx $acc4, $t0, $acc4 + mov $acc0, %rdx + adc $t1, $acc2 + shlx $poly1,$acc0,$t1 + adc $t0, $acc3 + shrx $poly1,$acc0,$t0 + adc \$0, $acc4 + + ######################################################################## + # First reduction step + add $t1, $acc1 + adc $t0, $acc2 + + mulx $poly3, $t0, $t1 + mov 8*1($b_ptr), %rdx + adc $t0, $acc3 + adc $t1, $acc4 + adc \$0, $acc5 + xor $acc0, $acc0 # $acc0=0,cf=0,of=0 + + ######################################################################## + # Multiply by b[1] + mulx 8*0+128($a_ptr), $t0, $t1 + adcx $t0, $acc1 + adox $t1, $acc2 + + mulx 8*1+128($a_ptr), $t0, $t1 + adcx $t0, $acc2 + adox $t1, $acc3 + + mulx 8*2+128($a_ptr), $t0, $t1 + adcx $t0, $acc3 + adox $t1, $acc4 + + mulx 8*3+128($a_ptr), $t0, $t1 + mov $acc1, %rdx + adcx $t0, $acc4 + shlx $poly1, $acc1, $t0 + adox $t1, $acc5 + shrx $poly1, $acc1, $t1 + + adcx $acc0, $acc5 + adox $acc0, $acc0 + adc \$0, $acc0 + + ######################################################################## + # Second reduction step + add $t0, $acc2 + adc $t1, $acc3 + + mulx $poly3, $t0, $t1 + mov 8*2($b_ptr), %rdx + adc $t0, $acc4 + adc $t1, $acc5 + adc \$0, $acc0 + xor $acc1 ,$acc1 # $acc1=0,cf=0,of=0 + + ######################################################################## + # Multiply by b[2] + mulx 8*0+128($a_ptr), $t0, $t1 + adcx $t0, $acc2 + adox $t1, $acc3 + + mulx 8*1+128($a_ptr), $t0, $t1 + adcx $t0, $acc3 + adox $t1, $acc4 + + mulx 8*2+128($a_ptr), $t0, $t1 + adcx $t0, $acc4 + adox $t1, $acc5 + + mulx 8*3+128($a_ptr), $t0, $t1 + mov $acc2, %rdx + adcx $t0, $acc5 + shlx $poly1, $acc2, $t0 + adox $t1, $acc0 + shrx $poly1, $acc2, $t1 + + adcx $acc1, $acc0 + adox $acc1, $acc1 + adc \$0, $acc1 + + ######################################################################## + # Third reduction step + add $t0, $acc3 + adc $t1, $acc4 + + mulx $poly3, $t0, $t1 + mov 8*3($b_ptr), %rdx + adc $t0, $acc5 + adc $t1, $acc0 + adc \$0, $acc1 + xor $acc2, $acc2 # $acc2=0,cf=0,of=0 + + ######################################################################## + # Multiply by b[3] + mulx 8*0+128($a_ptr), $t0, $t1 + adcx $t0, $acc3 + adox $t1, $acc4 + + mulx 8*1+128($a_ptr), $t0, $t1 + adcx $t0, $acc4 + adox $t1, $acc5 + + mulx 8*2+128($a_ptr), $t0, $t1 + adcx $t0, $acc5 + adox $t1, $acc0 + + mulx 8*3+128($a_ptr), $t0, $t1 + mov $acc3, %rdx + adcx $t0, $acc0 + shlx $poly1, $acc3, $t0 + adox $t1, $acc1 + shrx $poly1, $acc3, $t1 + + adcx $acc2, $acc1 + adox $acc2, $acc2 + adc \$0, $acc2 + + ######################################################################## + # Fourth reduction step + add $t0, $acc4 + adc $t1, $acc5 + + mulx $poly3, $t0, $t1 + mov $acc4, $t2 + mov .Lpoly+8*1(%rip), $poly1 + adc $t0, $acc0 + mov $acc5, $t3 + adc $t1, $acc1 + adc \$0, $acc2 + + ######################################################################## + # Branch-less conditional subtraction of P + xor %eax, %eax + mov $acc0, $t0 + sbb \$-1, $acc4 # .Lpoly[0] + sbb $poly1, $acc5 # .Lpoly[1] + sbb \$0, $acc0 # .Lpoly[2] + mov $acc1, $t1 + sbb $poly3, $acc1 # .Lpoly[3] + sbb \$0, $acc2 + + cmovc $t2, $acc4 + cmovc $t3, $acc5 + mov $acc4, 8*0($r_ptr) + cmovc $t0, $acc0 + mov $acc5, 8*1($r_ptr) + cmovc $t1, $acc1 + mov $acc0, 8*2($r_ptr) + mov $acc1, 8*3($r_ptr) + + ret +.size __ecp_nistz256_mul_montx,.-__ecp_nistz256_mul_montx + +.type __ecp_nistz256_sqr_montx,\@abi-omnipotent +.align 32 +__ecp_nistz256_sqr_montx: + mulx $acc6, $acc1, $acc2 # a[0]*a[1] + mulx $acc7, $t0, $acc3 # a[0]*a[2] + xor %eax, %eax + adc $t0, $acc2 + mulx $acc0, $t1, $acc4 # a[0]*a[3] + mov $acc6, %rdx + adc $t1, $acc3 + adc \$0, $acc4 + xor $acc5, $acc5 # $acc5=0,cf=0,of=0 + + ################################# + mulx $acc7, $t0, $t1 # a[1]*a[2] + adcx $t0, $acc3 + adox $t1, $acc4 + + mulx $acc0, $t0, $t1 # a[1]*a[3] + mov $acc7, %rdx + adcx $t0, $acc4 + adox $t1, $acc5 + adc \$0, $acc5 + + ################################# + mulx $acc0, $t0, $acc6 # a[2]*a[3] + mov 8*0+128($a_ptr), %rdx + xor $acc7, $acc7 # $acc7=0,cf=0,of=0 + adcx $acc1, $acc1 # acc1:6<<1 + adox $t0, $acc5 + adcx $acc2, $acc2 + adox $acc7, $acc6 # of=0 + + mulx %rdx, $acc0, $t1 + mov 8*1+128($a_ptr), %rdx + adcx $acc3, $acc3 + adox $t1, $acc1 + adcx $acc4, $acc4 + mulx %rdx, $t0, $t4 + mov 8*2+128($a_ptr), %rdx + adcx $acc5, $acc5 + adox $t0, $acc2 + adcx $acc6, $acc6 + .byte 0x67 + mulx %rdx, $t0, $t1 + mov 8*3+128($a_ptr), %rdx + adox $t4, $acc3 + adcx $acc7, $acc7 + adox $t0, $acc4 + mov \$32, $a_ptr + adox $t1, $acc5 + .byte 0x67,0x67 + mulx %rdx, $t0, $t4 + mov .Lpoly+8*3(%rip), %rdx + adox $t0, $acc6 + shlx $a_ptr, $acc0, $t0 + adox $t4, $acc7 + shrx $a_ptr, $acc0, $t4 + mov %rdx,$t1 + + # reduction step 1 + add $t0, $acc1 + adc $t4, $acc2 + + mulx $acc0, $t0, $acc0 + adc $t0, $acc3 + shlx $a_ptr, $acc1, $t0 + adc \$0, $acc0 + shrx $a_ptr, $acc1, $t4 + + # reduction step 2 + add $t0, $acc2 + adc $t4, $acc3 + + mulx $acc1, $t0, $acc1 + adc $t0, $acc0 + shlx $a_ptr, $acc2, $t0 + adc \$0, $acc1 + shrx $a_ptr, $acc2, $t4 + + # reduction step 3 + add $t0, $acc3 + adc $t4, $acc0 + + mulx $acc2, $t0, $acc2 + adc $t0, $acc1 + shlx $a_ptr, $acc3, $t0 + adc \$0, $acc2 + shrx $a_ptr, $acc3, $t4 + + # reduction step 4 + add $t0, $acc0 + adc $t4, $acc1 + + mulx $acc3, $t0, $acc3 + adc $t0, $acc2 + adc \$0, $acc3 + + xor $t3, $t3 + add $acc0, $acc4 # accumulate upper half + mov .Lpoly+8*1(%rip), $a_ptr + adc $acc1, $acc5 + mov $acc4, $acc0 + adc $acc2, $acc6 + adc $acc3, $acc7 + mov $acc5, $acc1 + adc \$0, $t3 + + sub \$-1, $acc4 # .Lpoly[0] + mov $acc6, $acc2 + sbb $a_ptr, $acc5 # .Lpoly[1] + sbb \$0, $acc6 # .Lpoly[2] + mov $acc7, $acc3 + sbb $t1, $acc7 # .Lpoly[3] + sbb \$0, $t3 + + cmovc $acc0, $acc4 + cmovc $acc1, $acc5 + mov $acc4, 8*0($r_ptr) + cmovc $acc2, $acc6 + mov $acc5, 8*1($r_ptr) + cmovc $acc3, $acc7 + mov $acc6, 8*2($r_ptr) + mov $acc7, 8*3($r_ptr) + + ret +.size __ecp_nistz256_sqr_montx,.-__ecp_nistz256_sqr_montx +___ +} +} +{ +my ($r_ptr,$in_ptr)=("%rdi","%rsi"); +my ($acc0,$acc1,$acc2,$acc3)=map("%r$_",(8..11)); +my ($t0,$t1,$t2)=("%rcx","%r12","%r13"); + +$code.=<<___; +################################################################################ +# void ecp_nistz256_from_mont( +# uint64_t res[4], +# uint64_t in[4]); +# This one performs Montgomery multiplication by 1, so we only need the reduction + +.globl ecp_nistz256_from_mont +.type ecp_nistz256_from_mont,\@function,2 +.align 32 +ecp_nistz256_from_mont: + push %r12 + push %r13 + + mov 8*0($in_ptr), %rax + mov .Lpoly+8*3(%rip), $t2 + mov 8*1($in_ptr), $acc1 + mov 8*2($in_ptr), $acc2 + mov 8*3($in_ptr), $acc3 + mov %rax, $acc0 + mov .Lpoly+8*1(%rip), $t1 + + ######################################### + # First iteration + mov %rax, $t0 + shl \$32, $acc0 + mulq $t2 + shr \$32, $t0 + add $acc0, $acc1 + adc $t0, $acc2 + adc %rax, $acc3 + mov $acc1, %rax + adc \$0, %rdx + + ######################################### + # Second iteration + mov $acc1, $t0 + shl \$32, $acc1 + mov %rdx, $acc0 + mulq $t2 + shr \$32, $t0 + add $acc1, $acc2 + adc $t0, $acc3 + adc %rax, $acc0 + mov $acc2, %rax + adc \$0, %rdx + + ########################################## + # Third iteration + mov $acc2, $t0 + shl \$32, $acc2 + mov %rdx, $acc1 + mulq $t2 + shr \$32, $t0 + add $acc2, $acc3 + adc $t0, $acc0 + adc %rax, $acc1 + mov $acc3, %rax + adc \$0, %rdx + + ########################################### + # Last iteration + mov $acc3, $t0 + shl \$32, $acc3 + mov %rdx, $acc2 + mulq $t2 + shr \$32, $t0 + add $acc3, $acc0 + adc $t0, $acc1 + mov $acc0, $t0 + adc %rax, $acc2 + mov $acc1, $in_ptr + adc \$0, %rdx + + ########################################### + # Branch-less conditional subtraction + sub \$-1, $acc0 + mov $acc2, %rax + sbb $t1, $acc1 + sbb \$0, $acc2 + mov %rdx, $acc3 + sbb $t2, %rdx + sbb $t2, $t2 + + cmovnz $t0, $acc0 + cmovnz $in_ptr, $acc1 + mov $acc0, 8*0($r_ptr) + cmovnz %rax, $acc2 + mov $acc1, 8*1($r_ptr) + cmovz %rdx, $acc3 + mov $acc2, 8*2($r_ptr) + mov $acc3, 8*3($r_ptr) + + pop %r13 + pop %r12 + ret +.size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont +___ +} +{ +my ($val,$in_t,$index)=$win64?("%rcx","%rdx","%r8d"):("%rdi","%rsi","%edx"); +my ($ONE,$INDEX,$Ra,$Rb,$Rc,$Rd,$Re,$Rf)=map("%xmm$_",(0..7)); +my ($M0,$T0a,$T0b,$T0c,$T0d,$T0e,$T0f,$TMP0)=map("%xmm$_",(8..15)); +my ($M1,$T2a,$T2b,$TMP2,$M2,$T2a,$T2b,$TMP2)=map("%xmm$_",(8..15)); + +$code.=<<___; +################################################################################ +# void ecp_nistz256_scatter_w5(uint64_t *val, uint64_t *in_t, int index); +.globl ecp_nistz256_scatter_w5 +.type ecp_nistz256_scatter_w5,\@abi-omnipotent +.align 32 +ecp_nistz256_scatter_w5: + lea -3($index,$index,2), $index + movdqa 0x00($in_t), %xmm0 + shl \$5, $index + movdqa 0x10($in_t), %xmm1 + movdqa 0x20($in_t), %xmm2 + movdqa 0x30($in_t), %xmm3 + movdqa 0x40($in_t), %xmm4 + movdqa 0x50($in_t), %xmm5 + movdqa %xmm0, 0x00($val,$index) + movdqa %xmm1, 0x10($val,$index) + movdqa %xmm2, 0x20($val,$index) + movdqa %xmm3, 0x30($val,$index) + movdqa %xmm4, 0x40($val,$index) + movdqa %xmm5, 0x50($val,$index) + + ret +.size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5 + +################################################################################ +# void ecp_nistz256_gather_w5(uint64_t *val, uint64_t *in_t, int index); +.globl ecp_nistz256_gather_w5 +.type ecp_nistz256_gather_w5,\@abi-omnipotent +.align 32 +ecp_nistz256_gather_w5: +___ +$code.=<<___ if ($avx>1); + mov OPENSSL_ia32cap_P+8(%rip), %eax + test \$`1<<5`, %eax + jnz .Lavx2_gather_w5 +___ +$code.=<<___ if ($win64); + lea -0x88(%rsp), %rax +.LSEH_begin_ecp_nistz256_gather_w5: + .byte 0x48,0x8d,0x60,0xe0 #lea -0x20(%rax), %rsp + .byte 0x0f,0x29,0x70,0xe0 #movaps %xmm6, -0x20(%rax) + .byte 0x0f,0x29,0x78,0xf0 #movaps %xmm7, -0x10(%rax) + .byte 0x44,0x0f,0x29,0x00 #movaps %xmm8, 0(%rax) + .byte 0x44,0x0f,0x29,0x48,0x10 #movaps %xmm9, 0x10(%rax) + .byte 0x44,0x0f,0x29,0x50,0x20 #movaps %xmm10, 0x20(%rax) + .byte 0x44,0x0f,0x29,0x58,0x30 #movaps %xmm11, 0x30(%rax) + .byte 0x44,0x0f,0x29,0x60,0x40 #movaps %xmm12, 0x40(%rax) + .byte 0x44,0x0f,0x29,0x68,0x50 #movaps %xmm13, 0x50(%rax) + .byte 0x44,0x0f,0x29,0x70,0x60 #movaps %xmm14, 0x60(%rax) + .byte 0x44,0x0f,0x29,0x78,0x70 #movaps %xmm15, 0x70(%rax) +___ +$code.=<<___; + movdqa .LOne(%rip), $ONE + movd $index, $INDEX + + pxor $Ra, $Ra + pxor $Rb, $Rb + pxor $Rc, $Rc + pxor $Rd, $Rd + pxor $Re, $Re + pxor $Rf, $Rf + + movdqa $ONE, $M0 + pshufd \$0, $INDEX, $INDEX + + mov \$16, %rax +.Lselect_loop_sse_w5: + + movdqa $M0, $TMP0 + paddd $ONE, $M0 + pcmpeqd $INDEX, $TMP0 + + movdqa 16*0($in_t), $T0a + movdqa 16*1($in_t), $T0b + movdqa 16*2($in_t), $T0c + movdqa 16*3($in_t), $T0d + movdqa 16*4($in_t), $T0e + movdqa 16*5($in_t), $T0f + lea 16*6($in_t), $in_t + + pand $TMP0, $T0a + pand $TMP0, $T0b + por $T0a, $Ra + pand $TMP0, $T0c + por $T0b, $Rb + pand $TMP0, $T0d + por $T0c, $Rc + pand $TMP0, $T0e + por $T0d, $Rd + pand $TMP0, $T0f + por $T0e, $Re + por $T0f, $Rf + + dec %rax + jnz .Lselect_loop_sse_w5 + + movdqu $Ra, 16*0($val) + movdqu $Rb, 16*1($val) + movdqu $Rc, 16*2($val) + movdqu $Rd, 16*3($val) + movdqu $Re, 16*4($val) + movdqu $Rf, 16*5($val) +___ +$code.=<<___ if ($win64); + movaps (%rsp), %xmm6 + movaps 0x10(%rsp), %xmm7 + movaps 0x20(%rsp), %xmm8 + movaps 0x30(%rsp), %xmm9 + movaps 0x40(%rsp), %xmm10 + movaps 0x50(%rsp), %xmm11 + movaps 0x60(%rsp), %xmm12 + movaps 0x70(%rsp), %xmm13 + movaps 0x80(%rsp), %xmm14 + movaps 0x90(%rsp), %xmm15 + lea 0xa8(%rsp), %rsp +.LSEH_end_ecp_nistz256_gather_w5: +___ +$code.=<<___; + ret +.size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5 + +################################################################################ +# void ecp_nistz256_scatter_w7(uint64_t *val, uint64_t *in_t, int index); +.globl ecp_nistz256_scatter_w7 +.type ecp_nistz256_scatter_w7,\@abi-omnipotent +.align 32 +ecp_nistz256_scatter_w7: + movdqu 0x00($in_t), %xmm0 + shl \$6, $index + movdqu 0x10($in_t), %xmm1 + movdqu 0x20($in_t), %xmm2 + movdqu 0x30($in_t), %xmm3 + movdqa %xmm0, 0x00($val,$index) + movdqa %xmm1, 0x10($val,$index) + movdqa %xmm2, 0x20($val,$index) + movdqa %xmm3, 0x30($val,$index) + + ret +.size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7 + +################################################################################ +# void ecp_nistz256_gather_w7(uint64_t *val, uint64_t *in_t, int index); +.globl ecp_nistz256_gather_w7 +.type ecp_nistz256_gather_w7,\@abi-omnipotent +.align 32 +ecp_nistz256_gather_w7: +___ +$code.=<<___ if ($avx>1); + mov OPENSSL_ia32cap_P+8(%rip), %eax + test \$`1<<5`, %eax + jnz .Lavx2_gather_w7 +___ +$code.=<<___ if ($win64); + lea -0x88(%rsp), %rax +.LSEH_begin_ecp_nistz256_gather_w7: + .byte 0x48,0x8d,0x60,0xe0 #lea -0x20(%rax), %rsp + .byte 0x0f,0x29,0x70,0xe0 #movaps %xmm6, -0x20(%rax) + .byte 0x0f,0x29,0x78,0xf0 #movaps %xmm7, -0x10(%rax) + .byte 0x44,0x0f,0x29,0x00 #movaps %xmm8, 0(%rax) + .byte 0x44,0x0f,0x29,0x48,0x10 #movaps %xmm9, 0x10(%rax) + .byte 0x44,0x0f,0x29,0x50,0x20 #movaps %xmm10, 0x20(%rax) + .byte 0x44,0x0f,0x29,0x58,0x30 #movaps %xmm11, 0x30(%rax) + .byte 0x44,0x0f,0x29,0x60,0x40 #movaps %xmm12, 0x40(%rax) + .byte 0x44,0x0f,0x29,0x68,0x50 #movaps %xmm13, 0x50(%rax) + .byte 0x44,0x0f,0x29,0x70,0x60 #movaps %xmm14, 0x60(%rax) + .byte 0x44,0x0f,0x29,0x78,0x70 #movaps %xmm15, 0x70(%rax) +___ +$code.=<<___; + movdqa .LOne(%rip), $M0 + movd $index, $INDEX + + pxor $Ra, $Ra + pxor $Rb, $Rb + pxor $Rc, $Rc + pxor $Rd, $Rd + + movdqa $M0, $ONE + pshufd \$0, $INDEX, $INDEX + mov \$64, %rax + +.Lselect_loop_sse_w7: + movdqa $M0, $TMP0 + paddd $ONE, $M0 + movdqa 16*0($in_t), $T0a + movdqa 16*1($in_t), $T0b + pcmpeqd $INDEX, $TMP0 + movdqa 16*2($in_t), $T0c + movdqa 16*3($in_t), $T0d + lea 16*4($in_t), $in_t + + pand $TMP0, $T0a + pand $TMP0, $T0b + por $T0a, $Ra + pand $TMP0, $T0c + por $T0b, $Rb + pand $TMP0, $T0d + por $T0c, $Rc + prefetcht0 255($in_t) + por $T0d, $Rd + + dec %rax + jnz .Lselect_loop_sse_w7 + + movdqu $Ra, 16*0($val) + movdqu $Rb, 16*1($val) + movdqu $Rc, 16*2($val) + movdqu $Rd, 16*3($val) +___ +$code.=<<___ if ($win64); + movaps (%rsp), %xmm6 + movaps 0x10(%rsp), %xmm7 + movaps 0x20(%rsp), %xmm8 + movaps 0x30(%rsp), %xmm9 + movaps 0x40(%rsp), %xmm10 + movaps 0x50(%rsp), %xmm11 + movaps 0x60(%rsp), %xmm12 + movaps 0x70(%rsp), %xmm13 + movaps 0x80(%rsp), %xmm14 + movaps 0x90(%rsp), %xmm15 + lea 0xa8(%rsp), %rsp +.LSEH_end_ecp_nistz256_gather_w7: +___ +$code.=<<___; + ret +.size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7 +___ +} +if ($avx>1) { +my ($val,$in_t,$index)=$win64?("%rcx","%rdx","%r8d"):("%rdi","%rsi","%edx"); +my ($TWO,$INDEX,$Ra,$Rb,$Rc)=map("%ymm$_",(0..4)); +my ($M0,$T0a,$T0b,$T0c,$TMP0)=map("%ymm$_",(5..9)); +my ($M1,$T1a,$T1b,$T1c,$TMP1)=map("%ymm$_",(10..14)); + +$code.=<<___; +################################################################################ +# void ecp_nistz256_avx2_gather_w5(uint64_t *val, uint64_t *in_t, int index); +.type ecp_nistz256_avx2_gather_w5,\@abi-omnipotent +.align 32 +ecp_nistz256_avx2_gather_w5: +.Lavx2_gather_w5: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -0x88(%rsp), %rax +.LSEH_begin_ecp_nistz256_avx2_gather_w5: + .byte 0x48,0x8d,0x60,0xe0 #lea -0x20(%rax), %rsp + .byte 0xc5,0xf8,0x29,0x70,0xe0 #vmovaps %xmm6, -0x20(%rax) + .byte 0xc5,0xf8,0x29,0x78,0xf0 #vmovaps %xmm7, -0x10(%rax) + .byte 0xc5,0x78,0x29,0x40,0x00 #vmovaps %xmm8, 8(%rax) + .byte 0xc5,0x78,0x29,0x48,0x10 #vmovaps %xmm9, 0x10(%rax) + .byte 0xc5,0x78,0x29,0x50,0x20 #vmovaps %xmm10, 0x20(%rax) + .byte 0xc5,0x78,0x29,0x58,0x30 #vmovaps %xmm11, 0x30(%rax) + .byte 0xc5,0x78,0x29,0x60,0x40 #vmovaps %xmm12, 0x40(%rax) + .byte 0xc5,0x78,0x29,0x68,0x50 #vmovaps %xmm13, 0x50(%rax) + .byte 0xc5,0x78,0x29,0x70,0x60 #vmovaps %xmm14, 0x60(%rax) + .byte 0xc5,0x78,0x29,0x78,0x70 #vmovaps %xmm15, 0x70(%rax) +___ +$code.=<<___; + vmovdqa .LTwo(%rip), $TWO + + vpxor $Ra, $Ra, $Ra + vpxor $Rb, $Rb, $Rb + vpxor $Rc, $Rc, $Rc + + vmovdqa .LOne(%rip), $M0 + vmovdqa .LTwo(%rip), $M1 + + vmovd $index, %xmm1 + vpermd $INDEX, $Ra, $INDEX + + mov \$8, %rax +.Lselect_loop_avx2_w5: + + vmovdqa 32*0($in_t), $T0a + vmovdqa 32*1($in_t), $T0b + vmovdqa 32*2($in_t), $T0c + + vmovdqa 32*3($in_t), $T1a + vmovdqa 32*4($in_t), $T1b + vmovdqa 32*5($in_t), $T1c + + vpcmpeqd $INDEX, $M0, $TMP0 + vpcmpeqd $INDEX, $M1, $TMP1 + + vpaddd $TWO, $M0, $M0 + vpaddd $TWO, $M1, $M1 + lea 32*6($in_t), $in_t + + vpand $TMP0, $T0a, $T0a + vpand $TMP0, $T0b, $T0b + vpand $TMP0, $T0c, $T0c + vpand $TMP1, $T1a, $T1a + vpand $TMP1, $T1b, $T1b + vpand $TMP1, $T1c, $T1c + + vpxor $T0a, $Ra, $Ra + vpxor $T0b, $Rb, $Rb + vpxor $T0c, $Rc, $Rc + vpxor $T1a, $Ra, $Ra + vpxor $T1b, $Rb, $Rb + vpxor $T1c, $Rc, $Rc + + dec %rax + jnz .Lselect_loop_avx2_w5 + + vmovdqu $Ra, 32*0($val) + vmovdqu $Rb, 32*1($val) + vmovdqu $Rc, 32*2($val) + vzeroupper +___ +$code.=<<___ if ($win64); + movaps (%rsp), %xmm6 + movaps 0x10(%rsp), %xmm7 + movaps 0x20(%rsp), %xmm8 + movaps 0x30(%rsp), %xmm9 + movaps 0x40(%rsp), %xmm10 + movaps 0x50(%rsp), %xmm11 + movaps 0x60(%rsp), %xmm12 + movaps 0x70(%rsp), %xmm13 + movaps 0x80(%rsp), %xmm14 + movaps 0x90(%rsp), %xmm15 + lea 0xa8(%rsp), %rsp +.LSEH_end_ecp_nistz256_avx2_gather_w5: +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_gather_w5,.-ecp_nistz256_avx2_gather_w5 +___ +} +if ($avx>1) { +my ($val,$in_t,$index)=$win64?("%rcx","%rdx","%r8d"):("%rdi","%rsi","%edx"); +my ($THREE,$INDEX,$Ra,$Rb)=map("%ymm$_",(0..3)); +my ($M0,$T0a,$T0b,$TMP0)=map("%ymm$_",(4..7)); +my ($M1,$T1a,$T1b,$TMP1)=map("%ymm$_",(8..11)); +my ($M2,$T2a,$T2b,$TMP2)=map("%ymm$_",(12..15)); + +$code.=<<___; + +################################################################################ +# void ecp_nistz256_avx2_gather_w7(uint64_t *val, uint64_t *in_t, int index); +.globl ecp_nistz256_avx2_gather_w7 +.type ecp_nistz256_avx2_gather_w7,\@abi-omnipotent +.align 32 +ecp_nistz256_avx2_gather_w7: +.Lavx2_gather_w7: + vzeroupper +___ +$code.=<<___ if ($win64); + lea -0x88(%rsp), %rax +.LSEH_begin_ecp_nistz256_avx2_gather_w7: + .byte 0x48,0x8d,0x60,0xe0 #lea -0x20(%rax), %rsp + .byte 0xc5,0xf8,0x29,0x70,0xe0 #vmovaps %xmm6, -0x20(%rax) + .byte 0xc5,0xf8,0x29,0x78,0xf0 #vmovaps %xmm7, -0x10(%rax) + .byte 0xc5,0x78,0x29,0x40,0x00 #vmovaps %xmm8, 8(%rax) + .byte 0xc5,0x78,0x29,0x48,0x10 #vmovaps %xmm9, 0x10(%rax) + .byte 0xc5,0x78,0x29,0x50,0x20 #vmovaps %xmm10, 0x20(%rax) + .byte 0xc5,0x78,0x29,0x58,0x30 #vmovaps %xmm11, 0x30(%rax) + .byte 0xc5,0x78,0x29,0x60,0x40 #vmovaps %xmm12, 0x40(%rax) + .byte 0xc5,0x78,0x29,0x68,0x50 #vmovaps %xmm13, 0x50(%rax) + .byte 0xc5,0x78,0x29,0x70,0x60 #vmovaps %xmm14, 0x60(%rax) + .byte 0xc5,0x78,0x29,0x78,0x70 #vmovaps %xmm15, 0x70(%rax) +___ +$code.=<<___; + vmovdqa .LThree(%rip), $THREE + + vpxor $Ra, $Ra, $Ra + vpxor $Rb, $Rb, $Rb + + vmovdqa .LOne(%rip), $M0 + vmovdqa .LTwo(%rip), $M1 + vmovdqa .LThree(%rip), $M2 + + vmovd $index, %xmm1 + vpermd $INDEX, $Ra, $INDEX + # Skip index = 0, because it is implicitly the point at infinity + + mov \$21, %rax +.Lselect_loop_avx2_w7: + + vmovdqa 32*0($in_t), $T0a + vmovdqa 32*1($in_t), $T0b + + vmovdqa 32*2($in_t), $T1a + vmovdqa 32*3($in_t), $T1b + + vmovdqa 32*4($in_t), $T2a + vmovdqa 32*5($in_t), $T2b + + vpcmpeqd $INDEX, $M0, $TMP0 + vpcmpeqd $INDEX, $M1, $TMP1 + vpcmpeqd $INDEX, $M2, $TMP2 + + vpaddd $THREE, $M0, $M0 + vpaddd $THREE, $M1, $M1 + vpaddd $THREE, $M2, $M2 + lea 32*6($in_t), $in_t + + vpand $TMP0, $T0a, $T0a + vpand $TMP0, $T0b, $T0b + vpand $TMP1, $T1a, $T1a + vpand $TMP1, $T1b, $T1b + vpand $TMP2, $T2a, $T2a + vpand $TMP2, $T2b, $T2b + + vpxor $T0a, $Ra, $Ra + vpxor $T0b, $Rb, $Rb + vpxor $T1a, $Ra, $Ra + vpxor $T1b, $Rb, $Rb + vpxor $T2a, $Ra, $Ra + vpxor $T2b, $Rb, $Rb + + dec %rax + jnz .Lselect_loop_avx2_w7 + + + vmovdqa 32*0($in_t), $T0a + vmovdqa 32*1($in_t), $T0b + + vpcmpeqd $INDEX, $M0, $TMP0 + + vpand $TMP0, $T0a, $T0a + vpand $TMP0, $T0b, $T0b + + vpxor $T0a, $Ra, $Ra + vpxor $T0b, $Rb, $Rb + + vmovdqu $Ra, 32*0($val) + vmovdqu $Rb, 32*1($val) + vzeroupper +___ +$code.=<<___ if ($win64); + movaps (%rsp), %xmm6 + movaps 0x10(%rsp), %xmm7 + movaps 0x20(%rsp), %xmm8 + movaps 0x30(%rsp), %xmm9 + movaps 0x40(%rsp), %xmm10 + movaps 0x50(%rsp), %xmm11 + movaps 0x60(%rsp), %xmm12 + movaps 0x70(%rsp), %xmm13 + movaps 0x80(%rsp), %xmm14 + movaps 0x90(%rsp), %xmm15 + lea 0xa8(%rsp), %rsp +.LSEH_end_ecp_nistz256_avx2_gather_w7: +___ +$code.=<<___; + ret +.size ecp_nistz256_avx2_gather_w7,.-ecp_nistz256_avx2_gather_w7 +___ +} else { +$code.=<<___; +.globl ecp_nistz256_avx2_gather_w7 +.type ecp_nistz256_avx2_gather_w7,\@function,3 +.align 32 +ecp_nistz256_avx2_gather_w7: + .byte 0x0f,0x0b # ud2 + ret +.size ecp_nistz256_avx2_gather_w7,.-ecp_nistz256_avx2_gather_w7 +___ +} +{{{ +######################################################################## +# This block implements higher level point_double, point_add and +# point_add_affine. The key to performance in this case is to allow +# out-of-order execution logic to overlap computations from next step +# with tail processing from current step. By using tailored calling +# sequence we minimize inter-step overhead to give processor better +# shot at overlapping operations... +# +# You will notice that input data is copied to stack. Trouble is that +# there are no registers to spare for holding original pointers and +# reloading them, pointers, would create undesired dependencies on +# effective addresses calculation paths. In other words it's too done +# to favour out-of-order execution logic. +# <appro@openssl.org> + +my ($r_ptr,$a_ptr,$b_org,$b_ptr)=("%rdi","%rsi","%rdx","%rbx"); +my ($acc0,$acc1,$acc2,$acc3,$acc4,$acc5,$acc6,$acc7)=map("%r$_",(8..15)); +my ($t0,$t1,$t2,$t3,$t4)=("%rax","%rbp","%rcx",$acc4,$acc4); +my ($poly1,$poly3)=($acc6,$acc7); + +sub load_for_mul () { +my ($a,$b,$src0) = @_; +my $bias = $src0 eq "%rax" ? 0 : -128; + +" mov $b, $src0 + lea $b, $b_ptr + mov 8*0+$a, $acc1 + mov 8*1+$a, $acc2 + lea $bias+$a, $a_ptr + mov 8*2+$a, $acc3 + mov 8*3+$a, $acc4" +} + +sub load_for_sqr () { +my ($a,$src0) = @_; +my $bias = $src0 eq "%rax" ? 0 : -128; + +" mov 8*0+$a, $src0 + mov 8*1+$a, $acc6 + lea $bias+$a, $a_ptr + mov 8*2+$a, $acc7 + mov 8*3+$a, $acc0" +} + + { +######################################################################## +# operate in 4-5-0-1 "name space" that matches multiplication output +# +my ($a0,$a1,$a2,$a3,$t3,$t4)=($acc4,$acc5,$acc0,$acc1,$acc2,$acc3); + +$code.=<<___; +.type __ecp_nistz256_add_toq,\@abi-omnipotent +.align 32 +__ecp_nistz256_add_toq: + xor $t4,$t4 + add 8*0($b_ptr), $a0 + adc 8*1($b_ptr), $a1 + mov $a0, $t0 + adc 8*2($b_ptr), $a2 + adc 8*3($b_ptr), $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub \$-1, $a0 + mov $a2, $t2 + sbb $poly1, $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb $poly3, $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_add_toq,.-__ecp_nistz256_add_toq + +.type __ecp_nistz256_sub_fromq,\@abi-omnipotent +.align 32 +__ecp_nistz256_sub_fromq: + sub 8*0($b_ptr), $a0 + sbb 8*1($b_ptr), $a1 + mov $a0, $t0 + sbb 8*2($b_ptr), $a2 + sbb 8*3($b_ptr), $a3 + mov $a1, $t1 + sbb $t4, $t4 + + add \$-1, $a0 + mov $a2, $t2 + adc $poly1, $a1 + adc \$0, $a2 + mov $a3, $t3 + adc $poly3, $a3 + test $t4, $t4 + + cmovz $t0, $a0 + cmovz $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovz $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovz $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_sub_fromq,.-__ecp_nistz256_sub_fromq + +.type __ecp_nistz256_subq,\@abi-omnipotent +.align 32 +__ecp_nistz256_subq: + sub $a0, $t0 + sbb $a1, $t1 + mov $t0, $a0 + sbb $a2, $t2 + sbb $a3, $t3 + mov $t1, $a1 + sbb $t4, $t4 + + add \$-1, $t0 + mov $t2, $a2 + adc $poly1, $t1 + adc \$0, $t2 + mov $t3, $a3 + adc $poly3, $t3 + test $t4, $t4 + + cmovnz $t0, $a0 + cmovnz $t1, $a1 + cmovnz $t2, $a2 + cmovnz $t3, $a3 + + ret +.size __ecp_nistz256_subq,.-__ecp_nistz256_subq + +.type __ecp_nistz256_mul_by_2q,\@abi-omnipotent +.align 32 +__ecp_nistz256_mul_by_2q: + xor $t4, $t4 + add $a0, $a0 # a0:a3+a0:a3 + adc $a1, $a1 + mov $a0, $t0 + adc $a2, $a2 + adc $a3, $a3 + mov $a1, $t1 + adc \$0, $t4 + + sub \$-1, $a0 + mov $a2, $t2 + sbb $poly1, $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb $poly3, $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_mul_by_2q,.-__ecp_nistz256_mul_by_2q +___ + } +sub gen_double () { + my $x = shift; + my ($src0,$sfx,$bias); + my ($S,$M,$Zsqr,$in_x,$tmp0)=map(32*$_,(0..4)); + + if ($x ne "x") { + $src0 = "%rax"; + $sfx = ""; + $bias = 0; + +$code.=<<___; +.globl ecp_nistz256_point_double +.type ecp_nistz256_point_double,\@function,2 +.align 32 +ecp_nistz256_point_double: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx + cmp \$0x80100, %ecx + je .Lpoint_doublex +___ + } else { + $src0 = "%rdx"; + $sfx = "x"; + $bias = 128; + +$code.=<<___; +.type ecp_nistz256_point_doublex,\@function,2 +.align 32 +ecp_nistz256_point_doublex: +.Lpoint_doublex: +___ + } +$code.=<<___; + push %rbp + push %rbx + push %r12 + push %r13 + push %r14 + push %r15 + sub \$32*5+8, %rsp + +.Lpoint_double_shortcut$x: + movdqu 0x00($a_ptr), %xmm0 # copy *(P256_POINT *)$a_ptr.x + mov $a_ptr, $b_ptr # backup copy + movdqu 0x10($a_ptr), %xmm1 + mov 0x20+8*0($a_ptr), $acc4 # load in_y in "5-4-0-1" order + mov 0x20+8*1($a_ptr), $acc5 + mov 0x20+8*2($a_ptr), $acc0 + mov 0x20+8*3($a_ptr), $acc1 + mov .Lpoly+8*1(%rip), $poly1 + mov .Lpoly+8*3(%rip), $poly3 + movdqa %xmm0, $in_x(%rsp) + movdqa %xmm1, $in_x+0x10(%rsp) + lea 0x20($r_ptr), $acc2 + lea 0x40($r_ptr), $acc3 + movq $r_ptr, %xmm0 + movq $acc2, %xmm1 + movq $acc3, %xmm2 + + lea $S(%rsp), $r_ptr + call __ecp_nistz256_mul_by_2$x # p256_mul_by_2(S, in_y); + + mov 0x40+8*0($a_ptr), $src0 + mov 0x40+8*1($a_ptr), $acc6 + mov 0x40+8*2($a_ptr), $acc7 + mov 0x40+8*3($a_ptr), $acc0 + lea 0x40-$bias($a_ptr), $a_ptr + lea $Zsqr(%rsp), $r_ptr + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Zsqr, in_z); + + `&load_for_sqr("$S(%rsp)", "$src0")` + lea $S(%rsp), $r_ptr + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(S, S); + + mov 0x20($b_ptr), $src0 # $b_ptr is still valid + mov 0x40+8*0($b_ptr), $acc1 + mov 0x40+8*1($b_ptr), $acc2 + mov 0x40+8*2($b_ptr), $acc3 + mov 0x40+8*3($b_ptr), $acc4 + lea 0x40-$bias($b_ptr), $a_ptr + lea 0x20($b_ptr), $b_ptr + movq %xmm2, $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(res_z, in_z, in_y); + call __ecp_nistz256_mul_by_2$x # p256_mul_by_2(res_z, res_z); + + mov $in_x+8*0(%rsp), $acc4 # "5-4-0-1" order + mov $in_x+8*1(%rsp), $acc5 + lea $Zsqr(%rsp), $b_ptr + mov $in_x+8*2(%rsp), $acc0 + mov $in_x+8*3(%rsp), $acc1 + lea $M(%rsp), $r_ptr + call __ecp_nistz256_add_to$x # p256_add(M, in_x, Zsqr); + + mov $in_x+8*0(%rsp), $acc4 # "5-4-0-1" order + mov $in_x+8*1(%rsp), $acc5 + lea $Zsqr(%rsp), $b_ptr + mov $in_x+8*2(%rsp), $acc0 + mov $in_x+8*3(%rsp), $acc1 + lea $Zsqr(%rsp), $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(Zsqr, in_x, Zsqr); + + `&load_for_sqr("$S(%rsp)", "$src0")` + movq %xmm1, $r_ptr + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(res_y, S); +___ +{ +######## ecp_nistz256_div_by_2(res_y, res_y); ########################## +# operate in 4-5-6-7 "name space" that matches squaring output +# +my ($poly1,$poly3)=($a_ptr,$t1); +my ($a0,$a1,$a2,$a3,$t3,$t4,$t1)=($acc4,$acc5,$acc6,$acc7,$acc0,$acc1,$acc2); + +$code.=<<___; + xor $t4, $t4 + mov $a0, $t0 + add \$-1, $a0 + mov $a1, $t1 + adc $poly1, $a1 + mov $a2, $t2 + adc \$0, $a2 + mov $a3, $t3 + adc $poly3, $a3 + adc \$0, $t4 + xor $a_ptr, $a_ptr # borrow $a_ptr + test \$1, $t0 + + cmovz $t0, $a0 + cmovz $t1, $a1 + cmovz $t2, $a2 + cmovz $t3, $a3 + cmovz $a_ptr, $t4 + + mov $a1, $t0 # a0:a3>>1 + shr \$1, $a0 + shl \$63, $t0 + mov $a2, $t1 + shr \$1, $a1 + or $t0, $a0 + shl \$63, $t1 + mov $a3, $t2 + shr \$1, $a2 + or $t1, $a1 + shl \$63, $t2 + mov $a0, 8*0($r_ptr) + shr \$1, $a3 + mov $a1, 8*1($r_ptr) + shl \$63, $t4 + or $t2, $a2 + or $t4, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) +___ +} +$code.=<<___; + `&load_for_mul("$M(%rsp)", "$Zsqr(%rsp)", "$src0")` + lea $M(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(M, M, Zsqr); + + lea $tmp0(%rsp), $r_ptr + call __ecp_nistz256_mul_by_2$x + + lea $M(%rsp), $b_ptr + lea $M(%rsp), $r_ptr + call __ecp_nistz256_add_to$x # p256_mul_by_3(M, M); + + `&load_for_mul("$S(%rsp)", "$in_x(%rsp)", "$src0")` + lea $S(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S, S, in_x); + + lea $tmp0(%rsp), $r_ptr + call __ecp_nistz256_mul_by_2$x # p256_mul_by_2(tmp0, S); + + `&load_for_sqr("$M(%rsp)", "$src0")` + movq %xmm0, $r_ptr + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(res_x, M); + + lea $tmp0(%rsp), $b_ptr + mov $acc6, $acc0 # harmonize sqr output and sub input + mov $acc7, $acc1 + mov $a_ptr, $poly1 + mov $t1, $poly3 + call __ecp_nistz256_sub_from$x # p256_sub(res_x, res_x, tmp0); + + mov $S+8*0(%rsp), $t0 + mov $S+8*1(%rsp), $t1 + mov $S+8*2(%rsp), $t2 + mov $S+8*3(%rsp), $acc2 # "4-5-0-1" order + lea $S(%rsp), $r_ptr + call __ecp_nistz256_sub$x # p256_sub(S, S, res_x); + + mov $M(%rsp), $src0 + lea $M(%rsp), $b_ptr + mov $acc4, $acc6 # harmonize sub output and mul input + xor %ecx, %ecx + mov $acc4, $S+8*0(%rsp) # have to save:-( + mov $acc5, $acc2 + mov $acc5, $S+8*1(%rsp) + cmovz $acc0, $acc3 + mov $acc0, $S+8*2(%rsp) + lea $S-$bias(%rsp), $a_ptr + cmovz $acc1, $acc4 + mov $acc1, $S+8*3(%rsp) + mov $acc6, $acc1 + lea $S(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S, S, M); + + movq %xmm1, $b_ptr + movq %xmm1, $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(res_y, S, res_y); + + add \$32*5+8, %rsp + pop %r15 + pop %r14 + pop %r13 + pop %r12 + pop %rbx + pop %rbp + ret +.size ecp_nistz256_point_double$sfx,.-ecp_nistz256_point_double$sfx +___ +} +&gen_double("q"); + +sub gen_add () { + my $x = shift; + my ($src0,$sfx,$bias); + my ($H,$Hsqr,$R,$Rsqr,$Hcub, + $U1,$U2,$S1,$S2, + $res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y,$in2_z)=map(32*$_,(0..17)); + my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr); + + if ($x ne "x") { + $src0 = "%rax"; + $sfx = ""; + $bias = 0; + +$code.=<<___; +.globl ecp_nistz256_point_add +.type ecp_nistz256_point_add,\@function,3 +.align 32 +ecp_nistz256_point_add: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx + cmp \$0x80100, %ecx + je .Lpoint_addx +___ + } else { + $src0 = "%rdx"; + $sfx = "x"; + $bias = 128; + +$code.=<<___; +.type ecp_nistz256_point_addx,\@function,3 +.align 32 +ecp_nistz256_point_addx: +.Lpoint_addx: +___ + } +$code.=<<___; + push %rbp + push %rbx + push %r12 + push %r13 + push %r14 + push %r15 + sub \$32*18+8, %rsp + + movdqu 0x00($a_ptr), %xmm0 # copy *(P256_POINT *)$a_ptr + movdqu 0x10($a_ptr), %xmm1 + movdqu 0x20($a_ptr), %xmm2 + movdqu 0x30($a_ptr), %xmm3 + movdqu 0x40($a_ptr), %xmm4 + movdqu 0x50($a_ptr), %xmm5 + mov $a_ptr, $b_ptr # reassign + mov $b_org, $a_ptr # reassign + movdqa %xmm0, $in1_x(%rsp) + movdqa %xmm1, $in1_x+0x10(%rsp) + movdqa %xmm2, $in1_y(%rsp) + movdqa %xmm3, $in1_y+0x10(%rsp) + movdqa %xmm4, $in1_z(%rsp) + movdqa %xmm5, $in1_z+0x10(%rsp) + por %xmm4, %xmm5 + + movdqu 0x00($a_ptr), %xmm0 # copy *(P256_POINT *)$b_ptr + pshufd \$0xb1, %xmm5, %xmm3 + movdqu 0x10($a_ptr), %xmm1 + movdqu 0x20($a_ptr), %xmm2 + por %xmm3, %xmm5 + movdqu 0x30($a_ptr), %xmm3 + mov 0x40+8*0($a_ptr), $src0 # load original in2_z + mov 0x40+8*1($a_ptr), $acc6 + mov 0x40+8*2($a_ptr), $acc7 + mov 0x40+8*3($a_ptr), $acc0 + movdqa %xmm0, $in2_x(%rsp) + pshufd \$0x1e, %xmm5, %xmm4 + movdqa %xmm1, $in2_x+0x10(%rsp) + movdqu 0x40($a_ptr),%xmm0 # in2_z again + movdqu 0x50($a_ptr),%xmm1 + movdqa %xmm2, $in2_y(%rsp) + movdqa %xmm3, $in2_y+0x10(%rsp) + por %xmm4, %xmm5 + pxor %xmm4, %xmm4 + por %xmm0, %xmm1 + movq $r_ptr, %xmm0 # save $r_ptr + + lea 0x40-$bias($a_ptr), $a_ptr # $a_ptr is still valid + mov $src0, $in2_z+8*0(%rsp) # make in2_z copy + mov $acc6, $in2_z+8*1(%rsp) + mov $acc7, $in2_z+8*2(%rsp) + mov $acc0, $in2_z+8*3(%rsp) + lea $Z2sqr(%rsp), $r_ptr # Z2^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Z2sqr, in2_z); + + pcmpeqd %xmm4, %xmm5 + pshufd \$0xb1, %xmm1, %xmm4 + por %xmm1, %xmm4 + pshufd \$0, %xmm5, %xmm5 # in1infty + pshufd \$0x1e, %xmm4, %xmm3 + por %xmm3, %xmm4 + pxor %xmm3, %xmm3 + pcmpeqd %xmm3, %xmm4 + pshufd \$0, %xmm4, %xmm4 # in2infty + mov 0x40+8*0($b_ptr), $src0 # load original in1_z + mov 0x40+8*1($b_ptr), $acc6 + mov 0x40+8*2($b_ptr), $acc7 + mov 0x40+8*3($b_ptr), $acc0 + movq $b_ptr, %xmm1 + + lea 0x40-$bias($b_ptr), $a_ptr + lea $Z1sqr(%rsp), $r_ptr # Z1^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Z1sqr, in1_z); + + `&load_for_mul("$Z2sqr(%rsp)", "$in2_z(%rsp)", "$src0")` + lea $S1(%rsp), $r_ptr # S1 = Z2^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S1, Z2sqr, in2_z); + + `&load_for_mul("$Z1sqr(%rsp)", "$in1_z(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr # S2 = Z1^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, Z1sqr, in1_z); + + `&load_for_mul("$S1(%rsp)", "$in1_y(%rsp)", "$src0")` + lea $S1(%rsp), $r_ptr # S1 = Y1*Z2^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S1, S1, in1_y); + + `&load_for_mul("$S2(%rsp)", "$in2_y(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr # S2 = Y2*Z1^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, S2, in2_y); + + lea $S1(%rsp), $b_ptr + lea $R(%rsp), $r_ptr # R = S2 - S1 + call __ecp_nistz256_sub_from$x # p256_sub(R, S2, S1); + + or $acc5, $acc4 # see if result is zero + movdqa %xmm4, %xmm2 + or $acc0, $acc4 + or $acc1, $acc4 + por %xmm5, %xmm2 # in1infty || in2infty + movq $acc4, %xmm3 + + `&load_for_mul("$Z2sqr(%rsp)", "$in1_x(%rsp)", "$src0")` + lea $U1(%rsp), $r_ptr # U1 = X1*Z2^2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(U1, in1_x, Z2sqr); + + `&load_for_mul("$Z1sqr(%rsp)", "$in2_x(%rsp)", "$src0")` + lea $U2(%rsp), $r_ptr # U2 = X2*Z1^2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(U2, in2_x, Z1sqr); + + lea $U1(%rsp), $b_ptr + lea $H(%rsp), $r_ptr # H = U2 - U1 + call __ecp_nistz256_sub_from$x # p256_sub(H, U2, U1); + + or $acc5, $acc4 # see if result is zero + or $acc0, $acc4 + or $acc1, $acc4 + + .byte 0x3e # predict taken + jnz .Ladd_proceed$x # is_equal(U1,U2)? + movq %xmm2, $acc0 + movq %xmm3, $acc1 + test $acc0, $acc0 + jnz .Ladd_proceed$x # (in1infty || in2infty)? + test $acc1, $acc1 + jz .Ladd_double$x # is_equal(S1,S2)? + + movq %xmm0, $r_ptr # restore $r_ptr + pxor %xmm0, %xmm0 + movdqu %xmm0, 0x00($r_ptr) + movdqu %xmm0, 0x10($r_ptr) + movdqu %xmm0, 0x20($r_ptr) + movdqu %xmm0, 0x30($r_ptr) + movdqu %xmm0, 0x40($r_ptr) + movdqu %xmm0, 0x50($r_ptr) + jmp .Ladd_done$x + +.align 32 +.Ladd_double$x: + movq %xmm1, $a_ptr # restore $a_ptr + movq %xmm0, $r_ptr # restore $r_ptr + add \$`32*(18-5)`, %rsp # difference in frame sizes + jmp .Lpoint_double_shortcut$x + +.align 32 +.Ladd_proceed$x: + `&load_for_sqr("$R(%rsp)", "$src0")` + lea $Rsqr(%rsp), $r_ptr # R^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Rsqr, R); + + `&load_for_mul("$H(%rsp)", "$in1_z(%rsp)", "$src0")` + lea $res_z(%rsp), $r_ptr # Z3 = H*Z1*Z2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(res_z, H, in1_z); + + `&load_for_sqr("$H(%rsp)", "$src0")` + lea $Hsqr(%rsp), $r_ptr # H^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Hsqr, H); + + `&load_for_mul("$res_z(%rsp)", "$in2_z(%rsp)", "$src0")` + lea $res_z(%rsp), $r_ptr # Z3 = H*Z1*Z2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(res_z, res_z, in2_z); + + `&load_for_mul("$Hsqr(%rsp)", "$H(%rsp)", "$src0")` + lea $Hcub(%rsp), $r_ptr # H^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(Hcub, Hsqr, H); + + `&load_for_mul("$Hsqr(%rsp)", "$U1(%rsp)", "$src0")` + lea $U2(%rsp), $r_ptr # U1*H^2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(U2, U1, Hsqr); +___ +{ +####################################################################### +# operate in 4-5-0-1 "name space" that matches multiplication output +# +my ($acc0,$acc1,$acc2,$acc3,$t3,$t4)=($acc4,$acc5,$acc0,$acc1,$acc2,$acc3); +my ($poly1, $poly3)=($acc6,$acc7); + +$code.=<<___; + #lea $U2(%rsp), $a_ptr + #lea $Hsqr(%rsp), $r_ptr # 2*U1*H^2 + #call __ecp_nistz256_mul_by_2 # ecp_nistz256_mul_by_2(Hsqr, U2); + + xor $t4, $t4 + add $acc0, $acc0 # a0:a3+a0:a3 + lea $Rsqr(%rsp), $a_ptr + adc $acc1, $acc1 + mov $acc0, $t0 + adc $acc2, $acc2 + adc $acc3, $acc3 + mov $acc1, $t1 + adc \$0, $t4 + + sub \$-1, $acc0 + mov $acc2, $t2 + sbb $poly1, $acc1 + sbb \$0, $acc2 + mov $acc3, $t3 + sbb $poly3, $acc3 + sbb \$0, $t4 + + cmovc $t0, $acc0 + mov 8*0($a_ptr), $t0 + cmovc $t1, $acc1 + mov 8*1($a_ptr), $t1 + cmovc $t2, $acc2 + mov 8*2($a_ptr), $t2 + cmovc $t3, $acc3 + mov 8*3($a_ptr), $t3 + + call __ecp_nistz256_sub$x # p256_sub(res_x, Rsqr, Hsqr); + + lea $Hcub(%rsp), $b_ptr + lea $res_x(%rsp), $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(res_x, res_x, Hcub); + + mov $U2+8*0(%rsp), $t0 + mov $U2+8*1(%rsp), $t1 + mov $U2+8*2(%rsp), $t2 + mov $U2+8*3(%rsp), $t3 + lea $res_y(%rsp), $r_ptr + + call __ecp_nistz256_sub$x # p256_sub(res_y, U2, res_x); + + mov $acc0, 8*0($r_ptr) # save the result, as + mov $acc1, 8*1($r_ptr) # __ecp_nistz256_sub doesn't + mov $acc2, 8*2($r_ptr) + mov $acc3, 8*3($r_ptr) +___ +} +$code.=<<___; + `&load_for_mul("$S1(%rsp)", "$Hcub(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, S1, Hcub); + + `&load_for_mul("$R(%rsp)", "$res_y(%rsp)", "$src0")` + lea $res_y(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(res_y, R, res_y); + + lea $S2(%rsp), $b_ptr + lea $res_y(%rsp), $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(res_y, res_y, S2); + + movq %xmm0, $r_ptr # restore $r_ptr + + movdqa %xmm5, %xmm0 # copy_conditional(res_z, in2_z, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_z(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_z+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand $in2_z(%rsp), %xmm2 + pand $in2_z+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_z, in1_z, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_z(%rsp), %xmm2 + pand $in1_z+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x40($r_ptr) + movdqu %xmm3, 0x50($r_ptr) + + movdqa %xmm5, %xmm0 # copy_conditional(res_x, in2_x, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_x(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_x+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand $in2_x(%rsp), %xmm2 + pand $in2_x+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_x, in1_x, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_x(%rsp), %xmm2 + pand $in1_x+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x00($r_ptr) + movdqu %xmm3, 0x10($r_ptr) + + movdqa %xmm5, %xmm0 # copy_conditional(res_y, in2_y, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_y(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_y+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand $in2_y(%rsp), %xmm2 + pand $in2_y+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_y, in1_y, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_y(%rsp), %xmm2 + pand $in1_y+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x20($r_ptr) + movdqu %xmm3, 0x30($r_ptr) + +.Ladd_done$x: + add \$32*18+8, %rsp + pop %r15 + pop %r14 + pop %r13 + pop %r12 + pop %rbx + pop %rbp + ret +.size ecp_nistz256_point_add$sfx,.-ecp_nistz256_point_add$sfx +___ +} +&gen_add("q"); + +sub gen_add_affine () { + my $x = shift; + my ($src0,$sfx,$bias); + my ($U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr, + $res_x,$res_y,$res_z, + $in1_x,$in1_y,$in1_z, + $in2_x,$in2_y)=map(32*$_,(0..14)); + my $Z1sqr = $S2; + + if ($x ne "x") { + $src0 = "%rax"; + $sfx = ""; + $bias = 0; + +$code.=<<___; +.globl ecp_nistz256_point_add_affine +.type ecp_nistz256_point_add_affine,\@function,3 +.align 32 +ecp_nistz256_point_add_affine: +___ +$code.=<<___ if ($addx); + mov \$0x80100, %ecx + and OPENSSL_ia32cap_P+8(%rip), %ecx + cmp \$0x80100, %ecx + je .Lpoint_add_affinex +___ + } else { + $src0 = "%rdx"; + $sfx = "x"; + $bias = 128; + +$code.=<<___; +.type ecp_nistz256_point_add_affinex,\@function,3 +.align 32 +ecp_nistz256_point_add_affinex: +.Lpoint_add_affinex: +___ + } +$code.=<<___; + push %rbp + push %rbx + push %r12 + push %r13 + push %r14 + push %r15 + sub \$32*15+8, %rsp + + movdqu 0x00($a_ptr), %xmm0 # copy *(P256_POINT *)$a_ptr + mov $b_org, $b_ptr # reassign + movdqu 0x10($a_ptr), %xmm1 + movdqu 0x20($a_ptr), %xmm2 + movdqu 0x30($a_ptr), %xmm3 + movdqu 0x40($a_ptr), %xmm4 + movdqu 0x50($a_ptr), %xmm5 + mov 0x40+8*0($a_ptr), $src0 # load original in1_z + mov 0x40+8*1($a_ptr), $acc6 + mov 0x40+8*2($a_ptr), $acc7 + mov 0x40+8*3($a_ptr), $acc0 + movdqa %xmm0, $in1_x(%rsp) + movdqa %xmm1, $in1_x+0x10(%rsp) + movdqa %xmm2, $in1_y(%rsp) + movdqa %xmm3, $in1_y+0x10(%rsp) + movdqa %xmm4, $in1_z(%rsp) + movdqa %xmm5, $in1_z+0x10(%rsp) + por %xmm4, %xmm5 + + movdqu 0x00($b_ptr), %xmm0 # copy *(P256_POINT_AFFINE *)$b_ptr + pshufd \$0xb1, %xmm5, %xmm3 + movdqu 0x10($b_ptr), %xmm1 + movdqu 0x20($b_ptr), %xmm2 + por %xmm3, %xmm5 + movdqu 0x30($b_ptr), %xmm3 + movdqa %xmm0, $in2_x(%rsp) + pshufd \$0x1e, %xmm5, %xmm4 + movdqa %xmm1, $in2_x+0x10(%rsp) + por %xmm0, %xmm1 + movq $r_ptr, %xmm0 # save $r_ptr + movdqa %xmm2, $in2_y(%rsp) + movdqa %xmm3, $in2_y+0x10(%rsp) + por %xmm2, %xmm3 + por %xmm4, %xmm5 + pxor %xmm4, %xmm4 + por %xmm1, %xmm3 + + lea 0x40-$bias($a_ptr), $a_ptr # $a_ptr is still valid + lea $Z1sqr(%rsp), $r_ptr # Z1^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Z1sqr, in1_z); + + pcmpeqd %xmm4, %xmm5 + pshufd \$0xb1, %xmm3, %xmm4 + mov 0x00($b_ptr), $src0 # $b_ptr is still valid + #lea 0x00($b_ptr), $b_ptr + mov $acc4, $acc1 # harmonize sqr output and mul input + por %xmm3, %xmm4 + pshufd \$0, %xmm5, %xmm5 # in1infty + pshufd \$0x1e, %xmm4, %xmm3 + mov $acc5, $acc2 + por %xmm3, %xmm4 + pxor %xmm3, %xmm3 + mov $acc6, $acc3 + pcmpeqd %xmm3, %xmm4 + pshufd \$0, %xmm4, %xmm4 # in2infty + + lea $Z1sqr-$bias(%rsp), $a_ptr + mov $acc7, $acc4 + lea $U2(%rsp), $r_ptr # U2 = X2*Z1^2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(U2, Z1sqr, in2_x); + + lea $in1_x(%rsp), $b_ptr + lea $H(%rsp), $r_ptr # H = U2 - U1 + call __ecp_nistz256_sub_from$x # p256_sub(H, U2, in1_x); + + `&load_for_mul("$Z1sqr(%rsp)", "$in1_z(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr # S2 = Z1^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, Z1sqr, in1_z); + + `&load_for_mul("$H(%rsp)", "$in1_z(%rsp)", "$src0")` + lea $res_z(%rsp), $r_ptr # Z3 = H*Z1*Z2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(res_z, H, in1_z); + + `&load_for_mul("$S2(%rsp)", "$in2_y(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr # S2 = Y2*Z1^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, S2, in2_y); + + lea $in1_y(%rsp), $b_ptr + lea $R(%rsp), $r_ptr # R = S2 - S1 + call __ecp_nistz256_sub_from$x # p256_sub(R, S2, in1_y); + + `&load_for_sqr("$H(%rsp)", "$src0")` + lea $Hsqr(%rsp), $r_ptr # H^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Hsqr, H); + + `&load_for_sqr("$R(%rsp)", "$src0")` + lea $Rsqr(%rsp), $r_ptr # R^2 + call __ecp_nistz256_sqr_mont$x # p256_sqr_mont(Rsqr, R); + + `&load_for_mul("$H(%rsp)", "$Hsqr(%rsp)", "$src0")` + lea $Hcub(%rsp), $r_ptr # H^3 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(Hcub, Hsqr, H); + + `&load_for_mul("$Hsqr(%rsp)", "$in1_x(%rsp)", "$src0")` + lea $U2(%rsp), $r_ptr # U1*H^2 + call __ecp_nistz256_mul_mont$x # p256_mul_mont(U2, in1_x, Hsqr); +___ +{ +####################################################################### +# operate in 4-5-0-1 "name space" that matches multiplication output +# +my ($acc0,$acc1,$acc2,$acc3,$t3,$t4)=($acc4,$acc5,$acc0,$acc1,$acc2,$acc3); +my ($poly1, $poly3)=($acc6,$acc7); + +$code.=<<___; + #lea $U2(%rsp), $a_ptr + #lea $Hsqr(%rsp), $r_ptr # 2*U1*H^2 + #call __ecp_nistz256_mul_by_2 # ecp_nistz256_mul_by_2(Hsqr, U2); + + xor $t4, $t4 + add $acc0, $acc0 # a0:a3+a0:a3 + lea $Rsqr(%rsp), $a_ptr + adc $acc1, $acc1 + mov $acc0, $t0 + adc $acc2, $acc2 + adc $acc3, $acc3 + mov $acc1, $t1 + adc \$0, $t4 + + sub \$-1, $acc0 + mov $acc2, $t2 + sbb $poly1, $acc1 + sbb \$0, $acc2 + mov $acc3, $t3 + sbb $poly3, $acc3 + sbb \$0, $t4 + + cmovc $t0, $acc0 + mov 8*0($a_ptr), $t0 + cmovc $t1, $acc1 + mov 8*1($a_ptr), $t1 + cmovc $t2, $acc2 + mov 8*2($a_ptr), $t2 + cmovc $t3, $acc3 + mov 8*3($a_ptr), $t3 + + call __ecp_nistz256_sub$x # p256_sub(res_x, Rsqr, Hsqr); + + lea $Hcub(%rsp), $b_ptr + lea $res_x(%rsp), $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(res_x, res_x, Hcub); + + mov $U2+8*0(%rsp), $t0 + mov $U2+8*1(%rsp), $t1 + mov $U2+8*2(%rsp), $t2 + mov $U2+8*3(%rsp), $t3 + lea $H(%rsp), $r_ptr + + call __ecp_nistz256_sub$x # p256_sub(H, U2, res_x); + + mov $acc0, 8*0($r_ptr) # save the result, as + mov $acc1, 8*1($r_ptr) # __ecp_nistz256_sub doesn't + mov $acc2, 8*2($r_ptr) + mov $acc3, 8*3($r_ptr) +___ +} +$code.=<<___; + `&load_for_mul("$Hcub(%rsp)", "$in1_y(%rsp)", "$src0")` + lea $S2(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(S2, Hcub, in1_y); + + `&load_for_mul("$H(%rsp)", "$R(%rsp)", "$src0")` + lea $H(%rsp), $r_ptr + call __ecp_nistz256_mul_mont$x # p256_mul_mont(H, H, R); + + lea $S2(%rsp), $b_ptr + lea $res_y(%rsp), $r_ptr + call __ecp_nistz256_sub_from$x # p256_sub(res_y, H, S2); + + movq %xmm0, $r_ptr # restore $r_ptr + + movdqa %xmm5, %xmm0 # copy_conditional(res_z, ONE, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_z(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_z+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand .LONE_mont(%rip), %xmm2 + pand .LONE_mont+0x10(%rip), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_z, in1_z, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_z(%rsp), %xmm2 + pand $in1_z+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x40($r_ptr) + movdqu %xmm3, 0x50($r_ptr) + + movdqa %xmm5, %xmm0 # copy_conditional(res_x, in2_x, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_x(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_x+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand $in2_x(%rsp), %xmm2 + pand $in2_x+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_x, in1_x, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_x(%rsp), %xmm2 + pand $in1_x+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x00($r_ptr) + movdqu %xmm3, 0x10($r_ptr) + + movdqa %xmm5, %xmm0 # copy_conditional(res_y, in2_y, in1infty); + movdqa %xmm5, %xmm1 + pandn $res_y(%rsp), %xmm0 + movdqa %xmm5, %xmm2 + pandn $res_y+0x10(%rsp), %xmm1 + movdqa %xmm5, %xmm3 + pand $in2_y(%rsp), %xmm2 + pand $in2_y+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + + movdqa %xmm4, %xmm0 # copy_conditional(res_y, in1_y, in2infty); + movdqa %xmm4, %xmm1 + pandn %xmm2, %xmm0 + movdqa %xmm4, %xmm2 + pandn %xmm3, %xmm1 + movdqa %xmm4, %xmm3 + pand $in1_y(%rsp), %xmm2 + pand $in1_y+0x10(%rsp), %xmm3 + por %xmm0, %xmm2 + por %xmm1, %xmm3 + movdqu %xmm2, 0x20($r_ptr) + movdqu %xmm3, 0x30($r_ptr) + + add \$32*15+8, %rsp + pop %r15 + pop %r14 + pop %r13 + pop %r12 + pop %rbx + pop %rbp + ret +.size ecp_nistz256_point_add_affine$sfx,.-ecp_nistz256_point_add_affine$sfx +___ +} +&gen_add_affine("q"); + +######################################################################## +# AD*X magic +# +if ($addx) { { +######################################################################## +# operate in 4-5-0-1 "name space" that matches multiplication output +# +my ($a0,$a1,$a2,$a3,$t3,$t4)=($acc4,$acc5,$acc0,$acc1,$acc2,$acc3); + +$code.=<<___; +.type __ecp_nistz256_add_tox,\@abi-omnipotent +.align 32 +__ecp_nistz256_add_tox: + xor $t4, $t4 + adc 8*0($b_ptr), $a0 + adc 8*1($b_ptr), $a1 + mov $a0, $t0 + adc 8*2($b_ptr), $a2 + adc 8*3($b_ptr), $a3 + mov $a1, $t1 + adc \$0, $t4 + + xor $t3, $t3 + sbb \$-1, $a0 + mov $a2, $t2 + sbb $poly1, $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb $poly3, $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_add_tox,.-__ecp_nistz256_add_tox + +.type __ecp_nistz256_sub_fromx,\@abi-omnipotent +.align 32 +__ecp_nistz256_sub_fromx: + xor $t4, $t4 + sbb 8*0($b_ptr), $a0 + sbb 8*1($b_ptr), $a1 + mov $a0, $t0 + sbb 8*2($b_ptr), $a2 + sbb 8*3($b_ptr), $a3 + mov $a1, $t1 + sbb \$0, $t4 + + xor $t3, $t3 + adc \$-1, $a0 + mov $a2, $t2 + adc $poly1, $a1 + adc \$0, $a2 + mov $a3, $t3 + adc $poly3, $a3 + + bt \$0, $t4 + cmovnc $t0, $a0 + cmovnc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovnc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovnc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_sub_fromx,.-__ecp_nistz256_sub_fromx + +.type __ecp_nistz256_subx,\@abi-omnipotent +.align 32 +__ecp_nistz256_subx: + xor $t4, $t4 + sbb $a0, $t0 + sbb $a1, $t1 + mov $t0, $a0 + sbb $a2, $t2 + sbb $a3, $t3 + mov $t1, $a1 + sbb \$0, $t4 + + xor $a3 ,$a3 + adc \$-1, $t0 + mov $t2, $a2 + adc $poly1, $t1 + adc \$0, $t2 + mov $t3, $a3 + adc $poly3, $t3 + + bt \$0, $t4 + cmovc $t0, $a0 + cmovc $t1, $a1 + cmovc $t2, $a2 + cmovc $t3, $a3 + + ret +.size __ecp_nistz256_subx,.-__ecp_nistz256_subx + +.type __ecp_nistz256_mul_by_2x,\@abi-omnipotent +.align 32 +__ecp_nistz256_mul_by_2x: + xor $t4, $t4 + adc $a0, $a0 # a0:a3+a0:a3 + adc $a1, $a1 + mov $a0, $t0 + adc $a2, $a2 + adc $a3, $a3 + mov $a1, $t1 + adc \$0, $t4 + + xor $t3, $t3 + sbb \$-1, $a0 + mov $a2, $t2 + sbb $poly1, $a1 + sbb \$0, $a2 + mov $a3, $t3 + sbb $poly3, $a3 + sbb \$0, $t4 + + cmovc $t0, $a0 + cmovc $t1, $a1 + mov $a0, 8*0($r_ptr) + cmovc $t2, $a2 + mov $a1, 8*1($r_ptr) + cmovc $t3, $a3 + mov $a2, 8*2($r_ptr) + mov $a3, 8*3($r_ptr) + + ret +.size __ecp_nistz256_mul_by_2x,.-__ecp_nistz256_mul_by_2x +___ + } +&gen_double("x"); +&gen_add("x"); +&gen_add_affine("x"); +} +}}} + +######################################################################## +# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7 +# +open TABLE,"<ecp_nistz256_table.c" or +open TABLE,"<${dir}../ecp_nistz256_table.c" or +die "failed to open ecp_nistz256_table.c:",$!; + +use integer; + +foreach(<TABLE>) { + s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo; +} +close TABLE; + +die "insane number of elements" if ($#arr != 64*16*37-1); + +print <<___; +.text +.globl ecp_nistz256_precomputed +.type ecp_nistz256_precomputed,\@object +.align 4096 +ecp_nistz256_precomputed: +___ +while (@line=splice(@arr,0,16)) { + print ".long\t",join(',',map { sprintf "0x%08x",$_} @line),"\n"; +} +print <<___; +.size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed +___ + +$code =~ s/\`([^\`]*)\`/eval $1/gem; +print $code; +close STDOUT; diff --git a/openssl-1.1.0h/crypto/ec/build.info b/openssl-1.1.0h/crypto/ec/build.info new file mode 100644 index 0000000..970c292 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/build.info @@ -0,0 +1,28 @@ +LIBS=../../libcrypto +SOURCE[../../libcrypto]=\ + ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c \ + ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c \ + ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c \ + ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c \ + ecp_oct.c ec2_oct.c ec_oct.c ec_kmeth.c ecdh_ossl.c ecdh_kdf.c \ + ecdsa_ossl.c ecdsa_sign.c ecdsa_vrf.c curve25519.c ecx_meth.c \ + {- $target{ec_asm_src} -} + +GENERATE[ecp_nistz256-x86.s]=asm/ecp_nistz256-x86.pl $(PERLASM_SCHEME) $(CFLAGS) $(LIB_CFLAGS) $(PROCESSOR) + +GENERATE[ecp_nistz256-x86_64.s]=asm/ecp_nistz256-x86_64.pl $(PERLASM_SCHEME) + +GENERATE[ecp_nistz256-avx2.s]=asm/ecp_nistz256-avx2.pl $(PERLASM_SCHEME) + +GENERATE[ecp_nistz256-sparcv9.S]=asm/ecp_nistz256-sparcv9.pl $(PERLASM_SCHEME) +INCLUDE[ecp_nistz256-sparcv9.o]=.. + +GENERATE[ecp_nistz256-armv4.S]=asm/ecp_nistz256-armv4.pl $(PERLASM_SCHEME) +INCLUDE[ecp_nistz256-armv4.o]=.. +GENERATE[ecp_nistz256-armv8.S]=asm/ecp_nistz256-armv8.pl $(PERLASM_SCHEME) +INCLUDE[ecp_nistz256-armv8.o]=.. + +BEGINRAW[Makefile] +{- $builddir -}/ecp_nistz256-%.S: {- $sourcedir -}/asm/ecp_nistz256-%.pl + CC="$(CC)" $(PERL) $< $(PERLASM_SCHEME) $@ +ENDRAW[Makefile] diff --git a/openssl-1.1.0h/crypto/ec/curve25519.c b/openssl-1.1.0h/crypto/ec/curve25519.c new file mode 100644 index 0000000..c8aa9aa --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/curve25519.c @@ -0,0 +1,3400 @@ +/* + * Copyright 2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP + * 20141124 (http://bench.cr.yp.to/supercop.html). + * + * The field functions are shared by Ed25519 and X25519 where possible. */ + +#include <string.h> +#include "ec_lcl.h" + + +/* fe means field element. Here the field is \Z/(2^255-19). An element t, + * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 + * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on + * context. */ +typedef int32_t fe[10]; + +static const int64_t kBottom25Bits = 0x1ffffffLL; +static const int64_t kBottom26Bits = 0x3ffffffLL; +static const int64_t kTop39Bits = 0xfffffffffe000000LL; +static const int64_t kTop38Bits = 0xfffffffffc000000LL; + +static uint64_t load_3(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + return result; +} + +static uint64_t load_4(const uint8_t *in) { + uint64_t result; + result = (uint64_t)in[0]; + result |= ((uint64_t)in[1]) << 8; + result |= ((uint64_t)in[2]) << 16; + result |= ((uint64_t)in[3]) << 24; + return result; +} + +static void fe_frombytes(fe h, const uint8_t *s) { + /* Ignores top bit of h. */ + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* Preconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Write p=2^255-19; q=floor(h/p). + * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + * + * Proof: + * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + * + * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + * Then 0<y<1. + * + * Write r=h-pq. + * Have 0<=r<=p-1=2^255-20. + * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + * + * Write x=r+19(2^-255)r+y. + * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + * + * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) + * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ +static void fe_tobytes(uint8_t *s, const fe h) { + int32_t h0 = h[0]; + int32_t h1 = h[1]; + int32_t h2 = h[2]; + int32_t h3 = h[3]; + int32_t h4 = h[4]; + int32_t h5 = h[5]; + int32_t h6 = h[6]; + int32_t h7 = h[7]; + int32_t h8 = h[8]; + int32_t h9 = h[9]; + int32_t q; + + q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + h1 += h0 >> 26; h0 &= kBottom26Bits; + h2 += h1 >> 25; h1 &= kBottom25Bits; + h3 += h2 >> 26; h2 &= kBottom26Bits; + h4 += h3 >> 25; h3 &= kBottom25Bits; + h5 += h4 >> 26; h4 &= kBottom26Bits; + h6 += h5 >> 25; h5 &= kBottom25Bits; + h7 += h6 >> 26; h6 &= kBottom26Bits; + h8 += h7 >> 25; h7 &= kBottom25Bits; + h9 += h8 >> 26; h8 &= kBottom26Bits; + h9 &= kBottom25Bits; + /* h10 = carry9 */ + + /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + * Have h0+...+2^230 h9 between 0 and 2^255-1; + * evidently 2^255 h10-2^255 q = 0. + * Goal: Output h0+...+2^230 h9. */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | ((uint32_t)(h1) << 2); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | ((uint32_t)(h2) << 3); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | ((uint32_t)(h3) << 5); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | ((uint32_t)(h4) << 6); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | ((uint32_t)(h6) << 1); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | ((uint32_t)(h7) << 3); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | ((uint32_t)(h8) << 4); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | ((uint32_t)(h9) << 6); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + +/* h = f */ +static void fe_copy(fe h, const fe f) { + memmove(h, f, sizeof(int32_t) * 10); +} + +/* h = 0 */ +static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } + +/* h = 1 */ +static void fe_1(fe h) { + memset(h, 0, sizeof(int32_t) * 10); + h[0] = 1; +} + +/* h = f + g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +static void fe_add(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] + g[i]; + } +} + +/* h = f - g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ +static void fe_sub(fe h, const fe f, const fe g) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = f[i] - g[i]; + } +} + +/* h = f * g + * Can overlap h with f or g. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * Notes on implementation strategy: + * + * Using schoolbook multiplication. + * Karatsuba would save a little in some cost models. + * + * Most multiplications by 2 and 19 are 32-bit precomputations; + * cheaper than 64-bit postcomputations. + * + * There is one remaining multiplication by 19 in the carry chain; + * one *19 precomputation can be merged into this, + * but the resulting data flow is considerably less clean. + * + * There are 12 carries below. + * 10 of them are 2-way parallelizable and vectorizable. + * Can get away with 11 carries, but then data flow is much deeper. + * + * With tighter constraints on inputs can squeeze carries into int32. */ +static void fe_mul(fe h, const fe f, const fe g) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; + int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; + int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; + int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; + int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; + int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; + int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; + int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; + int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; + int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* h = f * f + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * See fe_mul.c for discussion of implementation strategy. */ +static void fe_sq(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +static void fe_invert(fe out, const fe z) { + fe t0; + fe t1; + fe t2; + fe t3; + int i; + + /* + * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as + * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. + */ + + /* t0 = z ** 2 */ + fe_sq(t0, z); + + /* t1 = t0 ** (2 ** 2) = z ** 8 */ + fe_sq(t1, t0); + fe_sq(t1, t1); + + /* t1 = z * t1 = z ** 9 */ + fe_mul(t1, z, t1); + /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ + fe_mul(t0, t0, t1); + + /* t2 = t0 ** 2 = z ** 22 */ + fe_sq(t2, t0); + + /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ + fe_mul(t1, t1, t2); + + /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ + fe_sq(t2, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t2, t2); + } + + /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ + fe_mul(t1, t2, t1); + + /* Continuing similarly... */ + + /* t2 = z ** (2 ** 20 - 1) */ + fe_sq(t2, t1); + for (i = 1; i < 10; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + + /* t2 = z ** (2 ** 40 - 1) */ + fe_sq(t3, t2); + for (i = 1; i < 20; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + + /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ + for (i = 0; i < 10; ++i) { + fe_sq(t2, t2); + } + /* t1 = z ** (2 ** 50 - 1) */ + fe_mul(t1, t2, t1); + + /* t2 = z ** (2 ** 100 - 1) */ + fe_sq(t2, t1); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + fe_mul(t2, t2, t1); + + /* t2 = z ** (2 ** 200 - 1) */ + fe_sq(t3, t2); + for (i = 1; i < 100; ++i) { + fe_sq(t3, t3); + } + fe_mul(t2, t3, t2); + + /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ + fe_sq(t2, t2); + for (i = 1; i < 50; ++i) { + fe_sq(t2, t2); + } + + /* t1 = z ** (2 ** 250 - 1) */ + fe_mul(t1, t2, t1); + + /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ + fe_sq(t1, t1); + for (i = 1; i < 5; ++i) { + fe_sq(t1, t1); + } + + /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ + fe_mul(out, t1, t0); +} + +/* h = -f + * + * Preconditions: + * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +static void fe_neg(fe h, const fe f) { + unsigned i; + for (i = 0; i < 10; i++) { + h[i] = -f[i]; + } +} + +/* Replace (f,g) with (g,g) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +static void fe_cmov(fe f, const fe g, unsigned b) { + size_t i; + b = 0-b; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + } +} + +/* h = 2 * f * f + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + * + * See fe_mul.c for discussion of implementation strategy. */ +static void fe_sq2(fe h, const fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; + int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; + int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; + int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; + int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; + int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; + int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; + int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; + int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; + int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* ge means group element. + + * Here the group is the set of pairs (x,y) of field elements (see fe.h) + * satisfying -x^2 + y^2 = 1 + d x^2y^2 + * where d = -121665/121666. + * + * Representations: + * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z + * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT + * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T + * ge_precomp (Duif): (y+x,y-x,2dxy) */ + +typedef struct { + fe X; + fe Y; + fe Z; +} ge_p2; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p3; + +typedef struct { + fe X; + fe Y; + fe Z; + fe T; +} ge_p1p1; + +typedef struct { + fe yplusx; + fe yminusx; + fe xy2d; +} ge_precomp; + +typedef struct { + fe YplusX; + fe YminusX; + fe Z; + fe T2d; +} ge_cached; + +static void ge_p3_0(ge_p3 *h) { + fe_0(h->X); + fe_1(h->Y); + fe_1(h->Z); + fe_0(h->T); +} + +static void ge_precomp_0(ge_precomp *h) { + fe_1(h->yplusx); + fe_1(h->yminusx); + fe_0(h->xy2d); +} + +/* r = p */ +static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { + fe_copy(r->X, p->X); + fe_copy(r->Y, p->Y); + fe_copy(r->Z, p->Z); +} + +/* r = p */ +static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); +} + +/* r = p */ +static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { + fe_mul(r->X, p->X, p->T); + fe_mul(r->Y, p->Y, p->Z); + fe_mul(r->Z, p->Z, p->T); + fe_mul(r->T, p->X, p->Y); +} + +/* r = 2 * p */ +static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { + fe t0; + + fe_sq(r->X, p->X); + fe_sq(r->Z, p->Y); + fe_sq2(r->T, p->Z); + fe_add(r->Y, p->X, p->Y); + fe_sq(t0, r->Y); + fe_add(r->Y, r->Z, r->X); + fe_sub(r->Z, r->Z, r->X); + fe_sub(r->X, t0, r->Y); + fe_sub(r->T, r->T, r->Z); +} + +/* r = 2 * p */ +static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { + ge_p2 q; + ge_p3_to_p2(&q, p); + ge_p2_dbl(r, &q); +} + +/* r = p + q */ +static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { + fe t0; + + fe_add(r->X, p->Y, p->X); + fe_sub(r->Y, p->Y, p->X); + fe_mul(r->Z, r->X, q->yplusx); + fe_mul(r->Y, r->Y, q->yminusx); + fe_mul(r->T, q->xy2d, p->T); + fe_add(t0, p->Z, p->Z); + fe_sub(r->X, r->Z, r->Y); + fe_add(r->Y, r->Z, r->Y); + fe_add(r->Z, t0, r->T); + fe_sub(r->T, t0, r->T); +} + +static uint8_t equal(signed char b, signed char c) { + uint8_t ub = b; + uint8_t uc = c; + uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ + uint32_t y = x; /* 0: yes; 1..255: no */ + y -= 1; /* 4294967295: yes; 0..254: no */ + y >>= 31; /* 1: yes; 0: no */ + return y; +} + +static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { + fe_cmov(t->yplusx, u->yplusx, b); + fe_cmov(t->yminusx, u->yminusx, b); + fe_cmov(t->xy2d, u->xy2d, b); +} + +/* k25519Precomp[i][j] = (j+1)*256^i*B */ +static const ge_precomp k25519Precomp[32][8] = { + { + { + {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, + 27544626, -11754271, -6079156, 2047605}, + {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, + 5043384, 19500929, -15469378}, + {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, + 29287919, 11864899, -24514362, -4438546}, + }, + { + {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, + -11717903, -3814571, -358445, -10211303}, + {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, + -15616551, 11189268, -26829678, -5319081}, + {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, + -3128826, -9541118, -15472047, -4166697}, + }, + { + {15636291, -9688557, 24204773, -7912398, 616977, -16685262, + 27787600, -14772189, 28944400, -1550024}, + {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, + 16354577, -11775962, 7689662, 11199574}, + {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, + 7512774, 10017326, -17749093, -9920357}, + }, + { + {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, + -28926210, 15006023, 3284568, -6276540}, + {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, + 7464579, 9656445, 13059162, 10374397}, + {7798556, 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12694420, 33473243, -13382104}, + {33184999, 11180355, 15832085, -11385430, -1633671, 225884, + 15089336, -11023903, -6135662, 14480053}, + }, + { + {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, + 5496208, 13685227, 27595050, 8737275}, + {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, + -31008351, -12610604, 26498114, 66511}, + {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, + 30540766, -4286747, -13327787, -7515095}, + }, + { + {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, + 8205540, 13585437, -17127465, 15115439}, + {23711543, -672915, 31206561, -8362711, 6164647, -9709987, + -33535882, -1426096, 8236921, 16492939}, + {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, + 19574902, 10071562, 6708380, -6222424}, + }, + { + {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, + 9328700, 29955601, -11678310}, + {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, + -25892142, -12635595, -9917575, 6216608}, + {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, + 24822830, -6146567, -26767480, 7525079}, + }, + { + {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, + -910336, -2782495, -19386633, 11994101}, + {21691500, -13624626, -641331, -14367021, 3285881, -3483596, + -25064666, 9718258, -7477437, 13381418}, + {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, + 23111648, -6375247, 28535282, 15779576}, + }, + { + {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, + -14068454, 12021730, 9955285, -16303356}, + {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, + -18426029, 9924399, 20194861, 13380996}, + {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, + -1984914, 15707771, 26342023, 10146099}, + }, + }, + { + { + {-26016874, -219943, 21339191, -41388, 19745256, -2878700, + -29637280, 2227040, 21612326, -545728}, + {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, + 25764461, 12243797, -20856566, 11649658}, + {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, + 6114064, 33514190, 2333242}, + }, + { + {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, + -6679750, -12670638, 24350578, -13450001}, + {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, + -31536088, -10406836, 8317860, 12352766}, + {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, + -23552096, -2287550, 20712163, 6719373}, + }, + { + {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, + -3763210, 26224235, -3297458}, + {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, + 21728352, 9493610, 18620611, -16428628}, + {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, + -5269471, -9725556, -30701573, -16479657}, + }, + { + {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, + 12248509, -5240639, 13735342, 1934062}, + {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, + -15136294, -3765346, -21277997, 5473616}, + {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, + -7125085, 12469656, 29111212, -5451014}, + }, + { + {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, + 24367466, 6388839, -10295587, 452383}, + {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, + -24236251, -5915248, 15766062, 8407814}, + {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, + -8917023, -4388953, -8067909, 2276718}, + }, + { + {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, + -23827587, 5096219, 22740376, -7303417}, + {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, + 24051124, 13742383, -15637599, 13295222}, + {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, + -17720195, -4612972, -4451357, -14669444}, + }, + { + {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, + -2469266, -4141880, 7770569, 9620597}, + {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, + -1694323, -33502340, -14767970}, + {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, + 1220118, 30494170, -11440799}, + }, + { + {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, + -26739026, 926050, -1684339, -13333647}, + {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, + 9021034, 9078865, 3353509, 4033511}, + {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, + 23161163, 8839127, 27485041, 7356032}, + }, + }, + { + { + {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, + 2625015, 28431036, -16771834}, + {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, + -22545972, 14150565, 15970762, 4099461}, + {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, + 13617293, -9937143, 11465739, 8317062}, + }, + { + {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, + 14898637, 3848455, 20969334, -5157516}, + {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, + -21610826, -3649888, 11177095, 14989547}, + {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, + 13515641, 2581286, -28487508, 9930240}, + }, + { + {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, + 18345767, -13403753, 16291481, -5314038}, + {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, + 6957617, 4368891, 9788741}, + {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, + -21722536, -8613148, 16250552, -11111103}, + }, + { + {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, + 10604807, -30190403, 4782747}, + {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, + -9981571, 4383045, 22546403, 437323}, + {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, + 27343084, 2786261, -30633590, -14097016}, + }, + { + {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, + -19690631, 2355319, -19284671, -6114373}, + {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, + 18952177, 15496498, -29380133, 11754228}, + {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, + 7141596, 11724556, 22761615, -10134141}, + }, + { + {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, + -28741185, -12227393, 32851222, 11717399}, + {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, + 31474879, 3483633, -1193175, -4030831}, + {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, + 33142652, 6546660, -19985279, -3948376}, + }, + { + {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, + -8537131, -12833048, -30772034, -15486313}, + {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, + -31135347, -16049879, 10928917, 3011958}, + {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, + -30831056, -12805180, 18008031, 10258577}, + }, + { + {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, + -1853465, 1367120, 25127874, 6671743}, + {29701166, -14373934, -10878120, 9279288, -17568, 13127210, + 21382910, 11042292, 25838796, 4642684}, + {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, + 30468147, -13900640, 18423289, 4177476}, + }, + }, +}; + +static uint8_t negative(signed char b) { + uint32_t x = b; + x >>= 31; /* 1: yes; 0: no */ + return x; +} + +static void table_select(ge_precomp *t, int pos, signed char b) { + ge_precomp minust; + uint8_t bnegative = negative(b); + uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); + + ge_precomp_0(t); + cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); + cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); + cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); + cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); + cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); + cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); + cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); + cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); + fe_copy(minust.yplusx, t->yminusx); + fe_copy(minust.yminusx, t->yplusx); + fe_neg(minust.xy2d, t->xy2d); + cmov(t, &minust, bnegative); +} + +/* h = a * B + * where a = a[0]+256*a[1]+...+256^31 a[31] + * B is the Ed25519 base point (x,4/5) with x positive. + * + * Preconditions: + * a[31] <= 127 */ +static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { + signed char e[64]; + signed char carry; + ge_p1p1 r; + ge_p2 s; + ge_precomp t; + int i; + + for (i = 0; i < 32; ++i) { + e[2 * i + 0] = (a[i] >> 0) & 15; + e[2 * i + 1] = (a[i] >> 4) & 15; + } + /* each e[i] is between 0 and 15 */ + /* e[63] is between 0 and 7 */ + + carry = 0; + for (i = 0; i < 63; ++i) { + e[i] += carry; + carry = e[i] + 8; + carry >>= 4; + e[i] -= carry << 4; + } + e[63] += carry; + /* each e[i] is between -8 and 8 */ + + ge_p3_0(h); + for (i = 1; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } + + ge_p3_dbl(&r, h); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p2(&s, &r); + ge_p2_dbl(&r, &s); + ge_p1p1_to_p3(h, &r); + + for (i = 0; i < 64; i += 2) { + table_select(&t, i / 2, e[i]); + ge_madd(&r, h, &t); + ge_p1p1_to_p3(h, &r); + } + + OPENSSL_cleanse(e, sizeof(e)); +} + +/* Replace (f,g) with (g,f) if b == 1; + * replace (f,g) with (f,g) if b == 0. + * + * Preconditions: b in {0,1}. */ +static void fe_cswap(fe f, fe g, unsigned int b) { + size_t i; + b = 0-b; + for (i = 0; i < 10; i++) { + int32_t x = f[i] ^ g[i]; + x &= b; + f[i] ^= x; + g[i] ^= x; + } +} + +/* h = f * 121666 + * Can overlap h with f. + * + * Preconditions: + * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + * Postconditions: + * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ +static void fe_mul121666(fe h, fe f) { + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + int64_t h0 = f0 * (int64_t) 121666; + int64_t h1 = f1 * (int64_t) 121666; + int64_t h2 = f2 * (int64_t) 121666; + int64_t h3 = f3 * (int64_t) 121666; + int64_t h4 = f4 * (int64_t) 121666; + int64_t h5 = f5 * (int64_t) 121666; + int64_t h6 = f6 * (int64_t) 121666; + int64_t h7 = f7 * (int64_t) 121666; + int64_t h8 = f8 * (int64_t) 121666; + int64_t h9 = f9 * (int64_t) 121666; + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; + carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; + carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; + carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; + carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; + + carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; + carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; + carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; + carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; + carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +static void x25519_scalar_mult_generic(uint8_t out[32], + const uint8_t scalar[32], + const uint8_t point[32]) { + fe x1, x2, z2, x3, z3, tmp0, tmp1; + uint8_t e[32]; + unsigned swap = 0; + int pos; + + memcpy(e, scalar, 32); + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + fe_frombytes(x1, point); + fe_1(x2); + fe_0(z2); + fe_copy(x3, x1); + fe_1(z3); + + for (pos = 254; pos >= 0; --pos) { + unsigned b = 1 & (e[pos / 8] >> (pos & 7)); + swap ^= b; + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + swap = b; + fe_sub(tmp0, x3, z3); + fe_sub(tmp1, x2, z2); + fe_add(x2, x2, z2); + fe_add(z2, x3, z3); + fe_mul(z3, tmp0, x2); + fe_mul(z2, z2, tmp1); + fe_sq(tmp0, tmp1); + fe_sq(tmp1, x2); + fe_add(x3, z3, z2); + fe_sub(z2, z3, z2); + fe_mul(x2, tmp1, tmp0); + fe_sub(tmp1, tmp1, tmp0); + fe_sq(z2, z2); + fe_mul121666(z3, tmp1); + fe_sq(x3, x3); + fe_add(tmp0, tmp0, z3); + fe_mul(z3, x1, z2); + fe_mul(z2, tmp1, tmp0); + } + fe_cswap(x2, x3, swap); + fe_cswap(z2, z3, swap); + + fe_invert(z2, z2); + fe_mul(x2, x2, z2); + fe_tobytes(out, x2); + + OPENSSL_cleanse(e, sizeof(e)); +} + +static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], + const uint8_t point[32]) { + x25519_scalar_mult_generic(out, scalar, point); +} + +int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], + const uint8_t peer_public_value[32]) { + static const uint8_t kZeros[32] = {0}; + x25519_scalar_mult(out_shared_key, private_key, peer_public_value); + /* The all-zero output results when the input is a point of small order. */ + return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; +} + +void X25519_public_from_private(uint8_t out_public_value[32], + const uint8_t private_key[32]) { + uint8_t e[32]; + ge_p3 A; + fe zplusy, zminusy, zminusy_inv; + + memcpy(e, private_key, 32); + e[0] &= 248; + e[31] &= 127; + e[31] |= 64; + + ge_scalarmult_base(&A, e); + + /* We only need the u-coordinate of the curve25519 point. The map is + * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ + fe_add(zplusy, A.Z, A.Y); + fe_sub(zminusy, A.Z, A.Y); + fe_invert(zminusy_inv, zminusy); + fe_mul(zplusy, zplusy, zminusy_inv); + fe_tobytes(out_public_value, zplusy); + + OPENSSL_cleanse(e, sizeof(e)); +} diff --git a/openssl-1.1.0h/crypto/ec/ec2_mult.c b/openssl-1.1.0h/crypto/ec/ec2_mult.c new file mode 100644 index 0000000..e4a1ec5 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec2_mult.c @@ -0,0 +1,418 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The software is originally written by Sheueling Chang Shantz and + * Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <openssl/err.h> + +#include "internal/bn_int.h" +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_EC2M + +/*- + * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective + * coordinates. + * Uses algorithm Mdouble in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). + * modified to not require precomputation of c=b^{2^{m-1}}. + */ +static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, + BN_CTX *ctx) +{ + BIGNUM *t1; + int ret = 0; + + /* Since Mdouble is static we can guarantee that ctx != NULL. */ + BN_CTX_start(ctx); + t1 = BN_CTX_get(ctx); + if (t1 == NULL) + goto err; + + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, z, ctx)) + goto err; + if (!group->meth->field_mul(group, z, x, t1, ctx)) + goto err; + if (!group->meth->field_sqr(group, x, x, ctx)) + goto err; + if (!group->meth->field_sqr(group, t1, t1, ctx)) + goto err; + if (!group->meth->field_mul(group, t1, group->b, t1, ctx)) + goto err; + if (!BN_GF2m_add(x, x, t1)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery + * projective coordinates. + * Uses algorithm Madd in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). + */ +static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, + BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2, + BN_CTX *ctx) +{ + BIGNUM *t1, *t2; + int ret = 0; + + /* Since Madd is static we can guarantee that ctx != NULL. */ + BN_CTX_start(ctx); + t1 = BN_CTX_get(ctx); + t2 = BN_CTX_get(ctx); + if (t2 == NULL) + goto err; + + if (!BN_copy(t1, x)) + goto err; + if (!group->meth->field_mul(group, x1, x1, z2, ctx)) + goto err; + if (!group->meth->field_mul(group, z1, z1, x2, ctx)) + goto err; + if (!group->meth->field_mul(group, t2, x1, z1, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_sqr(group, z1, z1, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z1, t1, ctx)) + goto err; + if (!BN_GF2m_add(x1, x1, t2)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) + * using Montgomery point multiplication algorithm Mxy() in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). + * Returns: + * 0 on error + * 1 if return value should be the point at infinity + * 2 otherwise + */ +static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, + BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, + BN_CTX *ctx) +{ + BIGNUM *t3, *t4, *t5; + int ret = 0; + + if (BN_is_zero(z1)) { + BN_zero(x2); + BN_zero(z2); + return 1; + } + + if (BN_is_zero(z2)) { + if (!BN_copy(x2, x)) + return 0; + if (!BN_GF2m_add(z2, x, y)) + return 0; + return 2; + } + + /* Since Mxy is static we can guarantee that ctx != NULL. */ + BN_CTX_start(ctx); + t3 = BN_CTX_get(ctx); + t4 = BN_CTX_get(ctx); + t5 = BN_CTX_get(ctx); + if (t5 == NULL) + goto err; + + if (!BN_one(t5)) + goto err; + + if (!group->meth->field_mul(group, t3, z1, z2, ctx)) + goto err; + + if (!group->meth->field_mul(group, z1, z1, x, ctx)) + goto err; + if (!BN_GF2m_add(z1, z1, x1)) + goto err; + if (!group->meth->field_mul(group, z2, z2, x, ctx)) + goto err; + if (!group->meth->field_mul(group, x1, z2, x1, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, x2)) + goto err; + + if (!group->meth->field_mul(group, z2, z2, z1, ctx)) + goto err; + if (!group->meth->field_sqr(group, t4, x, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, y)) + goto err; + if (!group->meth->field_mul(group, t4, t4, t3, ctx)) + goto err; + if (!BN_GF2m_add(t4, t4, z2)) + goto err; + + if (!group->meth->field_mul(group, t3, t3, x, ctx)) + goto err; + if (!group->meth->field_div(group, t3, t5, t3, ctx)) + goto err; + if (!group->meth->field_mul(group, t4, t3, t4, ctx)) + goto err; + if (!group->meth->field_mul(group, x2, x1, t3, ctx)) + goto err; + if (!BN_GF2m_add(z2, x2, x)) + goto err; + + if (!group->meth->field_mul(group, z2, z2, t4, ctx)) + goto err; + if (!BN_GF2m_add(z2, z2, y)) + goto err; + + ret = 2; + + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Computes scalar*point and stores the result in r. + * point can not equal r. + * Uses a modified algorithm 2P of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). + * + * To protect against side-channel attack the function uses constant time swap, + * avoiding conditional branches. + */ +static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, + EC_POINT *r, + const BIGNUM *scalar, + const EC_POINT *point, + BN_CTX *ctx) +{ + BIGNUM *x1, *x2, *z1, *z2; + int ret = 0, i, group_top; + BN_ULONG mask, word; + + if (r == point) { + ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); + return 0; + } + + /* if result should be point at infinity */ + if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || + EC_POINT_is_at_infinity(group, point)) { + return EC_POINT_set_to_infinity(group, r); + } + + /* only support affine coordinates */ + if (!point->Z_is_one) + return 0; + + /* + * Since point_multiply is static we can guarantee that ctx != NULL. + */ + BN_CTX_start(ctx); + x1 = BN_CTX_get(ctx); + z1 = BN_CTX_get(ctx); + if (z1 == NULL) + goto err; + + x2 = r->X; + z2 = r->Y; + + group_top = bn_get_top(group->field); + if (bn_wexpand(x1, group_top) == NULL + || bn_wexpand(z1, group_top) == NULL + || bn_wexpand(x2, group_top) == NULL + || bn_wexpand(z2, group_top) == NULL) + goto err; + + if (!BN_GF2m_mod_arr(x1, point->X, group->poly)) + goto err; /* x1 = x */ + if (!BN_one(z1)) + goto err; /* z1 = 1 */ + if (!group->meth->field_sqr(group, z2, x1, ctx)) + goto err; /* z2 = x1^2 = x^2 */ + if (!group->meth->field_sqr(group, x2, z2, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, group->b)) + goto err; /* x2 = x^4 + b */ + + /* find top most bit and go one past it */ + i = bn_get_top(scalar) - 1; + mask = BN_TBIT; + word = bn_get_words(scalar)[i]; + while (!(word & mask)) + mask >>= 1; + mask >>= 1; + /* if top most bit was at word break, go to next word */ + if (!mask) { + i--; + mask = BN_TBIT; + } + + for (; i >= 0; i--) { + word = bn_get_words(scalar)[i]; + while (mask) { + BN_consttime_swap(word & mask, x1, x2, group_top); + BN_consttime_swap(word & mask, z1, z2, group_top); + if (!gf2m_Madd(group, point->X, x2, z2, x1, z1, ctx)) + goto err; + if (!gf2m_Mdouble(group, x1, z1, ctx)) + goto err; + BN_consttime_swap(word & mask, x1, x2, group_top); + BN_consttime_swap(word & mask, z1, z2, group_top); + mask >>= 1; + } + mask = BN_TBIT; + } + + /* convert out of "projective" coordinates */ + i = gf2m_Mxy(group, point->X, point->Y, x1, z1, x2, z2, ctx); + if (i == 0) + goto err; + else if (i == 1) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { + if (!BN_one(r->Z)) + goto err; + r->Z_is_one = 1; + } + + /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ + BN_set_negative(r->X, 0); + BN_set_negative(r->Y, 0); + + ret = 1; + + err: + BN_CTX_end(ctx); + return ret; +} + +/*- + * Computes the sum + * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] + * gracefully ignoring NULL scalar values. + */ +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + int ret = 0; + size_t i; + EC_POINT *p = NULL; + EC_POINT *acc = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + /* + * This implementation is more efficient than the wNAF implementation for + * 2 or fewer points. Use the ec_wNAF_mul implementation for 3 or more + * points, or if we can perform a fast multiplication based on + * precomputation. + */ + if ((scalar && (num > 1)) || (num > 2) + || (num == 0 && EC_GROUP_have_precompute_mult(group))) { + ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); + goto err; + } + + if ((p = EC_POINT_new(group)) == NULL) + goto err; + if ((acc = EC_POINT_new(group)) == NULL) + goto err; + + if (!EC_POINT_set_to_infinity(group, acc)) + goto err; + + if (scalar) { + if (!ec_GF2m_montgomery_point_multiply + (group, p, scalar, group->generator, ctx)) + goto err; + if (BN_is_negative(scalar)) + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } + + for (i = 0; i < num; i++) { + if (!ec_GF2m_montgomery_point_multiply + (group, p, scalars[i], points[i], ctx)) + goto err; + if (BN_is_negative(scalars[i])) + if (!group->meth->invert(group, p, ctx)) + goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) + goto err; + } + + if (!EC_POINT_copy(r, acc)) + goto err; + + ret = 1; + + err: + EC_POINT_free(p); + EC_POINT_free(acc); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Precomputation for point multiplication: fall back to wNAF methods because + * ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate + */ + +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + return ec_wNAF_precompute_mult(group, ctx); +} + +int ec_GF2m_have_precompute_mult(const EC_GROUP *group) +{ + return ec_wNAF_have_precompute_mult(group); +} + +#endif diff --git a/openssl-1.1.0h/crypto/ec/ec2_oct.c b/openssl-1.1.0h/crypto/ec/ec2_oct.c new file mode 100644 index 0000000..ea88ce8 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec2_oct.c @@ -0,0 +1,352 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The software is originally written by Sheueling Chang Shantz and + * Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <openssl/err.h> + +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_EC2M + +/*- + * Calculates and sets the affine coordinates of an EC_POINT from the given + * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. + * Note that the simple implementation only uses affine coordinates. + * + * The method is from the following publication: + * + * Harper, Menezes, Vanstone: + * "Public-Key Cryptosystems with Very Small Key Lengths", + * EUROCRYPT '92, Springer-Verlag LNCS 658, + * published February 1993 + * + * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe + * the same method, but claim no priority date earlier than July 29, 1994 + * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). + */ +int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x_, int y_bit, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *tmp, *x, *y, *z; + int ret = 0, z0; + + /* clear error queue */ + ERR_clear_error(); + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0) ? 1 : 0; + + BN_CTX_start(ctx); + tmp = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + z = BN_CTX_get(ctx); + if (z == NULL) + goto err; + + if (!BN_GF2m_mod_arr(x, x_, group->poly)) + goto err; + if (BN_is_zero(x)) { + if (!BN_GF2m_mod_sqrt_arr(y, group->b, group->poly, ctx)) + goto err; + } else { + if (!group->meth->field_sqr(group, tmp, x, ctx)) + goto err; + if (!group->meth->field_div(group, tmp, group->b, tmp, ctx)) + goto err; + if (!BN_GF2m_add(tmp, group->a, tmp)) + goto err; + if (!BN_GF2m_add(tmp, x, tmp)) + goto err; + if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN + && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) { + ERR_clear_error(); + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, + EC_R_INVALID_COMPRESSED_POINT); + } else + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, + ERR_R_BN_LIB); + goto err; + } + z0 = (BN_is_odd(z)) ? 1 : 0; + if (!group->meth->field_mul(group, y, x, z, ctx)) + goto err; + if (z0 != y_bit) { + if (!BN_GF2m_add(y, y, x)) + goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Converts an EC_POINT to an octet string. If buf is NULL, the encoded + * length will be returned. If the length len of buf is smaller than required + * an error will be returned. + */ +size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) +{ + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y, *yxi; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) { + /* encodes to a single 0 octet */ + if (buf != NULL) { + if (len < 1) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + /* ret := required output buffer length */ + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + ret = + (form == + POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) { + if (len < ret) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + + buf[0] = form; + if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (BN_is_odd(yxi)) + buf[0]++; + } + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED + || form == POINT_CONVERSION_HYBRID) { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return 0; +} + +/* + * Converts an octet string representation to an EC_POINT. Note that the + * simple implementation only uses affine coordinates. + */ +int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, + BN_CTX *ctx) +{ + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *yxi; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) { + if (len != 1) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + enc_len = + (form == + POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; + + if (len != enc_len) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) + goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, group->field) >= 0) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GF2m + (group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, group->field) >= 0) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) { + if (!group->meth->field_div(group, yxi, y, x, ctx)) + goto err; + if (y_bit != BN_is_odd(yxi)) { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + /* + * EC_POINT_set_affine_coordinates_GF2m is responsible for checking that + * the point is on the curve. + */ + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} +#endif diff --git a/openssl-1.1.0h/crypto/ec/ec2_smpl.c b/openssl-1.1.0h/crypto/ec/ec2_smpl.c new file mode 100644 index 0000000..cfeef5f --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec2_smpl.c @@ -0,0 +1,758 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The software is originally written by Sheueling Chang Shantz and + * Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <openssl/err.h> + +#include "internal/bn_int.h" +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_EC2M + +const EC_METHOD *EC_GF2m_simple_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_characteristic_two_field, + ec_GF2m_simple_group_init, + ec_GF2m_simple_group_finish, + ec_GF2m_simple_group_clear_finish, + ec_GF2m_simple_group_copy, + ec_GF2m_simple_group_set_curve, + ec_GF2m_simple_group_get_curve, + ec_GF2m_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GF2m_simple_group_check_discriminant, + ec_GF2m_simple_point_init, + ec_GF2m_simple_point_finish, + ec_GF2m_simple_point_clear_finish, + ec_GF2m_simple_point_copy, + ec_GF2m_simple_point_set_to_infinity, + 0 /* set_Jprojective_coordinates_GFp */ , + 0 /* get_Jprojective_coordinates_GFp */ , + ec_GF2m_simple_point_set_affine_coordinates, + ec_GF2m_simple_point_get_affine_coordinates, + 0, 0, 0, + ec_GF2m_simple_add, + ec_GF2m_simple_dbl, + ec_GF2m_simple_invert, + ec_GF2m_simple_is_at_infinity, + ec_GF2m_simple_is_on_curve, + ec_GF2m_simple_cmp, + ec_GF2m_simple_make_affine, + ec_GF2m_simple_points_make_affine, + + /* + * the following three method functions are defined in ec2_mult.c + */ + ec_GF2m_simple_mul, + ec_GF2m_precompute_mult, + ec_GF2m_have_precompute_mult, + + ec_GF2m_simple_field_mul, + ec_GF2m_simple_field_sqr, + ec_GF2m_simple_field_div, + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/* + * Initialize a GF(2^m)-based EC_GROUP structure. Note that all other members + * are handled by EC_GROUP_new. + */ +int ec_GF2m_simple_group_init(EC_GROUP *group) +{ + group->field = BN_new(); + group->a = BN_new(); + group->b = BN_new(); + + if (group->field == NULL || group->a == NULL || group->b == NULL) { + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); + return 0; + } + return 1; +} + +/* + * Free a GF(2^m)-based EC_GROUP structure. Note that all other members are + * handled by EC_GROUP_free. + */ +void ec_GF2m_simple_group_finish(EC_GROUP *group) +{ + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); +} + +/* + * Clear and free a GF(2^m)-based EC_GROUP structure. Note that all other + * members are handled by EC_GROUP_clear_free. + */ +void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) +{ + BN_clear_free(group->field); + BN_clear_free(group->a); + BN_clear_free(group->b); + group->poly[0] = 0; + group->poly[1] = 0; + group->poly[2] = 0; + group->poly[3] = 0; + group->poly[4] = 0; + group->poly[5] = -1; +} + +/* + * Copy a GF(2^m)-based EC_GROUP structure. Note that all other members are + * handled by EC_GROUP_copy. + */ +int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) +{ + if (!BN_copy(dest->field, src->field)) + return 0; + if (!BN_copy(dest->a, src->a)) + return 0; + if (!BN_copy(dest->b, src->b)) + return 0; + dest->poly[0] = src->poly[0]; + dest->poly[1] = src->poly[1]; + dest->poly[2] = src->poly[2]; + dest->poly[3] = src->poly[3]; + dest->poly[4] = src->poly[4]; + dest->poly[5] = src->poly[5]; + if (bn_wexpand(dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == + NULL) + return 0; + if (bn_wexpand(dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == + NULL) + return 0; + bn_set_all_zero(dest->a); + bn_set_all_zero(dest->b); + return 1; +} + +/* Set the curve parameters of an EC_GROUP structure. */ +int ec_GF2m_simple_group_set_curve(EC_GROUP *group, + const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0, i; + + /* group->field */ + if (!BN_copy(group->field, p)) + goto err; + i = BN_GF2m_poly2arr(group->field, group->poly, 6) - 1; + if ((i != 5) && (i != 3)) { + ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); + goto err; + } + + /* group->a */ + if (!BN_GF2m_mod_arr(group->a, a, group->poly)) + goto err; + if (bn_wexpand(group->a, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) + == NULL) + goto err; + bn_set_all_zero(group->a); + + /* group->b */ + if (!BN_GF2m_mod_arr(group->b, b, group->poly)) + goto err; + if (bn_wexpand(group->b, (int)(group->poly[0] + BN_BITS2 - 1) / BN_BITS2) + == NULL) + goto err; + bn_set_all_zero(group->b); + + ret = 1; + err: + return ret; +} + +/* + * Get the curve parameters of an EC_GROUP structure. If p, a, or b are NULL + * then there values will not be set but the method will return with success. + */ +int ec_GF2m_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, + BIGNUM *a, BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + + if (p != NULL) { + if (!BN_copy(p, group->field)) + return 0; + } + + if (a != NULL) { + if (!BN_copy(a, group->a)) + goto err; + } + + if (b != NULL) { + if (!BN_copy(b, group->b)) + goto err; + } + + ret = 1; + + err: + return ret; +} + +/* + * Gets the degree of the field. For a curve over GF(2^m) this is the value + * m. + */ +int ec_GF2m_simple_group_get_degree(const EC_GROUP *group) +{ + return BN_num_bits(group->field) - 1; +} + +/* + * Checks the discriminant of the curve. y^2 + x*y = x^3 + a*x^2 + b is an + * elliptic curve <=> b != 0 (mod p) + */ +int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *group, + BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *b; + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT, + ERR_R_MALLOC_FAILURE); + goto err; + } + } + BN_CTX_start(ctx); + b = BN_CTX_get(ctx); + if (b == NULL) + goto err; + + if (!BN_GF2m_mod_arr(b, group->b, group->poly)) + goto err; + + /* + * check the discriminant: y^2 + x*y = x^3 + a*x^2 + b is an elliptic + * curve <=> b != 0 (mod p) + */ + if (BN_is_zero(b)) + goto err; + + ret = 1; + + err: + if (ctx != NULL) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* Initializes an EC_POINT. */ +int ec_GF2m_simple_point_init(EC_POINT *point) +{ + point->X = BN_new(); + point->Y = BN_new(); + point->Z = BN_new(); + + if (point->X == NULL || point->Y == NULL || point->Z == NULL) { + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); + return 0; + } + return 1; +} + +/* Frees an EC_POINT. */ +void ec_GF2m_simple_point_finish(EC_POINT *point) +{ + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); +} + +/* Clears and frees an EC_POINT. */ +void ec_GF2m_simple_point_clear_finish(EC_POINT *point) +{ + BN_clear_free(point->X); + BN_clear_free(point->Y); + BN_clear_free(point->Z); + point->Z_is_one = 0; +} + +/* + * Copy the contents of one EC_POINT into another. Assumes dest is + * initialized. + */ +int ec_GF2m_simple_point_copy(EC_POINT *dest, const EC_POINT *src) +{ + if (!BN_copy(dest->X, src->X)) + return 0; + if (!BN_copy(dest->Y, src->Y)) + return 0; + if (!BN_copy(dest->Z, src->Z)) + return 0; + dest->Z_is_one = src->Z_is_one; + + return 1; +} + +/* + * Set an EC_POINT to the point at infinity. A point at infinity is + * represented by having Z=0. + */ +int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *group, + EC_POINT *point) +{ + point->Z_is_one = 0; + BN_zero(point->Z); + return 1; +} + +/* + * Set the coordinates of an EC_POINT using affine coordinates. Note that + * the simple implementation only uses affine coordinates. + */ +int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) +{ + int ret = 0; + if (x == NULL || y == NULL) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (!BN_copy(point->X, x)) + goto err; + BN_set_negative(point->X, 0); + if (!BN_copy(point->Y, y)) + goto err; + BN_set_negative(point->Y, 0); + if (!BN_copy(point->Z, BN_value_one())) + goto err; + BN_set_negative(point->Z, 0); + point->Z_is_one = 1; + ret = 1; + + err: + return ret; +} + +/* + * Gets the affine coordinates of an EC_POINT. Note that the simple + * implementation only uses affine coordinates. + */ +int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + int ret = 0; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + + if (BN_cmp(point->Z, BN_value_one())) { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (x != NULL) { + if (!BN_copy(x, point->X)) + goto err; + BN_set_negative(x, 0); + } + if (y != NULL) { + if (!BN_copy(y, point->Y)) + goto err; + BN_set_negative(y, 0); + } + ret = 1; + + err: + return ret; +} + +/* + * Computes a + b and stores the result in r. r could be a or b, a could be + * b. Uses algorithm A.10.2 of IEEE P1363. + */ +int ec_GF2m_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *x0, *y0, *x1, *y1, *x2, *y2, *s, *t; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, a)) { + if (!EC_POINT_copy(r, b)) + return 0; + return 1; + } + + if (EC_POINT_is_at_infinity(group, b)) { + if (!EC_POINT_copy(r, a)) + return 0; + return 1; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x0 = BN_CTX_get(ctx); + y0 = BN_CTX_get(ctx); + x1 = BN_CTX_get(ctx); + y1 = BN_CTX_get(ctx); + x2 = BN_CTX_get(ctx); + y2 = BN_CTX_get(ctx); + s = BN_CTX_get(ctx); + t = BN_CTX_get(ctx); + if (t == NULL) + goto err; + + if (a->Z_is_one) { + if (!BN_copy(x0, a->X)) + goto err; + if (!BN_copy(y0, a->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, x0, y0, ctx)) + goto err; + } + if (b->Z_is_one) { + if (!BN_copy(x1, b->X)) + goto err; + if (!BN_copy(y1, b->Y)) + goto err; + } else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, x1, y1, ctx)) + goto err; + } + + if (BN_GF2m_cmp(x0, x1)) { + if (!BN_GF2m_add(t, x0, x1)) + goto err; + if (!BN_GF2m_add(s, y0, y1)) + goto err; + if (!group->meth->field_div(group, s, s, t, ctx)) + goto err; + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, group->a)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, t)) + goto err; + } else { + if (BN_GF2m_cmp(y0, y1) || BN_is_zero(x1)) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + ret = 1; + goto err; + } + if (!group->meth->field_div(group, s, y1, x1, ctx)) + goto err; + if (!BN_GF2m_add(s, s, x1)) + goto err; + + if (!group->meth->field_sqr(group, x2, s, ctx)) + goto err; + if (!BN_GF2m_add(x2, x2, s)) + goto err; + if (!BN_GF2m_add(x2, x2, group->a)) + goto err; + } + + if (!BN_GF2m_add(y2, x1, x2)) + goto err; + if (!group->meth->field_mul(group, y2, y2, s, ctx)) + goto err; + if (!BN_GF2m_add(y2, y2, x2)) + goto err; + if (!BN_GF2m_add(y2, y2, y1)) + goto err; + + if (!EC_POINT_set_affine_coordinates_GF2m(group, r, x2, y2, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Computes 2 * a and stores the result in r. r could be a. Uses algorithm + * A.10.2 of IEEE P1363. + */ +int ec_GF2m_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ + return ec_GF2m_simple_add(group, r, a, a, ctx); +} + +int ec_GF2m_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ + if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) + /* point is its own inverse */ + return 1; + + if (!EC_POINT_make_affine(group, point, ctx)) + return 0; + return BN_GF2m_add(point->Y, point->X, point->Y); +} + +/* Indicates whether the given point is the point at infinity. */ +int ec_GF2m_simple_is_at_infinity(const EC_GROUP *group, + const EC_POINT *point) +{ + return BN_is_zero(point->Z); +} + +/*- + * Determines whether the given EC_POINT is an actual point on the curve defined + * in the EC_GROUP. A point is valid if it satisfies the Weierstrass equation: + * y^2 + x*y = x^3 + a*x^2 + b. + */ +int ec_GF2m_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, + BN_CTX *ctx) +{ + int ret = -1; + BN_CTX *new_ctx = NULL; + BIGNUM *lh, *y2; + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + + if (EC_POINT_is_at_infinity(group, point)) + return 1; + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + + /* only support affine coordinates */ + if (!point->Z_is_one) + return -1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + y2 = BN_CTX_get(ctx); + lh = BN_CTX_get(ctx); + if (lh == NULL) + goto err; + + /*- + * We have a curve defined by a Weierstrass equation + * y^2 + x*y = x^3 + a*x^2 + b. + * <=> x^3 + a*x^2 + x*y + b + y^2 = 0 + * <=> ((x + a) * x + y ) * x + b + y^2 = 0 + */ + if (!BN_GF2m_add(lh, point->X, group->a)) + goto err; + if (!field_mul(group, lh, lh, point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, point->Y)) + goto err; + if (!field_mul(group, lh, lh, point->X, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, group->b)) + goto err; + if (!field_sqr(group, y2, point->Y, ctx)) + goto err; + if (!BN_GF2m_add(lh, lh, y2)) + goto err; + ret = BN_is_zero(lh); + err: + if (ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/*- + * Indicates whether two points are equal. + * Return values: + * -1 error + * 0 equal (in affine coordinates) + * 1 not equal + */ +int ec_GF2m_simple_cmp(const EC_GROUP *group, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + BIGNUM *aX, *aY, *bX, *bY; + BN_CTX *new_ctx = NULL; + int ret = -1; + + if (EC_POINT_is_at_infinity(group, a)) { + return EC_POINT_is_at_infinity(group, b) ? 0 : 1; + } + + if (EC_POINT_is_at_infinity(group, b)) + return 1; + + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + aX = BN_CTX_get(ctx); + aY = BN_CTX_get(ctx); + bX = BN_CTX_get(ctx); + bY = BN_CTX_get(ctx); + if (bY == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, a, aX, aY, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(group, b, bX, bY, ctx)) + goto err; + ret = ((BN_cmp(aX, bX) == 0) && BN_cmp(aY, bY) == 0) ? 0 : 1; + + err: + if (ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* Forces the given EC_POINT to internally use affine coordinates. */ +int ec_GF2m_simple_make_affine(const EC_GROUP *group, EC_POINT *point, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + int ret = 0; + + if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) + return 1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) + goto err; + if (!BN_copy(point->X, x)) + goto err; + if (!BN_copy(point->Y, y)) + goto err; + if (!BN_one(point->Z)) + goto err; + point->Z_is_one = 1; + + ret = 1; + + err: + if (ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Forces each of the EC_POINTs in the given array to use affine coordinates. + */ +int ec_GF2m_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ + size_t i; + + for (i = 0; i < num; i++) { + if (!group->meth->make_affine(group, points[i], ctx)) + return 0; + } + + return 1; +} + +/* Wrapper to simple binary polynomial field multiplication implementation. */ +int ec_GF2m_simple_field_mul(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + return BN_GF2m_mod_mul_arr(r, a, b, group->poly, ctx); +} + +/* Wrapper to simple binary polynomial field squaring implementation. */ +int ec_GF2m_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + return BN_GF2m_mod_sqr_arr(r, a, group->poly, ctx); +} + +/* Wrapper to simple binary polynomial field division implementation. */ +int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + return BN_GF2m_mod_div(r, a, b, group->field, ctx); +} + +#endif diff --git a/openssl-1.1.0h/crypto/ec/ec_ameth.c b/openssl-1.1.0h/crypto/ec/ec_ameth.c new file mode 100644 index 0000000..b66adf2 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_ameth.c @@ -0,0 +1,885 @@ +/* + * Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <stdio.h> +#include "internal/cryptlib.h" +#include <openssl/x509.h> +#include <openssl/ec.h> +#include <openssl/bn.h> +#include <openssl/cms.h> +#include <openssl/asn1t.h> +#include "internal/asn1_int.h" +#include "internal/evp_int.h" +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_CMS +static int ecdh_cms_decrypt(CMS_RecipientInfo *ri); +static int ecdh_cms_encrypt(CMS_RecipientInfo *ri); +#endif + +static int eckey_param2type(int *pptype, void **ppval, EC_KEY *ec_key) +{ + const EC_GROUP *group; + int nid; + if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) { + ECerr(EC_F_ECKEY_PARAM2TYPE, EC_R_MISSING_PARAMETERS); + return 0; + } + if (EC_GROUP_get_asn1_flag(group) + && (nid = EC_GROUP_get_curve_name(group))) + /* we have a 'named curve' => just set the OID */ + { + *ppval = OBJ_nid2obj(nid); + *pptype = V_ASN1_OBJECT; + } else { /* explicit parameters */ + + ASN1_STRING *pstr = NULL; + pstr = ASN1_STRING_new(); + if (pstr == NULL) + return 0; + pstr->length = i2d_ECParameters(ec_key, &pstr->data); + if (pstr->length <= 0) { + ASN1_STRING_free(pstr); + ECerr(EC_F_ECKEY_PARAM2TYPE, ERR_R_EC_LIB); + return 0; + } + *ppval = pstr; + *pptype = V_ASN1_SEQUENCE; + } + return 1; +} + +static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) +{ + EC_KEY *ec_key = pkey->pkey.ec; + void *pval = NULL; + int ptype; + unsigned char *penc = NULL, *p; + int penclen; + + if (!eckey_param2type(&ptype, &pval, ec_key)) { + ECerr(EC_F_ECKEY_PUB_ENCODE, ERR_R_EC_LIB); + return 0; + } + penclen = i2o_ECPublicKey(ec_key, NULL); + if (penclen <= 0) + goto err; + penc = OPENSSL_malloc(penclen); + if (penc == NULL) + goto err; + p = penc; + penclen = i2o_ECPublicKey(ec_key, &p); + if (penclen <= 0) + goto err; + if (X509_PUBKEY_set0_param(pk, OBJ_nid2obj(EVP_PKEY_EC), + ptype, pval, penc, penclen)) + return 1; + err: + if (ptype == V_ASN1_OBJECT) + ASN1_OBJECT_free(pval); + else + ASN1_STRING_free(pval); + OPENSSL_free(penc); + return 0; +} + +static EC_KEY *eckey_type2param(int ptype, const void *pval) +{ + EC_KEY *eckey = NULL; + if (ptype == V_ASN1_SEQUENCE) { + const ASN1_STRING *pstr = pval; + const unsigned char *pm = NULL; + int pmlen; + pm = pstr->data; + pmlen = pstr->length; + if ((eckey = d2i_ECParameters(NULL, &pm, pmlen)) == NULL) { + ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); + goto ecerr; + } + } else if (ptype == V_ASN1_OBJECT) { + const ASN1_OBJECT *poid = pval; + EC_GROUP *group; + + /* + * type == V_ASN1_OBJECT => the parameters are given by an asn1 OID + */ + if ((eckey = EC_KEY_new()) == NULL) { + ECerr(EC_F_ECKEY_TYPE2PARAM, ERR_R_MALLOC_FAILURE); + goto ecerr; + } + group = EC_GROUP_new_by_curve_name(OBJ_obj2nid(poid)); + if (group == NULL) + goto ecerr; + EC_GROUP_set_asn1_flag(group, OPENSSL_EC_NAMED_CURVE); + if (EC_KEY_set_group(eckey, group) == 0) + goto ecerr; + EC_GROUP_free(group); + } else { + ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); + goto ecerr; + } + + return eckey; + + ecerr: + EC_KEY_free(eckey); + return NULL; +} + +static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) +{ + const unsigned char *p = NULL; + const void *pval; + int ptype, pklen; + EC_KEY *eckey = NULL; + X509_ALGOR *palg; + + if (!X509_PUBKEY_get0_param(NULL, &p, &pklen, &palg, pubkey)) + return 0; + X509_ALGOR_get0(NULL, &ptype, &pval, palg); + + eckey = eckey_type2param(ptype, pval); + + if (!eckey) { + ECerr(EC_F_ECKEY_PUB_DECODE, ERR_R_EC_LIB); + return 0; + } + + /* We have parameters now set public key */ + if (!o2i_ECPublicKey(&eckey, &p, pklen)) { + ECerr(EC_F_ECKEY_PUB_DECODE, EC_R_DECODE_ERROR); + goto ecerr; + } + + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; + + ecerr: + EC_KEY_free(eckey); + return 0; +} + +static int eckey_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b) +{ + int r; + const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec); + const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), + *pb = EC_KEY_get0_public_key(b->pkey.ec); + if (group == NULL || pa == NULL || pb == NULL) + return -2; + r = EC_POINT_cmp(group, pa, pb, NULL); + if (r == 0) + return 1; + if (r == 1) + return 0; + return -2; +} + +static int eckey_priv_decode(EVP_PKEY *pkey, const PKCS8_PRIV_KEY_INFO *p8) +{ + const unsigned char *p = NULL; + const void *pval; + int ptype, pklen; + EC_KEY *eckey = NULL; + const X509_ALGOR *palg; + + if (!PKCS8_pkey_get0(NULL, &p, &pklen, &palg, p8)) + return 0; + X509_ALGOR_get0(NULL, &ptype, &pval, palg); + + eckey = eckey_type2param(ptype, pval); + + if (!eckey) + goto ecliberr; + + /* We have parameters now set private key */ + if (!d2i_ECPrivateKey(&eckey, &p, pklen)) { + ECerr(EC_F_ECKEY_PRIV_DECODE, EC_R_DECODE_ERROR); + goto ecerr; + } + + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; + + ecliberr: + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + ecerr: + EC_KEY_free(eckey); + return 0; +} + +static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) +{ + EC_KEY ec_key = *(pkey->pkey.ec); + unsigned char *ep, *p; + int eplen, ptype; + void *pval; + unsigned int old_flags; + + if (!eckey_param2type(&ptype, &pval, &ec_key)) { + ECerr(EC_F_ECKEY_PRIV_ENCODE, EC_R_DECODE_ERROR); + return 0; + } + + /* set the private key */ + + /* + * do not include the parameters in the SEC1 private key see PKCS#11 + * 12.11 + */ + old_flags = EC_KEY_get_enc_flags(&ec_key); + EC_KEY_set_enc_flags(&ec_key, old_flags | EC_PKEY_NO_PARAMETERS); + + eplen = i2d_ECPrivateKey(&ec_key, NULL); + if (!eplen) { + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); + return 0; + } + ep = OPENSSL_malloc(eplen); + if (ep == NULL) { + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + p = ep; + if (!i2d_ECPrivateKey(&ec_key, &p)) { + OPENSSL_free(ep); + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); + return 0; + } + + if (!PKCS8_pkey_set0(p8, OBJ_nid2obj(NID_X9_62_id_ecPublicKey), 0, + ptype, pval, ep, eplen)) { + OPENSSL_free(ep); + return 0; + } + + return 1; +} + +static int int_ec_size(const EVP_PKEY *pkey) +{ + return ECDSA_size(pkey->pkey.ec); +} + +static int ec_bits(const EVP_PKEY *pkey) +{ + return EC_GROUP_order_bits(EC_KEY_get0_group(pkey->pkey.ec)); +} + +static int ec_security_bits(const EVP_PKEY *pkey) +{ + int ecbits = ec_bits(pkey); + if (ecbits >= 512) + return 256; + if (ecbits >= 384) + return 192; + if (ecbits >= 256) + return 128; + if (ecbits >= 224) + return 112; + if (ecbits >= 160) + return 80; + return ecbits / 2; +} + +static int ec_missing_parameters(const EVP_PKEY *pkey) +{ + if (pkey->pkey.ec == NULL || EC_KEY_get0_group(pkey->pkey.ec) == NULL) + return 1; + return 0; +} + +static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) +{ + EC_GROUP *group = EC_GROUP_dup(EC_KEY_get0_group(from->pkey.ec)); + + if (group == NULL) + return 0; + if (to->pkey.ec == NULL) { + to->pkey.ec = EC_KEY_new(); + if (to->pkey.ec == NULL) + goto err; + } + if (EC_KEY_set_group(to->pkey.ec, group) == 0) + goto err; + EC_GROUP_free(group); + return 1; + err: + EC_GROUP_free(group); + return 0; +} + +static int ec_cmp_parameters(const EVP_PKEY *a, const EVP_PKEY *b) +{ + const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), + *group_b = EC_KEY_get0_group(b->pkey.ec); + if (group_a == NULL || group_b == NULL) + return -2; + if (EC_GROUP_cmp(group_a, group_b, NULL)) + return 0; + else + return 1; +} + +static void int_ec_free(EVP_PKEY *pkey) +{ + EC_KEY_free(pkey->pkey.ec); +} + +typedef enum { + EC_KEY_PRINT_PRIVATE, + EC_KEY_PRINT_PUBLIC, + EC_KEY_PRINT_PARAM +} ec_print_t; + +static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, ec_print_t ktype) +{ + const char *ecstr; + unsigned char *priv = NULL, *pub = NULL; + size_t privlen = 0, publen = 0; + int ret = 0; + const EC_GROUP *group; + + if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) { + ECerr(EC_F_DO_EC_KEY_PRINT, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (ktype != EC_KEY_PRINT_PARAM && EC_KEY_get0_public_key(x) != NULL) { + publen = EC_KEY_key2buf(x, EC_KEY_get_conv_form(x), &pub, NULL); + if (publen == 0) + goto err; + } + + if (ktype == EC_KEY_PRINT_PRIVATE && EC_KEY_get0_private_key(x) != NULL) { + privlen = EC_KEY_priv2buf(x, &priv); + if (privlen == 0) + goto err; + } + + if (ktype == EC_KEY_PRINT_PRIVATE) + ecstr = "Private-Key"; + else if (ktype == EC_KEY_PRINT_PUBLIC) + ecstr = "Public-Key"; + else + ecstr = "ECDSA-Parameters"; + + if (!BIO_indent(bp, off, 128)) + goto err; + if (BIO_printf(bp, "%s: (%d bit)\n", ecstr, + EC_GROUP_order_bits(group)) <= 0) + goto err; + + if (privlen != 0) { + if (BIO_printf(bp, "%*spriv:\n", off, "") <= 0) + goto err; + if (ASN1_buf_print(bp, priv, privlen, off + 4) == 0) + goto err; + } + + if (publen != 0) { + if (BIO_printf(bp, "%*spub:\n", off, "") <= 0) + goto err; + if (ASN1_buf_print(bp, pub, publen, off + 4) == 0) + goto err; + } + + if (!ECPKParameters_print(bp, group, off)) + goto err; + ret = 1; + err: + if (!ret) + ECerr(EC_F_DO_EC_KEY_PRINT, ERR_R_EC_LIB); + OPENSSL_clear_free(priv, privlen); + OPENSSL_free(pub); + return ret; +} + +static int eckey_param_decode(EVP_PKEY *pkey, + const unsigned char **pder, int derlen) +{ + EC_KEY *eckey; + + if ((eckey = d2i_ECParameters(NULL, pder, derlen)) == NULL) { + ECerr(EC_F_ECKEY_PARAM_DECODE, ERR_R_EC_LIB); + return 0; + } + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; +} + +static int eckey_param_encode(const EVP_PKEY *pkey, unsigned char **pder) +{ + return i2d_ECParameters(pkey->pkey.ec, pder); +} + +static int eckey_param_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) +{ + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, EC_KEY_PRINT_PARAM); +} + +static int eckey_pub_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) +{ + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, EC_KEY_PRINT_PUBLIC); +} + +static int eckey_priv_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) +{ + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, EC_KEY_PRINT_PRIVATE); +} + +static int old_ec_priv_decode(EVP_PKEY *pkey, + const unsigned char **pder, int derlen) +{ + EC_KEY *ec; + + if ((ec = d2i_ECPrivateKey(NULL, pder, derlen)) == NULL) { + ECerr(EC_F_OLD_EC_PRIV_DECODE, EC_R_DECODE_ERROR); + return 0; + } + EVP_PKEY_assign_EC_KEY(pkey, ec); + return 1; +} + +static int old_ec_priv_encode(const EVP_PKEY *pkey, unsigned char **pder) +{ + return i2d_ECPrivateKey(pkey->pkey.ec, pder); +} + +static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) +{ + switch (op) { + case ASN1_PKEY_CTRL_PKCS7_SIGN: + if (arg1 == 0) { + int snid, hnid; + X509_ALGOR *alg1, *alg2; + PKCS7_SIGNER_INFO_get0_algs(arg2, NULL, &alg1, &alg2); + if (alg1 == NULL || alg1->algorithm == NULL) + return -1; + hnid = OBJ_obj2nid(alg1->algorithm); + if (hnid == NID_undef) + return -1; + if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) + return -1; + X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); + } + return 1; +#ifndef OPENSSL_NO_CMS + case ASN1_PKEY_CTRL_CMS_SIGN: + if (arg1 == 0) { + int snid, hnid; + X509_ALGOR *alg1, *alg2; + CMS_SignerInfo_get0_algs(arg2, NULL, NULL, &alg1, &alg2); + if (alg1 == NULL || alg1->algorithm == NULL) + return -1; + hnid = OBJ_obj2nid(alg1->algorithm); + if (hnid == NID_undef) + return -1; + if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) + return -1; + X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); + } + return 1; + + case ASN1_PKEY_CTRL_CMS_ENVELOPE: + if (arg1 == 1) + return ecdh_cms_decrypt(arg2); + else if (arg1 == 0) + return ecdh_cms_encrypt(arg2); + return -2; + + case ASN1_PKEY_CTRL_CMS_RI_TYPE: + *(int *)arg2 = CMS_RECIPINFO_AGREE; + return 1; +#endif + + case ASN1_PKEY_CTRL_DEFAULT_MD_NID: + *(int *)arg2 = NID_sha256; + return 2; + + case ASN1_PKEY_CTRL_SET1_TLS_ENCPT: + return EC_KEY_oct2key(EVP_PKEY_get0_EC_KEY(pkey), arg2, arg1, NULL); + + case ASN1_PKEY_CTRL_GET1_TLS_ENCPT: + return EC_KEY_key2buf(EVP_PKEY_get0_EC_KEY(pkey), + POINT_CONVERSION_UNCOMPRESSED, arg2, NULL); + + default: + return -2; + + } + +} + +const EVP_PKEY_ASN1_METHOD eckey_asn1_meth = { + EVP_PKEY_EC, + EVP_PKEY_EC, + 0, + "EC", + "OpenSSL EC algorithm", + + eckey_pub_decode, + eckey_pub_encode, + eckey_pub_cmp, + eckey_pub_print, + + eckey_priv_decode, + eckey_priv_encode, + eckey_priv_print, + + int_ec_size, + ec_bits, + ec_security_bits, + + eckey_param_decode, + eckey_param_encode, + ec_missing_parameters, + ec_copy_parameters, + ec_cmp_parameters, + eckey_param_print, + 0, + + int_ec_free, + ec_pkey_ctrl, + old_ec_priv_decode, + old_ec_priv_encode +}; + +int EC_KEY_print(BIO *bp, const EC_KEY *x, int off) +{ + int private = EC_KEY_get0_private_key(x) != NULL; + + return do_EC_KEY_print(bp, x, off, + private ? EC_KEY_PRINT_PRIVATE : EC_KEY_PRINT_PUBLIC); +} + +int ECParameters_print(BIO *bp, const EC_KEY *x) +{ + return do_EC_KEY_print(bp, x, 4, EC_KEY_PRINT_PARAM); +} + +#ifndef OPENSSL_NO_CMS + +static int ecdh_cms_set_peerkey(EVP_PKEY_CTX *pctx, + X509_ALGOR *alg, ASN1_BIT_STRING *pubkey) +{ + const ASN1_OBJECT *aoid; + int atype; + const void *aval; + int rv = 0; + EVP_PKEY *pkpeer = NULL; + EC_KEY *ecpeer = NULL; + const unsigned char *p; + int plen; + X509_ALGOR_get0(&aoid, &atype, &aval, alg); + if (OBJ_obj2nid(aoid) != NID_X9_62_id_ecPublicKey) + goto err; + /* If absent parameters get group from main key */ + if (atype == V_ASN1_UNDEF || atype == V_ASN1_NULL) { + const EC_GROUP *grp; + EVP_PKEY *pk; + pk = EVP_PKEY_CTX_get0_pkey(pctx); + if (!pk) + goto err; + grp = EC_KEY_get0_group(pk->pkey.ec); + ecpeer = EC_KEY_new(); + if (ecpeer == NULL) + goto err; + if (!EC_KEY_set_group(ecpeer, grp)) + goto err; + } else { + ecpeer = eckey_type2param(atype, aval); + if (!ecpeer) + goto err; + } + /* We have parameters now set public key */ + plen = ASN1_STRING_length(pubkey); + p = ASN1_STRING_get0_data(pubkey); + if (!p || !plen) + goto err; + if (!o2i_ECPublicKey(&ecpeer, &p, plen)) + goto err; + pkpeer = EVP_PKEY_new(); + if (pkpeer == NULL) + goto err; + EVP_PKEY_set1_EC_KEY(pkpeer, ecpeer); + if (EVP_PKEY_derive_set_peer(pctx, pkpeer) > 0) + rv = 1; + err: + EC_KEY_free(ecpeer); + EVP_PKEY_free(pkpeer); + return rv; +} + +/* Set KDF parameters based on KDF NID */ +static int ecdh_cms_set_kdf_param(EVP_PKEY_CTX *pctx, int eckdf_nid) +{ + int kdf_nid, kdfmd_nid, cofactor; + const EVP_MD *kdf_md; + if (eckdf_nid == NID_undef) + return 0; + + /* Lookup KDF type, cofactor mode and digest */ + if (!OBJ_find_sigid_algs(eckdf_nid, &kdfmd_nid, &kdf_nid)) + return 0; + + if (kdf_nid == NID_dh_std_kdf) + cofactor = 0; + else if (kdf_nid == NID_dh_cofactor_kdf) + cofactor = 1; + else + return 0; + + if (EVP_PKEY_CTX_set_ecdh_cofactor_mode(pctx, cofactor) <= 0) + return 0; + + if (EVP_PKEY_CTX_set_ecdh_kdf_type(pctx, EVP_PKEY_ECDH_KDF_X9_62) <= 0) + return 0; + + kdf_md = EVP_get_digestbynid(kdfmd_nid); + if (!kdf_md) + return 0; + + if (EVP_PKEY_CTX_set_ecdh_kdf_md(pctx, kdf_md) <= 0) + return 0; + return 1; +} + +static int ecdh_cms_set_shared_info(EVP_PKEY_CTX *pctx, CMS_RecipientInfo *ri) +{ + int rv = 0; + + X509_ALGOR *alg, *kekalg = NULL; + ASN1_OCTET_STRING *ukm; + const unsigned char *p; + unsigned char *der = NULL; + int plen, keylen; + const EVP_CIPHER *kekcipher; + EVP_CIPHER_CTX *kekctx; + + if (!CMS_RecipientInfo_kari_get0_alg(ri, &alg, &ukm)) + return 0; + + if (!ecdh_cms_set_kdf_param(pctx, OBJ_obj2nid(alg->algorithm))) { + ECerr(EC_F_ECDH_CMS_SET_SHARED_INFO, EC_R_KDF_PARAMETER_ERROR); + return 0; + } + + if (alg->parameter->type != V_ASN1_SEQUENCE) + return 0; + + p = alg->parameter->value.sequence->data; + plen = alg->parameter->value.sequence->length; + kekalg = d2i_X509_ALGOR(NULL, &p, plen); + if (!kekalg) + goto err; + kekctx = CMS_RecipientInfo_kari_get0_ctx(ri); + if (!kekctx) + goto err; + kekcipher = EVP_get_cipherbyobj(kekalg->algorithm); + if (!kekcipher || EVP_CIPHER_mode(kekcipher) != EVP_CIPH_WRAP_MODE) + goto err; + if (!EVP_EncryptInit_ex(kekctx, kekcipher, NULL, NULL, NULL)) + goto err; + if (EVP_CIPHER_asn1_to_param(kekctx, kekalg->parameter) <= 0) + goto err; + + keylen = EVP_CIPHER_CTX_key_length(kekctx); + if (EVP_PKEY_CTX_set_ecdh_kdf_outlen(pctx, keylen) <= 0) + goto err; + + plen = CMS_SharedInfo_encode(&der, kekalg, ukm, keylen); + + if (!plen) + goto err; + + if (EVP_PKEY_CTX_set0_ecdh_kdf_ukm(pctx, der, plen) <= 0) + goto err; + der = NULL; + + rv = 1; + err: + X509_ALGOR_free(kekalg); + OPENSSL_free(der); + return rv; +} + +static int ecdh_cms_decrypt(CMS_RecipientInfo *ri) +{ + EVP_PKEY_CTX *pctx; + pctx = CMS_RecipientInfo_get0_pkey_ctx(ri); + if (!pctx) + return 0; + /* See if we need to set peer key */ + if (!EVP_PKEY_CTX_get0_peerkey(pctx)) { + X509_ALGOR *alg; + ASN1_BIT_STRING *pubkey; + if (!CMS_RecipientInfo_kari_get0_orig_id(ri, &alg, &pubkey, + NULL, NULL, NULL)) + return 0; + if (!alg || !pubkey) + return 0; + if (!ecdh_cms_set_peerkey(pctx, alg, pubkey)) { + ECerr(EC_F_ECDH_CMS_DECRYPT, EC_R_PEER_KEY_ERROR); + return 0; + } + } + /* Set ECDH derivation parameters and initialise unwrap context */ + if (!ecdh_cms_set_shared_info(pctx, ri)) { + ECerr(EC_F_ECDH_CMS_DECRYPT, EC_R_SHARED_INFO_ERROR); + return 0; + } + return 1; +} + +static int ecdh_cms_encrypt(CMS_RecipientInfo *ri) +{ + EVP_PKEY_CTX *pctx; + EVP_PKEY *pkey; + EVP_CIPHER_CTX *ctx; + int keylen; + X509_ALGOR *talg, *wrap_alg = NULL; + const ASN1_OBJECT *aoid; + ASN1_BIT_STRING *pubkey; + ASN1_STRING *wrap_str; + ASN1_OCTET_STRING *ukm; + unsigned char *penc = NULL; + int penclen; + int rv = 0; + int ecdh_nid, kdf_type, kdf_nid, wrap_nid; + const EVP_MD *kdf_md; + pctx = CMS_RecipientInfo_get0_pkey_ctx(ri); + if (!pctx) + return 0; + /* Get ephemeral key */ + pkey = EVP_PKEY_CTX_get0_pkey(pctx); + if (!CMS_RecipientInfo_kari_get0_orig_id(ri, &talg, &pubkey, + NULL, NULL, NULL)) + goto err; + X509_ALGOR_get0(&aoid, NULL, NULL, talg); + /* Is everything uninitialised? */ + if (aoid == OBJ_nid2obj(NID_undef)) { + + EC_KEY *eckey = pkey->pkey.ec; + /* Set the key */ + unsigned char *p; + + penclen = i2o_ECPublicKey(eckey, NULL); + if (penclen <= 0) + goto err; + penc = OPENSSL_malloc(penclen); + if (penc == NULL) + goto err; + p = penc; + penclen = i2o_ECPublicKey(eckey, &p); + if (penclen <= 0) + goto err; + ASN1_STRING_set0(pubkey, penc, penclen); + pubkey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); + pubkey->flags |= ASN1_STRING_FLAG_BITS_LEFT; + + penc = NULL; + X509_ALGOR_set0(talg, OBJ_nid2obj(NID_X9_62_id_ecPublicKey), + V_ASN1_UNDEF, NULL); + } + + /* See if custom parameters set */ + kdf_type = EVP_PKEY_CTX_get_ecdh_kdf_type(pctx); + if (kdf_type <= 0) + goto err; + if (!EVP_PKEY_CTX_get_ecdh_kdf_md(pctx, &kdf_md)) + goto err; + ecdh_nid = EVP_PKEY_CTX_get_ecdh_cofactor_mode(pctx); + if (ecdh_nid < 0) + goto err; + else if (ecdh_nid == 0) + ecdh_nid = NID_dh_std_kdf; + else if (ecdh_nid == 1) + ecdh_nid = NID_dh_cofactor_kdf; + + if (kdf_type == EVP_PKEY_ECDH_KDF_NONE) { + kdf_type = EVP_PKEY_ECDH_KDF_X9_62; + if (EVP_PKEY_CTX_set_ecdh_kdf_type(pctx, kdf_type) <= 0) + goto err; + } else + /* Unknown KDF */ + goto err; + if (kdf_md == NULL) { + /* Fixme later for better MD */ + kdf_md = EVP_sha1(); + if (EVP_PKEY_CTX_set_ecdh_kdf_md(pctx, kdf_md) <= 0) + goto err; + } + + if (!CMS_RecipientInfo_kari_get0_alg(ri, &talg, &ukm)) + goto err; + + /* Lookup NID for KDF+cofactor+digest */ + + if (!OBJ_find_sigid_by_algs(&kdf_nid, EVP_MD_type(kdf_md), ecdh_nid)) + goto err; + /* Get wrap NID */ + ctx = CMS_RecipientInfo_kari_get0_ctx(ri); + wrap_nid = EVP_CIPHER_CTX_type(ctx); + keylen = EVP_CIPHER_CTX_key_length(ctx); + + /* Package wrap algorithm in an AlgorithmIdentifier */ + + wrap_alg = X509_ALGOR_new(); + if (wrap_alg == NULL) + goto err; + wrap_alg->algorithm = OBJ_nid2obj(wrap_nid); + wrap_alg->parameter = ASN1_TYPE_new(); + if (wrap_alg->parameter == NULL) + goto err; + if (EVP_CIPHER_param_to_asn1(ctx, wrap_alg->parameter) <= 0) + goto err; + if (ASN1_TYPE_get(wrap_alg->parameter) == NID_undef) { + ASN1_TYPE_free(wrap_alg->parameter); + wrap_alg->parameter = NULL; + } + + if (EVP_PKEY_CTX_set_ecdh_kdf_outlen(pctx, keylen) <= 0) + goto err; + + penclen = CMS_SharedInfo_encode(&penc, wrap_alg, ukm, keylen); + + if (!penclen) + goto err; + + if (EVP_PKEY_CTX_set0_ecdh_kdf_ukm(pctx, penc, penclen) <= 0) + goto err; + penc = NULL; + + /* + * Now need to wrap encoding of wrap AlgorithmIdentifier into parameter + * of another AlgorithmIdentifier. + */ + penclen = i2d_X509_ALGOR(wrap_alg, &penc); + if (!penc || !penclen) + goto err; + wrap_str = ASN1_STRING_new(); + if (wrap_str == NULL) + goto err; + ASN1_STRING_set0(wrap_str, penc, penclen); + penc = NULL; + X509_ALGOR_set0(talg, OBJ_nid2obj(kdf_nid), V_ASN1_SEQUENCE, wrap_str); + + rv = 1; + + err: + OPENSSL_free(penc); + X509_ALGOR_free(wrap_alg); + return rv; +} + +#endif diff --git a/openssl-1.1.0h/crypto/ec/ec_asn1.c b/openssl-1.1.0h/crypto/ec/ec_asn1.c new file mode 100644 index 0000000..271178f --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_asn1.c @@ -0,0 +1,1237 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <string.h> +#include "ec_lcl.h" +#include <openssl/err.h> +#include <openssl/asn1t.h> +#include <openssl/objects.h> + +int EC_GROUP_get_basis_type(const EC_GROUP *group) +{ + int i; + + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != + NID_X9_62_characteristic_two_field) + /* everything else is currently not supported */ + return 0; + + /* Find the last non-zero element of group->poly[] */ + for (i = 0; + i < (int)OSSL_NELEM(group->poly) && group->poly[i] != 0; + i++) + continue; + + if (i == 4) + return NID_X9_62_ppBasis; + else if (i == 2) + return NID_X9_62_tpBasis; + else + /* everything else is currently not supported */ + return 0; +} + +#ifndef OPENSSL_NO_EC2M +int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) +{ + if (group == NULL) + return 0; + + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != + NID_X9_62_characteristic_two_field + || !((group->poly[0] != 0) && (group->poly[1] != 0) + && (group->poly[2] == 0))) { + ECerr(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + + if (k) + *k = group->poly[1]; + + return 1; +} + +int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, + unsigned int *k2, unsigned int *k3) +{ + if (group == NULL) + return 0; + + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) != + NID_X9_62_characteristic_two_field + || !((group->poly[0] != 0) && (group->poly[1] != 0) + && (group->poly[2] != 0) && (group->poly[3] != 0) + && (group->poly[4] == 0))) { + ECerr(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + + if (k1) + *k1 = group->poly[3]; + if (k2) + *k2 = group->poly[2]; + if (k3) + *k3 = group->poly[1]; + + return 1; +} +#endif + +/* some structures needed for the asn1 encoding */ +typedef struct x9_62_pentanomial_st { + long k1; + long k2; + long k3; +} X9_62_PENTANOMIAL; + +typedef struct x9_62_characteristic_two_st { + long m; + ASN1_OBJECT *type; + union { + char *ptr; + /* NID_X9_62_onBasis */ + ASN1_NULL *onBasis; + /* NID_X9_62_tpBasis */ + ASN1_INTEGER *tpBasis; + /* NID_X9_62_ppBasis */ + X9_62_PENTANOMIAL *ppBasis; + /* anything else */ + ASN1_TYPE *other; + } p; +} X9_62_CHARACTERISTIC_TWO; + +typedef struct x9_62_fieldid_st { + ASN1_OBJECT *fieldType; + union { + char *ptr; + /* NID_X9_62_prime_field */ + ASN1_INTEGER *prime; + /* NID_X9_62_characteristic_two_field */ + X9_62_CHARACTERISTIC_TWO *char_two; + /* anything else */ + ASN1_TYPE *other; + } p; +} X9_62_FIELDID; + +typedef struct x9_62_curve_st { + ASN1_OCTET_STRING *a; + ASN1_OCTET_STRING *b; + ASN1_BIT_STRING *seed; +} X9_62_CURVE; + +struct ec_parameters_st { + long version; + X9_62_FIELDID *fieldID; + X9_62_CURVE *curve; + ASN1_OCTET_STRING *base; + ASN1_INTEGER *order; + ASN1_INTEGER *cofactor; +} /* ECPARAMETERS */ ; + +struct ecpk_parameters_st { + int type; + union { + ASN1_OBJECT *named_curve; + ECPARAMETERS *parameters; + ASN1_NULL *implicitlyCA; + } value; +} /* ECPKPARAMETERS */ ; + +/* SEC1 ECPrivateKey */ +typedef struct ec_privatekey_st { + long version; + ASN1_OCTET_STRING *privateKey; + ECPKPARAMETERS *parameters; + ASN1_BIT_STRING *publicKey; +} EC_PRIVATEKEY; + +/* the OpenSSL ASN.1 definitions */ +ASN1_SEQUENCE(X9_62_PENTANOMIAL) = { + ASN1_SIMPLE(X9_62_PENTANOMIAL, k1, LONG), + ASN1_SIMPLE(X9_62_PENTANOMIAL, k2, LONG), + ASN1_SIMPLE(X9_62_PENTANOMIAL, k3, LONG) +} static_ASN1_SEQUENCE_END(X9_62_PENTANOMIAL) + +DECLARE_ASN1_ALLOC_FUNCTIONS(X9_62_PENTANOMIAL) +IMPLEMENT_ASN1_ALLOC_FUNCTIONS(X9_62_PENTANOMIAL) + +ASN1_ADB_TEMPLATE(char_two_def) = ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, p.other, ASN1_ANY); + +ASN1_ADB(X9_62_CHARACTERISTIC_TWO) = { + ADB_ENTRY(NID_X9_62_onBasis, ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, p.onBasis, ASN1_NULL)), + ADB_ENTRY(NID_X9_62_tpBasis, ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, p.tpBasis, ASN1_INTEGER)), + ADB_ENTRY(NID_X9_62_ppBasis, ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, p.ppBasis, X9_62_PENTANOMIAL)) +} ASN1_ADB_END(X9_62_CHARACTERISTIC_TWO, 0, type, 0, &char_two_def_tt, NULL); + +ASN1_SEQUENCE(X9_62_CHARACTERISTIC_TWO) = { + ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, m, LONG), + ASN1_SIMPLE(X9_62_CHARACTERISTIC_TWO, type, ASN1_OBJECT), + ASN1_ADB_OBJECT(X9_62_CHARACTERISTIC_TWO) +} static_ASN1_SEQUENCE_END(X9_62_CHARACTERISTIC_TWO) + +DECLARE_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) +IMPLEMENT_ASN1_ALLOC_FUNCTIONS(X9_62_CHARACTERISTIC_TWO) + +ASN1_ADB_TEMPLATE(fieldID_def) = ASN1_SIMPLE(X9_62_FIELDID, p.other, ASN1_ANY); + +ASN1_ADB(X9_62_FIELDID) = { + ADB_ENTRY(NID_X9_62_prime_field, ASN1_SIMPLE(X9_62_FIELDID, p.prime, ASN1_INTEGER)), + ADB_ENTRY(NID_X9_62_characteristic_two_field, ASN1_SIMPLE(X9_62_FIELDID, p.char_two, X9_62_CHARACTERISTIC_TWO)) +} ASN1_ADB_END(X9_62_FIELDID, 0, fieldType, 0, &fieldID_def_tt, NULL); + +ASN1_SEQUENCE(X9_62_FIELDID) = { + ASN1_SIMPLE(X9_62_FIELDID, fieldType, ASN1_OBJECT), + ASN1_ADB_OBJECT(X9_62_FIELDID) +} static_ASN1_SEQUENCE_END(X9_62_FIELDID) + +ASN1_SEQUENCE(X9_62_CURVE) = { + ASN1_SIMPLE(X9_62_CURVE, a, ASN1_OCTET_STRING), + ASN1_SIMPLE(X9_62_CURVE, b, ASN1_OCTET_STRING), + ASN1_OPT(X9_62_CURVE, seed, ASN1_BIT_STRING) +} static_ASN1_SEQUENCE_END(X9_62_CURVE) + +ASN1_SEQUENCE(ECPARAMETERS) = { + ASN1_SIMPLE(ECPARAMETERS, version, LONG), + ASN1_SIMPLE(ECPARAMETERS, fieldID, X9_62_FIELDID), + ASN1_SIMPLE(ECPARAMETERS, curve, X9_62_CURVE), + ASN1_SIMPLE(ECPARAMETERS, base, ASN1_OCTET_STRING), + ASN1_SIMPLE(ECPARAMETERS, order, ASN1_INTEGER), + ASN1_OPT(ECPARAMETERS, cofactor, ASN1_INTEGER) +} ASN1_SEQUENCE_END(ECPARAMETERS) + +DECLARE_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) +IMPLEMENT_ASN1_ALLOC_FUNCTIONS(ECPARAMETERS) + +ASN1_CHOICE(ECPKPARAMETERS) = { + ASN1_SIMPLE(ECPKPARAMETERS, value.named_curve, ASN1_OBJECT), + ASN1_SIMPLE(ECPKPARAMETERS, value.parameters, ECPARAMETERS), + ASN1_SIMPLE(ECPKPARAMETERS, value.implicitlyCA, ASN1_NULL) +} ASN1_CHOICE_END(ECPKPARAMETERS) + +DECLARE_ASN1_FUNCTIONS_const(ECPKPARAMETERS) +DECLARE_ASN1_ENCODE_FUNCTIONS_const(ECPKPARAMETERS, ECPKPARAMETERS) +IMPLEMENT_ASN1_FUNCTIONS_const(ECPKPARAMETERS) + +ASN1_SEQUENCE(EC_PRIVATEKEY) = { + ASN1_SIMPLE(EC_PRIVATEKEY, version, LONG), + ASN1_SIMPLE(EC_PRIVATEKEY, privateKey, ASN1_OCTET_STRING), + ASN1_EXP_OPT(EC_PRIVATEKEY, parameters, ECPKPARAMETERS, 0), + ASN1_EXP_OPT(EC_PRIVATEKEY, publicKey, ASN1_BIT_STRING, 1) +} static_ASN1_SEQUENCE_END(EC_PRIVATEKEY) + +DECLARE_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) +DECLARE_ASN1_ENCODE_FUNCTIONS_const(EC_PRIVATEKEY, EC_PRIVATEKEY) +IMPLEMENT_ASN1_FUNCTIONS_const(EC_PRIVATEKEY) + +/* some declarations of internal function */ + +/* ec_asn1_group2field() sets the values in a X9_62_FIELDID object */ +static int ec_asn1_group2fieldid(const EC_GROUP *, X9_62_FIELDID *); +/* ec_asn1_group2curve() sets the values in a X9_62_CURVE object */ +static int ec_asn1_group2curve(const EC_GROUP *, X9_62_CURVE *); + +/* the function definitions */ + +static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) +{ + int ok = 0, nid; + BIGNUM *tmp = NULL; + + if (group == NULL || field == NULL) + return 0; + + /* clear the old values (if necessary) */ + ASN1_OBJECT_free(field->fieldType); + ASN1_TYPE_free(field->p.other); + + nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); + /* set OID for the field */ + if ((field->fieldType = OBJ_nid2obj(nid)) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); + goto err; + } + + if (nid == NID_X9_62_prime_field) { + if ((tmp = BN_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); + goto err; + } + /* the parameters are specified by the prime number p */ + if (!EC_GROUP_get_curve_GFp(group, tmp, NULL, NULL, NULL)) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); + goto err; + } + /* set the prime number */ + field->p.prime = BN_to_ASN1_INTEGER(tmp, NULL); + if (field->p.prime == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_ASN1_LIB); + goto err; + } + } else if (nid == NID_X9_62_characteristic_two_field) +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else + { + int field_type; + X9_62_CHARACTERISTIC_TWO *char_two; + + field->p.char_two = X9_62_CHARACTERISTIC_TWO_new(); + char_two = field->p.char_two; + + if (char_two == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); + goto err; + } + + char_two->m = (long)EC_GROUP_get_degree(group); + + field_type = EC_GROUP_get_basis_type(group); + + if (field_type == 0) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_EC_LIB); + goto err; + } + /* set base type OID */ + if ((char_two->type = OBJ_nid2obj(field_type)) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_OBJ_LIB); + goto err; + } + + if (field_type == NID_X9_62_tpBasis) { + unsigned int k; + + if (!EC_GROUP_get_trinomial_basis(group, &k)) + goto err; + + char_two->p.tpBasis = ASN1_INTEGER_new(); + if (char_two->p.tpBasis == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); + goto err; + } + if (!ASN1_INTEGER_set(char_two->p.tpBasis, (long)k)) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_ASN1_LIB); + goto err; + } + } else if (field_type == NID_X9_62_ppBasis) { + unsigned int k1, k2, k3; + + if (!EC_GROUP_get_pentanomial_basis(group, &k1, &k2, &k3)) + goto err; + + char_two->p.ppBasis = X9_62_PENTANOMIAL_new(); + if (char_two->p.ppBasis == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* set k? values */ + char_two->p.ppBasis->k1 = (long)k1; + char_two->p.ppBasis->k2 = (long)k2; + char_two->p.ppBasis->k3 = (long)k3; + } else { /* field_type == NID_X9_62_onBasis */ + + /* for ONB the parameters are (asn1) NULL */ + char_two->p.onBasis = ASN1_NULL_new(); + if (char_two->p.onBasis == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, ERR_R_MALLOC_FAILURE); + goto err; + } + } + } +#endif + else { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_UNSUPPORTED_FIELD); + goto err; + } + + ok = 1; + + err: + BN_free(tmp); + return (ok); +} + +static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) +{ + int ok = 0, nid; + BIGNUM *tmp_1 = NULL, *tmp_2 = NULL; + unsigned char *buffer_1 = NULL, *buffer_2 = NULL, + *a_buf = NULL, *b_buf = NULL; + size_t len_1, len_2; + unsigned char char_zero = 0; + + if (!group || !curve || !curve->a || !curve->b) + return 0; + + if ((tmp_1 = BN_new()) == NULL || (tmp_2 = BN_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); + goto err; + } + + nid = EC_METHOD_get_field_type(EC_GROUP_method_of(group)); + + /* get a and b */ + if (nid == NID_X9_62_prime_field) { + if (!EC_GROUP_get_curve_GFp(group, NULL, tmp_1, tmp_2, NULL)) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); + goto err; + } + } +#ifndef OPENSSL_NO_EC2M + else { /* nid == NID_X9_62_characteristic_two_field */ + + if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_EC_LIB); + goto err; + } + } +#endif + len_1 = (size_t)BN_num_bytes(tmp_1); + len_2 = (size_t)BN_num_bytes(tmp_2); + + if (len_1 == 0) { + /* len_1 == 0 => a == 0 */ + a_buf = &char_zero; + len_1 = 1; + } else { + if ((buffer_1 = OPENSSL_malloc(len_1)) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); + goto err; + } + if ((len_1 = BN_bn2bin(tmp_1, buffer_1)) == 0) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); + goto err; + } + a_buf = buffer_1; + } + + if (len_2 == 0) { + /* len_2 == 0 => b == 0 */ + b_buf = &char_zero; + len_2 = 1; + } else { + if ((buffer_2 = OPENSSL_malloc(len_2)) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); + goto err; + } + if ((len_2 = BN_bn2bin(tmp_2, buffer_2)) == 0) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_BN_LIB); + goto err; + } + b_buf = buffer_2; + } + + /* set a and b */ + if (!ASN1_OCTET_STRING_set(curve->a, a_buf, len_1) || + !ASN1_OCTET_STRING_set(curve->b, b_buf, len_2)) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); + goto err; + } + + /* set the seed (optional) */ + if (group->seed) { + if (!curve->seed) + if ((curve->seed = ASN1_BIT_STRING_new()) == NULL) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_MALLOC_FAILURE); + goto err; + } + curve->seed->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); + curve->seed->flags |= ASN1_STRING_FLAG_BITS_LEFT; + if (!ASN1_BIT_STRING_set(curve->seed, group->seed, + (int)group->seed_len)) { + ECerr(EC_F_EC_ASN1_GROUP2CURVE, ERR_R_ASN1_LIB); + goto err; + } + } else { + ASN1_BIT_STRING_free(curve->seed); + curve->seed = NULL; + } + + ok = 1; + + err: + OPENSSL_free(buffer_1); + OPENSSL_free(buffer_2); + BN_free(tmp_1); + BN_free(tmp_2); + return (ok); +} + +ECPARAMETERS *EC_GROUP_get_ecparameters(const EC_GROUP *group, + ECPARAMETERS *params) +{ + size_t len = 0; + ECPARAMETERS *ret = NULL; + const BIGNUM *tmp; + unsigned char *buffer = NULL; + const EC_POINT *point = NULL; + point_conversion_form_t form; + + if (params == NULL) { + if ((ret = ECPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_MALLOC_FAILURE); + goto err; + } + } else + ret = params; + + /* set the version (always one) */ + ret->version = (long)0x1; + + /* set the fieldID */ + if (!ec_asn1_group2fieldid(group, ret->fieldID)) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + + /* set the curve */ + if (!ec_asn1_group2curve(group, ret->curve)) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + + /* set the base point */ + if ((point = EC_GROUP_get0_generator(group)) == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, EC_R_UNDEFINED_GENERATOR); + goto err; + } + + form = EC_GROUP_get_point_conversion_form(group); + + len = EC_POINT_point2buf(group, point, form, &buffer, NULL); + if (len == 0) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + if (ret->base == NULL && (ret->base = ASN1_OCTET_STRING_new()) == NULL) { + OPENSSL_free(buffer); + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_MALLOC_FAILURE); + goto err; + } + ASN1_STRING_set0(ret->base, buffer, len); + + /* set the order */ + tmp = EC_GROUP_get0_order(group); + if (tmp == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + ret->order = BN_to_ASN1_INTEGER(tmp, ret->order); + if (ret->order == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_ASN1_LIB); + goto err; + } + + /* set the cofactor (optional) */ + tmp = EC_GROUP_get0_cofactor(group); + if (tmp != NULL) { + ret->cofactor = BN_to_ASN1_INTEGER(tmp, ret->cofactor); + if (ret->cofactor == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPARAMETERS, ERR_R_ASN1_LIB); + goto err; + } + } + + return ret; + + err: + if (params == NULL) + ECPARAMETERS_free(ret); + return NULL; +} + +ECPKPARAMETERS *EC_GROUP_get_ecpkparameters(const EC_GROUP *group, + ECPKPARAMETERS *params) +{ + int ok = 1, tmp; + ECPKPARAMETERS *ret = params; + + if (ret == NULL) { + if ((ret = ECPKPARAMETERS_new()) == NULL) { + ECerr(EC_F_EC_GROUP_GET_ECPKPARAMETERS, ERR_R_MALLOC_FAILURE); + return NULL; + } + } else { + if (ret->type == 0) + ASN1_OBJECT_free(ret->value.named_curve); + else if (ret->type == 1 && ret->value.parameters) + ECPARAMETERS_free(ret->value.parameters); + } + + if (EC_GROUP_get_asn1_flag(group)) { + /* + * use the asn1 OID to describe the the elliptic curve parameters + */ + tmp = EC_GROUP_get_curve_name(group); + if (tmp) { + ret->type = 0; + if ((ret->value.named_curve = OBJ_nid2obj(tmp)) == NULL) + ok = 0; + } else + /* we don't know the nid => ERROR */ + ok = 0; + } else { + /* use the ECPARAMETERS structure */ + ret->type = 1; + if ((ret->value.parameters = + EC_GROUP_get_ecparameters(group, NULL)) == NULL) + ok = 0; + } + + if (!ok) { + ECPKPARAMETERS_free(ret); + return NULL; + } + return ret; +} + +EC_GROUP *EC_GROUP_new_from_ecparameters(const ECPARAMETERS *params) +{ + int ok = 0, tmp; + EC_GROUP *ret = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL; + EC_POINT *point = NULL; + long field_bits; + + if (!params->fieldID || !params->fieldID->fieldType || + !params->fieldID->p.ptr) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + + /* now extract the curve parameters a and b */ + if (!params->curve || !params->curve->a || + !params->curve->a->data || !params->curve->b || + !params->curve->b->data) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + a = BN_bin2bn(params->curve->a->data, params->curve->a->length, NULL); + if (a == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_BN_LIB); + goto err; + } + b = BN_bin2bn(params->curve->b->data, params->curve->b->length, NULL); + if (b == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_BN_LIB); + goto err; + } + + /* get the field parameters */ + tmp = OBJ_obj2nid(params->fieldID->fieldType); + if (tmp == NID_X9_62_characteristic_two_field) +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else + { + X9_62_CHARACTERISTIC_TWO *char_two; + + char_two = params->fieldID->p.char_two; + + field_bits = char_two->m; + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_FIELD_TOO_LARGE); + goto err; + } + + if ((p = BN_new()) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* get the base type */ + tmp = OBJ_obj2nid(char_two->type); + + if (tmp == NID_X9_62_tpBasis) { + long tmp_long; + + if (!char_two->p.tpBasis) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + + tmp_long = ASN1_INTEGER_get(char_two->p.tpBasis); + + if (!(char_two->m > tmp_long && tmp_long > 0)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, + EC_R_INVALID_TRINOMIAL_BASIS); + goto err; + } + + /* create the polynomial */ + if (!BN_set_bit(p, (int)char_two->m)) + goto err; + if (!BN_set_bit(p, (int)tmp_long)) + goto err; + if (!BN_set_bit(p, 0)) + goto err; + } else if (tmp == NID_X9_62_ppBasis) { + X9_62_PENTANOMIAL *penta; + + penta = char_two->p.ppBasis; + if (!penta) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + + if (! + (char_two->m > penta->k3 && penta->k3 > penta->k2 + && penta->k2 > penta->k1 && penta->k1 > 0)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, + EC_R_INVALID_PENTANOMIAL_BASIS); + goto err; + } + + /* create the polynomial */ + if (!BN_set_bit(p, (int)char_two->m)) + goto err; + if (!BN_set_bit(p, (int)penta->k1)) + goto err; + if (!BN_set_bit(p, (int)penta->k2)) + goto err; + if (!BN_set_bit(p, (int)penta->k3)) + goto err; + if (!BN_set_bit(p, 0)) + goto err; + } else if (tmp == NID_X9_62_onBasis) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_NOT_IMPLEMENTED); + goto err; + } else { /* error */ + + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + + /* create the EC_GROUP structure */ + ret = EC_GROUP_new_curve_GF2m(p, a, b, NULL); + } +#endif + else if (tmp == NID_X9_62_prime_field) { + /* we have a curve over a prime field */ + /* extract the prime number */ + if (!params->fieldID->p.prime) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + p = ASN1_INTEGER_to_BN(params->fieldID->p.prime, NULL); + if (p == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_ASN1_LIB); + goto err; + } + + if (BN_is_negative(p) || BN_is_zero(p)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_INVALID_FIELD); + goto err; + } + + field_bits = BN_num_bits(p); + if (field_bits > OPENSSL_ECC_MAX_FIELD_BITS) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_FIELD_TOO_LARGE); + goto err; + } + + /* create the EC_GROUP structure */ + ret = EC_GROUP_new_curve_GFp(p, a, b, NULL); + } else { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_INVALID_FIELD); + goto err; + } + + if (ret == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + + /* extract seed (optional) */ + if (params->curve->seed != NULL) { + OPENSSL_free(ret->seed); + if ((ret->seed = OPENSSL_malloc(params->curve->seed->length)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_MALLOC_FAILURE); + goto err; + } + memcpy(ret->seed, params->curve->seed->data, + params->curve->seed->length); + ret->seed_len = params->curve->seed->length; + } + + if (!params->order || !params->base || !params->base->data) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_ASN1_ERROR); + goto err; + } + + if ((point = EC_POINT_new(ret)) == NULL) + goto err; + + /* set the point conversion form */ + EC_GROUP_set_point_conversion_form(ret, (point_conversion_form_t) + (params->base->data[0] & ~0x01)); + + /* extract the ec point */ + if (!EC_POINT_oct2point(ret, point, params->base->data, + params->base->length, NULL)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + + /* extract the order */ + if ((a = ASN1_INTEGER_to_BN(params->order, a)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_ASN1_LIB); + goto err; + } + if (BN_is_negative(a) || BN_is_zero(a)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_INVALID_GROUP_ORDER); + goto err; + } + if (BN_num_bits(a) > (int)field_bits + 1) { /* Hasse bound */ + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, EC_R_INVALID_GROUP_ORDER); + goto err; + } + + /* extract the cofactor (optional) */ + if (params->cofactor == NULL) { + BN_free(b); + b = NULL; + } else if ((b = ASN1_INTEGER_to_BN(params->cofactor, b)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_ASN1_LIB); + goto err; + } + /* set the generator, order and cofactor (if present) */ + if (!EC_GROUP_set_generator(ret, point, a, b)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS, ERR_R_EC_LIB); + goto err; + } + + ok = 1; + + err: + if (!ok) { + EC_GROUP_clear_free(ret); + ret = NULL; + } + + BN_free(p); + BN_free(a); + BN_free(b); + EC_POINT_free(point); + return (ret); +} + +EC_GROUP *EC_GROUP_new_from_ecpkparameters(const ECPKPARAMETERS *params) +{ + EC_GROUP *ret = NULL; + int tmp = 0; + + if (params == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS, EC_R_MISSING_PARAMETERS); + return NULL; + } + + if (params->type == 0) { /* the curve is given by an OID */ + tmp = OBJ_obj2nid(params->value.named_curve); + if ((ret = EC_GROUP_new_by_curve_name(tmp)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS, + EC_R_EC_GROUP_NEW_BY_NAME_FAILURE); + return NULL; + } + EC_GROUP_set_asn1_flag(ret, OPENSSL_EC_NAMED_CURVE); + } else if (params->type == 1) { /* the parameters are given by a + * ECPARAMETERS structure */ + ret = EC_GROUP_new_from_ecparameters(params->value.parameters); + if (!ret) { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS, ERR_R_EC_LIB); + return NULL; + } + EC_GROUP_set_asn1_flag(ret, 0x0); + } else if (params->type == 2) { /* implicitlyCA */ + return NULL; + } else { + ECerr(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS, EC_R_ASN1_ERROR); + return NULL; + } + + return ret; +} + +/* EC_GROUP <-> DER encoding of ECPKPARAMETERS */ + +EC_GROUP *d2i_ECPKParameters(EC_GROUP **a, const unsigned char **in, long len) +{ + EC_GROUP *group = NULL; + ECPKPARAMETERS *params = NULL; + const unsigned char *p = *in; + + if ((params = d2i_ECPKPARAMETERS(NULL, &p, len)) == NULL) { + ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_D2I_ECPKPARAMETERS_FAILURE); + ECPKPARAMETERS_free(params); + return NULL; + } + + if ((group = EC_GROUP_new_from_ecpkparameters(params)) == NULL) { + ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_PKPARAMETERS2GROUP_FAILURE); + ECPKPARAMETERS_free(params); + return NULL; + } + + if (a) { + EC_GROUP_clear_free(*a); + *a = group; + } + + ECPKPARAMETERS_free(params); + *in = p; + return (group); +} + +int i2d_ECPKParameters(const EC_GROUP *a, unsigned char **out) +{ + int ret = 0; + ECPKPARAMETERS *tmp = EC_GROUP_get_ecpkparameters(a, NULL); + if (tmp == NULL) { + ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_GROUP2PKPARAMETERS_FAILURE); + return 0; + } + if ((ret = i2d_ECPKPARAMETERS(tmp, out)) == 0) { + ECerr(EC_F_I2D_ECPKPARAMETERS, EC_R_I2D_ECPKPARAMETERS_FAILURE); + ECPKPARAMETERS_free(tmp); + return 0; + } + ECPKPARAMETERS_free(tmp); + return (ret); +} + +/* some EC_KEY functions */ + +EC_KEY *d2i_ECPrivateKey(EC_KEY **a, const unsigned char **in, long len) +{ + EC_KEY *ret = NULL; + EC_PRIVATEKEY *priv_key = NULL; + const unsigned char *p = *in; + + if ((priv_key = d2i_EC_PRIVATEKEY(NULL, &p, len)) == NULL) { + ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); + return NULL; + } + + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { + ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); + goto err; + } + } else + ret = *a; + + if (priv_key->parameters) { + EC_GROUP_clear_free(ret->group); + ret->group = EC_GROUP_new_from_ecpkparameters(priv_key->parameters); + } + + if (ret->group == NULL) { + ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + + ret->version = priv_key->version; + + if (priv_key->privateKey) { + ASN1_OCTET_STRING *pkey = priv_key->privateKey; + if (EC_KEY_oct2priv(ret, ASN1_STRING_get0_data(pkey), + ASN1_STRING_length(pkey)) == 0) + goto err; + } else { + ECerr(EC_F_D2I_ECPRIVATEKEY, EC_R_MISSING_PRIVATE_KEY); + goto err; + } + + EC_POINT_clear_free(ret->pub_key); + ret->pub_key = EC_POINT_new(ret->group); + if (ret->pub_key == NULL) { + ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + + if (priv_key->publicKey) { + const unsigned char *pub_oct; + int pub_oct_len; + + pub_oct = ASN1_STRING_get0_data(priv_key->publicKey); + pub_oct_len = ASN1_STRING_length(priv_key->publicKey); + if (!EC_KEY_oct2key(ret, pub_oct, pub_oct_len, NULL)) { + ECerr(EC_F_D2I_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + } else { + if (ret->group->meth->keygenpub == NULL + || ret->group->meth->keygenpub(ret) == 0) + goto err; + /* Remember the original private-key-only encoding. */ + ret->enc_flag |= EC_PKEY_NO_PUBKEY; + } + + if (a) + *a = ret; + EC_PRIVATEKEY_free(priv_key); + *in = p; + return (ret); + + err: + if (a == NULL || *a != ret) + EC_KEY_free(ret); + EC_PRIVATEKEY_free(priv_key); + return NULL; +} + +int i2d_ECPrivateKey(EC_KEY *a, unsigned char **out) +{ + int ret = 0, ok = 0; + unsigned char *priv= NULL, *pub= NULL; + size_t privlen = 0, publen = 0; + + EC_PRIVATEKEY *priv_key = NULL; + + if (a == NULL || a->group == NULL || + (!(a->enc_flag & EC_PKEY_NO_PUBKEY) && a->pub_key == NULL)) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_PASSED_NULL_PARAMETER); + goto err; + } + + if ((priv_key = EC_PRIVATEKEY_new()) == NULL) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); + goto err; + } + + priv_key->version = a->version; + + privlen = EC_KEY_priv2buf(a, &priv); + + if (privlen == 0) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + + ASN1_STRING_set0(priv_key->privateKey, priv, privlen); + priv = NULL; + + if (!(a->enc_flag & EC_PKEY_NO_PARAMETERS)) { + if ((priv_key->parameters = + EC_GROUP_get_ecpkparameters(a->group, + priv_key->parameters)) == NULL) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + } + + if (!(a->enc_flag & EC_PKEY_NO_PUBKEY)) { + priv_key->publicKey = ASN1_BIT_STRING_new(); + if (priv_key->publicKey == NULL) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_MALLOC_FAILURE); + goto err; + } + + publen = EC_KEY_key2buf(a, a->conv_form, &pub, NULL); + + if (publen == 0) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + + priv_key->publicKey->flags &= ~(ASN1_STRING_FLAG_BITS_LEFT | 0x07); + priv_key->publicKey->flags |= ASN1_STRING_FLAG_BITS_LEFT; + ASN1_STRING_set0(priv_key->publicKey, pub, publen); + pub = NULL; + } + + if ((ret = i2d_EC_PRIVATEKEY(priv_key, out)) == 0) { + ECerr(EC_F_I2D_ECPRIVATEKEY, ERR_R_EC_LIB); + goto err; + } + ok = 1; + err: + OPENSSL_clear_free(priv, privlen); + OPENSSL_free(pub); + EC_PRIVATEKEY_free(priv_key); + return (ok ? ret : 0); +} + +int i2d_ECParameters(EC_KEY *a, unsigned char **out) +{ + if (a == NULL) { + ECerr(EC_F_I2D_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + return i2d_ECPKParameters(a->group, out); +} + +EC_KEY *d2i_ECParameters(EC_KEY **a, const unsigned char **in, long len) +{ + EC_KEY *ret; + + if (in == NULL || *in == NULL) { + ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_PASSED_NULL_PARAMETER); + return NULL; + } + + if (a == NULL || *a == NULL) { + if ((ret = EC_KEY_new()) == NULL) { + ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_MALLOC_FAILURE); + return NULL; + } + } else + ret = *a; + + if (!d2i_ECPKParameters(&ret->group, in, len)) { + ECerr(EC_F_D2I_ECPARAMETERS, ERR_R_EC_LIB); + if (a == NULL || *a != ret) + EC_KEY_free(ret); + return NULL; + } + + if (a) + *a = ret; + + return ret; +} + +EC_KEY *o2i_ECPublicKey(EC_KEY **a, const unsigned char **in, long len) +{ + EC_KEY *ret = NULL; + + if (a == NULL || (*a) == NULL || (*a)->group == NULL) { + /* + * sorry, but a EC_GROUP-structure is necessary to set the public key + */ + ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + ret = *a; + if (!EC_KEY_oct2key(ret, *in, len, NULL)) { + ECerr(EC_F_O2I_ECPUBLICKEY, ERR_R_EC_LIB); + return 0; + } + *in += len; + return ret; +} + +int i2o_ECPublicKey(const EC_KEY *a, unsigned char **out) +{ + size_t buf_len = 0; + int new_buffer = 0; + + if (a == NULL) { + ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + buf_len = EC_POINT_point2oct(a->group, a->pub_key, + a->conv_form, NULL, 0, NULL); + + if (out == NULL || buf_len == 0) + /* out == NULL => just return the length of the octet string */ + return buf_len; + + if (*out == NULL) { + if ((*out = OPENSSL_malloc(buf_len)) == NULL) { + ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_MALLOC_FAILURE); + return 0; + } + new_buffer = 1; + } + if (!EC_POINT_point2oct(a->group, a->pub_key, a->conv_form, + *out, buf_len, NULL)) { + ECerr(EC_F_I2O_ECPUBLICKEY, ERR_R_EC_LIB); + if (new_buffer) { + OPENSSL_free(*out); + *out = NULL; + } + return 0; + } + if (!new_buffer) + *out += buf_len; + return buf_len; +} + +ASN1_SEQUENCE(ECDSA_SIG) = { + ASN1_SIMPLE(ECDSA_SIG, r, CBIGNUM), + ASN1_SIMPLE(ECDSA_SIG, s, CBIGNUM) +} static_ASN1_SEQUENCE_END(ECDSA_SIG) + +DECLARE_ASN1_FUNCTIONS_const(ECDSA_SIG) +DECLARE_ASN1_ENCODE_FUNCTIONS_const(ECDSA_SIG, ECDSA_SIG) +IMPLEMENT_ASN1_ENCODE_FUNCTIONS_const_fname(ECDSA_SIG, ECDSA_SIG, ECDSA_SIG) + +ECDSA_SIG *ECDSA_SIG_new(void) +{ + ECDSA_SIG *sig = OPENSSL_zalloc(sizeof(*sig)); + if (sig == NULL) + ECerr(EC_F_ECDSA_SIG_NEW, ERR_R_MALLOC_FAILURE); + return sig; +} + +void ECDSA_SIG_free(ECDSA_SIG *sig) +{ + if (sig == NULL) + return; + BN_clear_free(sig->r); + BN_clear_free(sig->s); + OPENSSL_free(sig); +} + +void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) +{ + if (pr != NULL) + *pr = sig->r; + if (ps != NULL) + *ps = sig->s; +} + +int ECDSA_SIG_set0(ECDSA_SIG *sig, BIGNUM *r, BIGNUM *s) +{ + if (r == NULL || s == NULL) + return 0; + BN_clear_free(sig->r); + BN_clear_free(sig->s); + sig->r = r; + sig->s = s; + return 1; +} + +int ECDSA_size(const EC_KEY *r) +{ + int ret, i; + ASN1_INTEGER bs; + unsigned char buf[4]; + const EC_GROUP *group; + + if (r == NULL) + return 0; + group = EC_KEY_get0_group(r); + if (group == NULL) + return 0; + + i = EC_GROUP_order_bits(group); + if (i == 0) + return 0; + bs.length = (i + 7) / 8; + bs.data = buf; + bs.type = V_ASN1_INTEGER; + /* If the top bit is set the asn1 encoding is 1 larger. */ + buf[0] = 0xff; + + i = i2d_ASN1_INTEGER(&bs, NULL); + i += i; /* r and s */ + ret = ASN1_object_size(1, i, V_ASN1_SEQUENCE); + return (ret); +} diff --git a/openssl-1.1.0h/crypto/ec/ec_check.c b/openssl-1.1.0h/crypto/ec/ec_check.c new file mode 100644 index 0000000..eeb06ec --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_check.c @@ -0,0 +1,72 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include "ec_lcl.h" +#include <openssl/err.h> + +int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + const BIGNUM *order; + BN_CTX *new_ctx = NULL; + EC_POINT *point = NULL; + + /* Custom curves assumed to be correct */ + if ((group->meth->flags & EC_FLAGS_CUSTOM_CURVE) != 0) + return 1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + ECerr(EC_F_EC_GROUP_CHECK, ERR_R_MALLOC_FAILURE); + goto err; + } + } + + /* check the discriminant */ + if (!EC_GROUP_check_discriminant(group, ctx)) { + ECerr(EC_F_EC_GROUP_CHECK, EC_R_DISCRIMINANT_IS_ZERO); + goto err; + } + + /* check the generator */ + if (group->generator == NULL) { + ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_GENERATOR); + goto err; + } + if (EC_POINT_is_on_curve(group, group->generator, ctx) <= 0) { + ECerr(EC_F_EC_GROUP_CHECK, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + + /* check the order of the generator */ + if ((point = EC_POINT_new(group)) == NULL) + goto err; + order = EC_GROUP_get0_order(group); + if (order == NULL) + goto err; + if (BN_is_zero(order)) { + ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_ORDER); + goto err; + } + + if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx)) + goto err; + if (!EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GROUP_CHECK, EC_R_INVALID_GROUP_ORDER); + goto err; + } + + ret = 1; + + err: + BN_CTX_free(new_ctx); + EC_POINT_free(point); + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_curve.c b/openssl-1.1.0h/crypto/ec/ec_curve.c new file mode 100644 index 0000000..f8a3846 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_curve.c @@ -0,0 +1,3169 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * Portions of the attached software ("Contribution") are developed by + * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. + * + * The Contribution is licensed pursuant to the OpenSSL open source + * license provided above. + * + * The elliptic curve binary polynomial software is originally written by + * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <string.h> +#include "ec_lcl.h" +#include <openssl/err.h> +#include <openssl/obj_mac.h> +#include <openssl/opensslconf.h> +#include "e_os.h" + +typedef struct { + int field_type, /* either NID_X9_62_prime_field or + * NID_X9_62_characteristic_two_field */ + seed_len, param_len; + unsigned int cofactor; /* promoted to BN_ULONG */ +} EC_CURVE_DATA; + +/* the nist prime curves */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_NIST_PRIME_192 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + /* seed */ + 0x30, 0x45, 0xAE, 0x6F, 0xC8, 0x42, 0x2F, 0x64, 0xED, 0x57, 0x95, 0x28, + 0xD3, 0x81, 0x20, 0xEA, 0xE1, 0x21, 0x96, 0xD5, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x64, 0x21, 0x05, 0x19, 0xE5, 0x9C, 0x80, 0xE7, 0x0F, 0xA7, 0xE9, 0xAB, + 0x72, 0x24, 0x30, 0x49, 0xFE, 0xB8, 0xDE, 0xEC, 0xC1, 0x46, 0xB9, 0xB1, + /* x */ + 0x18, 0x8D, 0xA8, 0x0E, 0xB0, 0x30, 0x90, 0xF6, 0x7C, 0xBF, 0x20, 0xEB, + 0x43, 0xA1, 0x88, 0x00, 0xF4, 0xFF, 0x0A, 0xFD, 0x82, 0xFF, 0x10, 0x12, + /* y */ + 0x07, 0x19, 0x2b, 0x95, 0xff, 0xc8, 0xda, 0x78, 0x63, 0x10, 0x11, 0xed, + 0x6b, 0x24, 0xcd, 0xd5, 0x73, 0xf9, 0x77, 0xa1, 0x1e, 0x79, 0x48, 0x11, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x99, 0xDE, 0xF8, 0x36, 0x14, 0x6B, 0xC9, 0xB1, 0xB4, 0xD2, 0x28, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 28 * 6]; +} _EC_NIST_PRIME_224 = { + { + NID_X9_62_prime_field, 20, 28, 1 + }, + { + /* seed */ + 0xBD, 0x71, 0x34, 0x47, 0x99, 0xD5, 0xC7, 0xFC, 0xDC, 0x45, 0xB5, 0x9F, + 0xA3, 0xB9, 0xAB, 0x8F, 0x6A, 0x94, 0x8B, 0xC5, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, + /* b */ + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, 0x32, 0x56, + 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, 0x27, 0x0B, 0x39, 0x43, + 0x23, 0x55, 0xFF, 0xB4, + /* x */ + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, 0x90, 0xB9, + 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xD6, + 0x11, 0x5C, 0x1D, 0x21, + /* y */ + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6, + 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, 0x44, 0xd5, 0x81, 0x99, + 0x85, 0x00, 0x7e, 0x34, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, 0x13, 0xDD, 0x29, 0x45, + 0x5C, 0x5C, 0x2A, 0x3D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 48 * 6]; +} _EC_NIST_PRIME_384 = { + { + NID_X9_62_prime_field, 20, 48, 1 + }, + { + /* seed */ + 0xA3, 0x35, 0x92, 0x6A, 0xA3, 0x19, 0xA2, 0x7A, 0x1D, 0x00, 0x89, 0x6A, + 0x67, 0x73, 0xA4, 0x82, 0x7A, 0xCD, 0xAC, 0x73, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B, + 0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12, + 0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D, + 0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF, + /* x */ + 0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E, + 0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98, + 0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D, + 0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7, + /* y */ + 0x36, 0x17, 0xde, 0x4a, 0x96, 0x26, 0x2c, 0x6f, 0x5d, 0x9e, 0x98, 0xbf, + 0x92, 0x92, 0xdc, 0x29, 0xf8, 0xf4, 0x1d, 0xbd, 0x28, 0x9a, 0x14, 0x7c, + 0xe9, 0xda, 0x31, 0x13, 0xb5, 0xf0, 0xb8, 0xc0, 0x0a, 0x60, 0xb1, 0xce, + 0x1d, 0x7e, 0x81, 0x9d, 0x7a, 0x43, 0x1d, 0x7c, 0x90, 0xea, 0x0e, 0x5f, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xC7, 0x63, 0x4D, 0x81, 0xF4, 0x37, 0x2D, 0xDF, 0x58, 0x1A, 0x0D, 0xB2, + 0x48, 0xB0, 0xA7, 0x7A, 0xEC, 0xEC, 0x19, 0x6A, 0xCC, 0xC5, 0x29, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 66 * 6]; +} _EC_NIST_PRIME_521 = { + { + NID_X9_62_prime_field, 20, 66, 1 + }, + { + /* seed */ + 0xD0, 0x9E, 0x88, 0x00, 0x29, 0x1C, 0xB8, 0x53, 0x96, 0xCC, 0x67, 0x17, + 0x39, 0x32, 0x84, 0xAA, 0xA0, 0xDA, 0x64, 0xBA, + /* p */ + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x00, 0x51, 0x95, 0x3E, 0xB9, 0x61, 0x8E, 0x1C, 0x9A, 0x1F, 0x92, 0x9A, + 0x21, 0xA0, 0xB6, 0x85, 0x40, 0xEE, 0xA2, 0xDA, 0x72, 0x5B, 0x99, 0xB3, + 0x15, 0xF3, 0xB8, 0xB4, 0x89, 0x91, 0x8E, 0xF1, 0x09, 0xE1, 0x56, 0x19, + 0x39, 0x51, 0xEC, 0x7E, 0x93, 0x7B, 0x16, 0x52, 0xC0, 0xBD, 0x3B, 0xB1, + 0xBF, 0x07, 0x35, 0x73, 0xDF, 0x88, 0x3D, 0x2C, 0x34, 0xF1, 0xEF, 0x45, + 0x1F, 0xD4, 0x6B, 0x50, 0x3F, 0x00, + /* x */ + 0x00, 0xC6, 0x85, 0x8E, 0x06, 0xB7, 0x04, 0x04, 0xE9, 0xCD, 0x9E, 0x3E, + 0xCB, 0x66, 0x23, 0x95, 0xB4, 0x42, 0x9C, 0x64, 0x81, 0x39, 0x05, 0x3F, + 0xB5, 0x21, 0xF8, 0x28, 0xAF, 0x60, 0x6B, 0x4D, 0x3D, 0xBA, 0xA1, 0x4B, + 0x5E, 0x77, 0xEF, 0xE7, 0x59, 0x28, 0xFE, 0x1D, 0xC1, 0x27, 0xA2, 0xFF, + 0xA8, 0xDE, 0x33, 0x48, 0xB3, 0xC1, 0x85, 0x6A, 0x42, 0x9B, 0xF9, 0x7E, + 0x7E, 0x31, 0xC2, 0xE5, 0xBD, 0x66, + /* y */ + 0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, 0xc0, 0x04, 0x5c, 0x8a, + 0x5f, 0xb4, 0x2c, 0x7d, 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, + 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, 0x66, 0x2c, 0x97, 0xee, + 0x72, 0x99, 0x5e, 0xf4, 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, + 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, 0xc2, 0x40, 0x88, 0xbe, + 0x94, 0x76, 0x9f, 0xd1, 0x66, 0x50, + /* order */ + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFA, 0x51, 0x86, + 0x87, 0x83, 0xBF, 0x2F, 0x96, 0x6B, 0x7F, 0xCC, 0x01, 0x48, 0xF7, 0x09, + 0xA5, 0xD0, 0x3B, 0xB5, 0xC9, 0xB8, 0x89, 0x9C, 0x47, 0xAE, 0xBB, 0x6F, + 0xB7, 0x1E, 0x91, 0x38, 0x64, 0x09 + } +}; + +/* the x9.62 prime curves (minus the nist prime curves) */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_X9_62_PRIME_192V2 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + /* seed */ + 0x31, 0xA9, 0x2E, 0xE2, 0x02, 0x9F, 0xD1, 0x0D, 0x90, 0x1B, 0x11, 0x3E, + 0x99, 0x07, 0x10, 0xF0, 0xD2, 0x1A, 0xC6, 0xB6, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0xCC, 0x22, 0xD6, 0xDF, 0xB9, 0x5C, 0x6B, 0x25, 0xE4, 0x9C, 0x0D, 0x63, + 0x64, 0xA4, 0xE5, 0x98, 0x0C, 0x39, 0x3A, 0xA2, 0x16, 0x68, 0xD9, 0x53, + /* x */ + 0xEE, 0xA2, 0xBA, 0xE7, 0xE1, 0x49, 0x78, 0x42, 0xF2, 0xDE, 0x77, 0x69, + 0xCF, 0xE9, 0xC9, 0x89, 0xC0, 0x72, 0xAD, 0x69, 0x6F, 0x48, 0x03, 0x4A, + /* y */ + 0x65, 0x74, 0xd1, 0x1d, 0x69, 0xb6, 0xec, 0x7a, 0x67, 0x2b, 0xb8, 0x2a, + 0x08, 0x3d, 0xf2, 0xf2, 0xb0, 0x84, 0x7d, 0xe9, 0x70, 0xb2, 0xde, 0x15, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0x5F, 0xB1, 0xA7, 0x24, 0xDC, 0x80, 0x41, 0x86, 0x48, 0xD8, 0xDD, 0x31 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_X9_62_PRIME_192V3 = { + { + NID_X9_62_prime_field, 20, 24, 1 + }, + { + /* seed */ + 0xC4, 0x69, 0x68, 0x44, 0x35, 0xDE, 0xB3, 0x78, 0xC4, 0xB6, 0x5C, 0xA9, + 0x59, 0x1E, 0x2A, 0x57, 0x63, 0x05, 0x9A, 0x2E, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x22, 0x12, 0x3D, 0xC2, 0x39, 0x5A, 0x05, 0xCA, 0xA7, 0x42, 0x3D, 0xAE, + 0xCC, 0xC9, 0x47, 0x60, 0xA7, 0xD4, 0x62, 0x25, 0x6B, 0xD5, 0x69, 0x16, + /* x */ + 0x7D, 0x29, 0x77, 0x81, 0x00, 0xC6, 0x5A, 0x1D, 0xA1, 0x78, 0x37, 0x16, + 0x58, 0x8D, 0xCE, 0x2B, 0x8B, 0x4A, 0xEE, 0x8E, 0x22, 0x8F, 0x18, 0x96, + /* y */ + 0x38, 0xa9, 0x0f, 0x22, 0x63, 0x73, 0x37, 0x33, 0x4b, 0x49, 0xdc, 0xb6, + 0x6a, 0x6d, 0xc8, 0xf9, 0x97, 0x8a, 0xca, 0x76, 0x48, 0xa9, 0x43, 0xb0, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7A, 0x62, 0xD0, 0x31, 0xC8, 0x3F, 0x42, 0x94, 0xF6, 0x40, 0xEC, 0x13 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_PRIME_239V1 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + /* seed */ + 0xE4, 0x3B, 0xB4, 0x60, 0xF0, 0xB8, 0x0C, 0xC0, 0xC0, 0xB0, 0x75, 0x79, + 0x8E, 0x94, 0x80, 0x60, 0xF8, 0x32, 0x1B, 0x7D, + /* p */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x6B, 0x01, 0x6C, 0x3B, 0xDC, 0xF1, 0x89, 0x41, 0xD0, 0xD6, 0x54, 0x92, + 0x14, 0x75, 0xCA, 0x71, 0xA9, 0xDB, 0x2F, 0xB2, 0x7D, 0x1D, 0x37, 0x79, + 0x61, 0x85, 0xC2, 0x94, 0x2C, 0x0A, + /* x */ + 0x0F, 0xFA, 0x96, 0x3C, 0xDC, 0xA8, 0x81, 0x6C, 0xCC, 0x33, 0xB8, 0x64, + 0x2B, 0xED, 0xF9, 0x05, 0xC3, 0xD3, 0x58, 0x57, 0x3D, 0x3F, 0x27, 0xFB, + 0xBD, 0x3B, 0x3C, 0xB9, 0xAA, 0xAF, + /* y */ + 0x7d, 0xeb, 0xe8, 0xe4, 0xe9, 0x0a, 0x5d, 0xae, 0x6e, 0x40, 0x54, 0xca, + 0x53, 0x0b, 0xa0, 0x46, 0x54, 0xb3, 0x68, 0x18, 0xce, 0x22, 0x6b, 0x39, + 0xfc, 0xcb, 0x7b, 0x02, 0xf1, 0xae, + /* order */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0x9E, 0x5E, 0x9A, 0x9F, 0x5D, 0x90, 0x71, 0xFB, 0xD1, + 0x52, 0x26, 0x88, 0x90, 0x9D, 0x0B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_PRIME_239V2 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + /* seed */ + 0xE8, 0xB4, 0x01, 0x16, 0x04, 0x09, 0x53, 0x03, 0xCA, 0x3B, 0x80, 0x99, + 0x98, 0x2B, 0xE0, 0x9F, 0xCB, 0x9A, 0xE6, 0x16, + /* p */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x61, 0x7F, 0xAB, 0x68, 0x32, 0x57, 0x6C, 0xBB, 0xFE, 0xD5, 0x0D, 0x99, + 0xF0, 0x24, 0x9C, 0x3F, 0xEE, 0x58, 0xB9, 0x4B, 0xA0, 0x03, 0x8C, 0x7A, + 0xE8, 0x4C, 0x8C, 0x83, 0x2F, 0x2C, + /* x */ + 0x38, 0xAF, 0x09, 0xD9, 0x87, 0x27, 0x70, 0x51, 0x20, 0xC9, 0x21, 0xBB, + 0x5E, 0x9E, 0x26, 0x29, 0x6A, 0x3C, 0xDC, 0xF2, 0xF3, 0x57, 0x57, 0xA0, + 0xEA, 0xFD, 0x87, 0xB8, 0x30, 0xE7, + /* y */ + 0x5b, 0x01, 0x25, 0xe4, 0xdb, 0xea, 0x0e, 0xc7, 0x20, 0x6d, 0xa0, 0xfc, + 0x01, 0xd9, 0xb0, 0x81, 0x32, 0x9f, 0xb5, 0x55, 0xde, 0x6e, 0xf4, 0x60, + 0x23, 0x7d, 0xff, 0x8b, 0xe4, 0xba, + /* order */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x80, 0x00, 0x00, 0xCF, 0xA7, 0xE8, 0x59, 0x43, 0x77, 0xD4, 0x14, 0xC0, + 0x38, 0x21, 0xBC, 0x58, 0x20, 0x63 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_PRIME_239V3 = { + { + NID_X9_62_prime_field, 20, 30, 1 + }, + { + /* seed */ + 0x7D, 0x73, 0x74, 0x16, 0x8F, 0xFE, 0x34, 0x71, 0xB6, 0x0A, 0x85, 0x76, + 0x86, 0xA1, 0x94, 0x75, 0xD3, 0xBF, 0xA2, 0xFF, + /* p */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x25, 0x57, 0x05, 0xFA, 0x2A, 0x30, 0x66, 0x54, 0xB1, 0xF4, 0xCB, 0x03, + 0xD6, 0xA7, 0x50, 0xA3, 0x0C, 0x25, 0x01, 0x02, 0xD4, 0x98, 0x87, 0x17, + 0xD9, 0xBA, 0x15, 0xAB, 0x6D, 0x3E, + /* x */ + 0x67, 0x68, 0xAE, 0x8E, 0x18, 0xBB, 0x92, 0xCF, 0xCF, 0x00, 0x5C, 0x94, + 0x9A, 0xA2, 0xC6, 0xD9, 0x48, 0x53, 0xD0, 0xE6, 0x60, 0xBB, 0xF8, 0x54, + 0xB1, 0xC9, 0x50, 0x5F, 0xE9, 0x5A, + /* y */ + 0x16, 0x07, 0xe6, 0x89, 0x8f, 0x39, 0x0c, 0x06, 0xbc, 0x1d, 0x55, 0x2b, + 0xad, 0x22, 0x6f, 0x3b, 0x6f, 0xcf, 0xe4, 0x8b, 0x6e, 0x81, 0x84, 0x99, + 0xaf, 0x18, 0xe3, 0xed, 0x6c, 0xf3, + /* order */ + 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0x7F, 0xFF, 0xFF, 0x97, 0x5D, 0xEB, 0x41, 0xB3, 0xA6, 0x05, 0x7C, 0x3C, + 0x43, 0x21, 0x46, 0x52, 0x65, 0x51 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 32 * 6]; +} _EC_X9_62_PRIME_256V1 = { + { + NID_X9_62_prime_field, 20, 32, 1 + }, + { + /* seed */ + 0xC4, 0x9D, 0x36, 0x08, 0x86, 0xE7, 0x04, 0x93, 0x6A, 0x66, 0x78, 0xE1, + 0x13, 0x9D, 0x26, 0xB7, 0x81, 0x9F, 0x7E, 0x90, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0x5A, 0xC6, 0x35, 0xD8, 0xAA, 0x3A, 0x93, 0xE7, 0xB3, 0xEB, 0xBD, 0x55, + 0x76, 0x98, 0x86, 0xBC, 0x65, 0x1D, 0x06, 0xB0, 0xCC, 0x53, 0xB0, 0xF6, + 0x3B, 0xCE, 0x3C, 0x3E, 0x27, 0xD2, 0x60, 0x4B, + /* x */ + 0x6B, 0x17, 0xD1, 0xF2, 0xE1, 0x2C, 0x42, 0x47, 0xF8, 0xBC, 0xE6, 0xE5, + 0x63, 0xA4, 0x40, 0xF2, 0x77, 0x03, 0x7D, 0x81, 0x2D, 0xEB, 0x33, 0xA0, + 0xF4, 0xA1, 0x39, 0x45, 0xD8, 0x98, 0xC2, 0x96, + /* y */ + 0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, 0x8e, 0xe7, 0xeb, 0x4a, + 0x7c, 0x0f, 0x9e, 0x16, 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, + 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xBC, 0xE6, 0xFA, 0xAD, 0xA7, 0x17, 0x9E, 0x84, + 0xF3, 0xB9, 0xCA, 0xC2, 0xFC, 0x63, 0x25, 0x51 + } +}; + +/* the secg prime curves (minus the nist and x9.62 prime curves) */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} _EC_SECG_PRIME_112R1 = { + { + NID_X9_62_prime_field, 20, 14, 1 + }, + { + /* seed */ + 0x00, 0xF5, 0x0B, 0x02, 0x8E, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, + 0x51, 0x75, 0x29, 0x04, 0x72, 0x78, 0x3F, 0xB1, + /* p */ + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, 0xBE, 0xAD, + 0x20, 0x8B, + /* a */ + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, 0xBE, 0xAD, + 0x20, 0x88, + /* b */ + 0x65, 0x9E, 0xF8, 0xBA, 0x04, 0x39, 0x16, 0xEE, 0xDE, 0x89, 0x11, 0x70, + 0x2B, 0x22, + /* x */ + 0x09, 0x48, 0x72, 0x39, 0x99, 0x5A, 0x5E, 0xE7, 0x6B, 0x55, 0xF9, 0xC2, + 0xF0, 0x98, + /* y */ + 0xa8, 0x9c, 0xe5, 0xaf, 0x87, 0x24, 0xc0, 0xa2, 0x3e, 0x0e, 0x0f, 0xf7, + 0x75, 0x00, + /* order */ + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x76, 0x28, 0xDF, 0xAC, 0x65, + 0x61, 0xC5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 14 * 6]; +} _EC_SECG_PRIME_112R2 = { + { + NID_X9_62_prime_field, 20, 14, 4 + }, + { + /* seed */ + 0x00, 0x27, 0x57, 0xA1, 0x11, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, + 0x51, 0x75, 0x53, 0x16, 0xC0, 0x5E, 0x0B, 0xD4, + /* p */ + 0xDB, 0x7C, 0x2A, 0xBF, 0x62, 0xE3, 0x5E, 0x66, 0x80, 0x76, 0xBE, 0xAD, + 0x20, 0x8B, + /* a */ + 0x61, 0x27, 0xC2, 0x4C, 0x05, 0xF3, 0x8A, 0x0A, 0xAA, 0xF6, 0x5C, 0x0E, + 0xF0, 0x2C, + /* b */ + 0x51, 0xDE, 0xF1, 0x81, 0x5D, 0xB5, 0xED, 0x74, 0xFC, 0xC3, 0x4C, 0x85, + 0xD7, 0x09, + /* x */ + 0x4B, 0xA3, 0x0A, 0xB5, 0xE8, 0x92, 0xB4, 0xE1, 0x64, 0x9D, 0xD0, 0x92, + 0x86, 0x43, + /* y */ + 0xad, 0xcd, 0x46, 0xf5, 0x88, 0x2e, 0x37, 0x47, 0xde, 0xf3, 0x6e, 0x95, + 0x6e, 0x97, + /* order */ + 0x36, 0xDF, 0x0A, 0xAF, 0xD8, 0xB8, 0xD7, 0x59, 0x7C, 0xA1, 0x05, 0x20, + 0xD0, 0x4B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} _EC_SECG_PRIME_128R1 = { + { + NID_X9_62_prime_field, 20, 16, 1 + }, + { + /* seed */ + 0x00, 0x0E, 0x0D, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, + 0x0C, 0xC0, 0x3A, 0x44, 0x73, 0xD0, 0x36, 0x79, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFC, + /* b */ + 0xE8, 0x75, 0x79, 0xC1, 0x10, 0x79, 0xF4, 0x3D, 0xD8, 0x24, 0x99, 0x3C, + 0x2C, 0xEE, 0x5E, 0xD3, + /* x */ + 0x16, 0x1F, 0xF7, 0x52, 0x8B, 0x89, 0x9B, 0x2D, 0x0C, 0x28, 0x60, 0x7C, + 0xA5, 0x2C, 0x5B, 0x86, + /* y */ + 0xcf, 0x5a, 0xc8, 0x39, 0x5b, 0xaf, 0xeb, 0x13, 0xc0, 0x2d, 0xa2, 0x92, + 0xdd, 0xed, 0x7a, 0x83, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFE, 0x00, 0x00, 0x00, 0x00, 0x75, 0xA3, 0x0D, 0x1B, + 0x90, 0x38, 0xA1, 0x15 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 16 * 6]; +} _EC_SECG_PRIME_128R2 = { + { + NID_X9_62_prime_field, 20, 16, 4 + }, + { + /* seed */ + 0x00, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, 0x12, 0xD8, + 0xF0, 0x34, 0x31, 0xFC, 0xE6, 0x3B, 0x88, 0xF4, + /* p */ + 0xFF, 0xFF, 0xFF, 0xFD, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, + /* a */ + 0xD6, 0x03, 0x19, 0x98, 0xD1, 0xB3, 0xBB, 0xFE, 0xBF, 0x59, 0xCC, 0x9B, + 0xBF, 0xF9, 0xAE, 0xE1, + /* b */ + 0x5E, 0xEE, 0xFC, 0xA3, 0x80, 0xD0, 0x29, 0x19, 0xDC, 0x2C, 0x65, 0x58, + 0xBB, 0x6D, 0x8A, 0x5D, + /* x */ + 0x7B, 0x6A, 0xA5, 0xD8, 0x5E, 0x57, 0x29, 0x83, 0xE6, 0xFB, 0x32, 0xA7, + 0xCD, 0xEB, 0xC1, 0x40, + /* y */ + 0x27, 0xb6, 0x91, 0x6a, 0x89, 0x4d, 0x3a, 0xee, 0x71, 0x06, 0xfe, 0x80, + 0x5f, 0xc3, 0x4b, 0x44, + /* order */ + 0x3F, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xBE, 0x00, 0x24, 0x72, + 0x06, 0x13, 0xB5, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} _EC_SECG_PRIME_160K1 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { + /* no seed */ + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, 0x73, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + /* x */ + 0x00, 0x3B, 0x4C, 0x38, 0x2C, 0xE3, 0x7A, 0xA1, 0x92, 0xA4, 0x01, 0x9E, + 0x76, 0x30, 0x36, 0xF4, 0xF5, 0xDD, 0x4D, 0x7E, 0xBB, + /* y */ + 0x00, 0x93, 0x8c, 0xf9, 0x35, 0x31, 0x8f, 0xdc, 0xed, 0x6b, 0xc2, 0x82, + 0x86, 0x53, 0x17, 0x33, 0xc3, 0xf0, 0x3c, 0x4f, 0xee, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xB8, + 0xFA, 0x16, 0xDF, 0xAB, 0x9A, 0xCA, 0x16, 0xB6, 0xB3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} _EC_SECG_PRIME_160R1 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + /* seed */ + 0x10, 0x53, 0xCD, 0xE4, 0x2C, 0x14, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x53, 0x3B, 0xF3, 0xF8, 0x33, 0x45, + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, + /* a */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFC, + /* b */ + 0x00, 0x1C, 0x97, 0xBE, 0xFC, 0x54, 0xBD, 0x7A, 0x8B, 0x65, 0xAC, 0xF8, + 0x9F, 0x81, 0xD4, 0xD4, 0xAD, 0xC5, 0x65, 0xFA, 0x45, + /* x */ + 0x00, 0x4A, 0x96, 0xB5, 0x68, 0x8E, 0xF5, 0x73, 0x28, 0x46, 0x64, 0x69, + 0x89, 0x68, 0xC3, 0x8B, 0xB9, 0x13, 0xCB, 0xFC, 0x82, + /* y */ + 0x00, 0x23, 0xa6, 0x28, 0x55, 0x31, 0x68, 0x94, 0x7d, 0x59, 0xdc, 0xc9, + 0x12, 0x04, 0x23, 0x51, 0x37, 0x7a, 0xc5, 0xfb, 0x32, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xF4, + 0xC8, 0xF9, 0x27, 0xAE, 0xD3, 0xCA, 0x75, 0x22, 0x57 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} _EC_SECG_PRIME_160R2 = { + { + NID_X9_62_prime_field, 20, 21, 1 + }, + { + /* seed */ + 0xB9, 0x9B, 0x99, 0xB0, 0x99, 0xB3, 0x23, 0xE0, 0x27, 0x09, 0xA4, 0xD6, + 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x51, + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, 0x73, + /* a */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xAC, 0x70, + /* b */ + 0x00, 0xB4, 0xE1, 0x34, 0xD3, 0xFB, 0x59, 0xEB, 0x8B, 0xAB, 0x57, 0x27, + 0x49, 0x04, 0x66, 0x4D, 0x5A, 0xF5, 0x03, 0x88, 0xBA, + /* x */ + 0x00, 0x52, 0xDC, 0xB0, 0x34, 0x29, 0x3A, 0x11, 0x7E, 0x1F, 0x4F, 0xF1, + 0x1B, 0x30, 0xF7, 0x19, 0x9D, 0x31, 0x44, 0xCE, 0x6D, + /* y */ + 0x00, 0xfe, 0xaf, 0xfe, 0xf2, 0xe3, 0x31, 0xf2, 0x96, 0xe0, 0x71, 0xfa, + 0x0d, 0xf9, 0x98, 0x2c, 0xfe, 0xa7, 0xd4, 0x3f, 0x2e, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x35, + 0x1E, 0xE7, 0x86, 0xA8, 0x18, 0xF3, 0xA1, 0xA1, 0x6B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} _EC_SECG_PRIME_192K1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { + /* no seed */ + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xEE, 0x37, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03, + /* x */ + 0xDB, 0x4F, 0xF1, 0x0E, 0xC0, 0x57, 0xE9, 0xAE, 0x26, 0xB0, 0x7D, 0x02, + 0x80, 0xB7, 0xF4, 0x34, 0x1D, 0xA5, 0xD1, 0xB1, 0xEA, 0xE0, 0x6C, 0x7D, + /* y */ + 0x9b, 0x2f, 0x2f, 0x6d, 0x9c, 0x56, 0x28, 0xa7, 0x84, 0x41, 0x63, 0xd0, + 0x15, 0xbe, 0x86, 0x34, 0x40, 0x82, 0xaa, 0x88, 0xd9, 0x5e, 0x2f, 0x9d, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, + 0x26, 0xF2, 0xFC, 0x17, 0x0F, 0x69, 0x46, 0x6A, 0x74, 0xDE, 0xFD, 0x8D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 29 * 6]; +} _EC_SECG_PRIME_224K1 = { + { + NID_X9_62_prime_field, 0, 29, 1 + }, + { + /* no seed */ + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFE, 0xFF, 0xFF, 0xE5, 0x6D, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x05, + /* x */ + 0x00, 0xA1, 0x45, 0x5B, 0x33, 0x4D, 0xF0, 0x99, 0xDF, 0x30, 0xFC, 0x28, + 0xA1, 0x69, 0xA4, 0x67, 0xE9, 0xE4, 0x70, 0x75, 0xA9, 0x0F, 0x7E, 0x65, + 0x0E, 0xB6, 0xB7, 0xA4, 0x5C, + /* y */ + 0x00, 0x7e, 0x08, 0x9f, 0xed, 0x7f, 0xba, 0x34, 0x42, 0x82, 0xca, 0xfb, + 0xd6, 0xf7, 0xe3, 0x19, 0xf7, 0xc0, 0xb0, 0xbd, 0x59, 0xe2, 0xca, 0x4b, + 0xdb, 0x55, 0x6d, 0x61, 0xa5, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, 0xDC, 0xE8, 0xD2, 0xEC, 0x61, 0x84, 0xCA, 0xF0, 0xA9, + 0x71, 0x76, 0x9F, 0xB1, 0xF7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} _EC_SECG_PRIME_256K1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { + /* no seed */ + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFC, 0x2F, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + /* x */ + 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, + 0xCE, 0x87, 0x0B, 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, + 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, 0x98, + /* y */ + 0x48, 0x3a, 0xda, 0x77, 0x26, 0xa3, 0xc4, 0x65, 0x5d, 0xa4, 0xfb, 0xfc, + 0x0e, 0x11, 0x08, 0xa8, 0xfd, 0x17, 0xb4, 0x48, 0xa6, 0x85, 0x54, 0x19, + 0x9c, 0x47, 0xd0, 0x8f, 0xfb, 0x10, 0xd4, 0xb8, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B, + 0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x41 + } +}; + +/* some wap/wtls curves */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} _EC_WTLS_8 = { + { + NID_X9_62_prime_field, 0, 15, 1 + }, + { + /* no seed */ + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFD, 0xE7, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x03, + /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, + /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x02, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xEC, 0xEA, 0x55, 0x1A, + 0xD8, 0x37, 0xE9 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} _EC_WTLS_9 = { + { + NID_X9_62_prime_field, 0, 21, 1 + }, + { + /* no seed */ + /* p */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC, 0x80, 0x8F, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03, + /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xCD, + 0xC9, 0x8A, 0xE0, 0xE2, 0xDE, 0x57, 0x4A, 0xBF, 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} _EC_WTLS_12 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { + /* no seed */ + /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFE, + /* b */ + 0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, 0x32, 0x56, + 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, 0x27, 0x0B, 0x39, 0x43, + 0x23, 0x55, 0xFF, 0xB4, + /* x */ + 0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, 0x90, 0xB9, + 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xD6, + 0x11, 0x5C, 0x1D, 0x21, + /* y */ + 0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6, + 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, 0x44, 0xd5, 0x81, 0x99, + 0x85, 0x00, 0x7e, 0x34, + /* order */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0x16, 0xA2, 0xE0, 0xB8, 0xF0, 0x3E, 0x13, 0xDD, 0x29, 0x45, + 0x5C, 0x5C, 0x2A, 0x3D + } +}; + +#ifndef OPENSSL_NO_EC2M + +/* characteristic two curves */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} _EC_SECG_CHAR2_113R1 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + /* seed */ + 0x10, 0xE7, 0x23, 0xAB, 0x14, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, + 0x17, 0x56, 0xFE, 0xBF, 0x8F, 0xCB, 0x49, 0xA9, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x02, 0x01, + /* a */ + 0x00, 0x30, 0x88, 0x25, 0x0C, 0xA6, 0xE7, 0xC7, 0xFE, 0x64, 0x9C, 0xE8, + 0x58, 0x20, 0xF7, + /* b */ + 0x00, 0xE8, 0xBE, 0xE4, 0xD3, 0xE2, 0x26, 0x07, 0x44, 0x18, 0x8B, 0xE0, + 0xE9, 0xC7, 0x23, + /* x */ + 0x00, 0x9D, 0x73, 0x61, 0x6F, 0x35, 0xF4, 0xAB, 0x14, 0x07, 0xD7, 0x35, + 0x62, 0xC1, 0x0F, + /* y */ + 0x00, 0xA5, 0x28, 0x30, 0x27, 0x79, 0x58, 0xEE, 0x84, 0xD1, 0x31, 0x5E, + 0xD3, 0x18, 0x86, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xD9, 0xCC, 0xEC, 0x8A, + 0x39, 0xE5, 0x6F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 15 * 6]; +} _EC_SECG_CHAR2_113R2 = { + { + NID_X9_62_characteristic_two_field, 20, 15, 2 + }, + { + /* seed */ + 0x10, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, 0xF4, 0xD6, + 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x5D, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x02, 0x01, + /* a */ + 0x00, 0x68, 0x99, 0x18, 0xDB, 0xEC, 0x7E, 0x5A, 0x0D, 0xD6, 0xDF, 0xC0, + 0xAA, 0x55, 0xC7, + /* b */ + 0x00, 0x95, 0xE9, 0xA9, 0xEC, 0x9B, 0x29, 0x7B, 0xD4, 0xBF, 0x36, 0xE0, + 0x59, 0x18, 0x4F, + /* x */ + 0x01, 0xA5, 0x7A, 0x6A, 0x7B, 0x26, 0xCA, 0x5E, 0xF5, 0x2F, 0xCD, 0xB8, + 0x16, 0x47, 0x97, + /* y */ + 0x00, 0xB3, 0xAD, 0xC9, 0x4E, 0xD1, 0xFE, 0x67, 0x4C, 0x06, 0xE6, 0x95, + 0xBA, 0xBA, 0x1D, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x08, 0x78, 0x9B, 0x24, + 0x96, 0xAF, 0x93 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} _EC_SECG_CHAR2_131R1 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + /* seed */ + 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, 0x98, 0x5B, 0xD3, + 0xAD, 0xBA, 0xDA, 0x21, 0xB4, 0x3A, 0x97, 0xE2, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, 0x0D, + /* a */ + 0x07, 0xA1, 0x1B, 0x09, 0xA7, 0x6B, 0x56, 0x21, 0x44, 0x41, 0x8F, 0xF3, + 0xFF, 0x8C, 0x25, 0x70, 0xB8, + /* b */ + 0x02, 0x17, 0xC0, 0x56, 0x10, 0x88, 0x4B, 0x63, 0xB9, 0xC6, 0xC7, 0x29, + 0x16, 0x78, 0xF9, 0xD3, 0x41, + /* x */ + 0x00, 0x81, 0xBA, 0xF9, 0x1F, 0xDF, 0x98, 0x33, 0xC4, 0x0F, 0x9C, 0x18, + 0x13, 0x43, 0x63, 0x83, 0x99, + /* y */ + 0x07, 0x8C, 0x6E, 0x7E, 0xA3, 0x8C, 0x00, 0x1F, 0x73, 0xC8, 0x13, 0x4B, + 0x1B, 0x4E, 0xF9, 0xE1, 0x50, + /* order */ + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x31, 0x23, 0x95, + 0x3A, 0x94, 0x64, 0xB5, 0x4D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 17 * 6]; +} _EC_SECG_CHAR2_131R2 = { + { + NID_X9_62_characteristic_two_field, 20, 17, 2 + }, + { + /* seed */ + 0x98, 0x5B, 0xD3, 0xAD, 0xBA, 0xD4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x5A, 0x21, 0xB4, 0x3A, 0x97, 0xE3, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, 0x0D, + /* a */ + 0x03, 0xE5, 0xA8, 0x89, 0x19, 0xD7, 0xCA, 0xFC, 0xBF, 0x41, 0x5F, 0x07, + 0xC2, 0x17, 0x65, 0x73, 0xB2, + /* b */ + 0x04, 0xB8, 0x26, 0x6A, 0x46, 0xC5, 0x56, 0x57, 0xAC, 0x73, 0x4C, 0xE3, + 0x8F, 0x01, 0x8F, 0x21, 0x92, + /* x */ + 0x03, 0x56, 0xDC, 0xD8, 0xF2, 0xF9, 0x50, 0x31, 0xAD, 0x65, 0x2D, 0x23, + 0x95, 0x1B, 0xB3, 0x66, 0xA8, + /* y */ + 0x06, 0x48, 0xF0, 0x6D, 0x86, 0x79, 0x40, 0xA5, 0x36, 0x6D, 0x9E, 0x26, + 0x5D, 0xE9, 0xEB, 0x24, 0x0F, + /* order */ + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x69, 0x54, 0xA2, + 0x33, 0x04, 0x9B, 0xA9, 0x8F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} _EC_NIST_CHAR2_163K = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { + /* no seed */ + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xC9, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x02, 0xFE, 0x13, 0xC0, 0x53, 0x7B, 0xBC, 0x11, 0xAC, 0xAA, 0x07, 0xD7, + 0x93, 0xDE, 0x4E, 0x6D, 0x5E, 0x5C, 0x94, 0xEE, 0xE8, + /* y */ + 0x02, 0x89, 0x07, 0x0F, 0xB0, 0x5D, 0x38, 0xFF, 0x58, 0x32, 0x1F, 0x2E, + 0x80, 0x05, 0x36, 0xD5, 0x38, 0xCC, 0xDA, 0xA3, 0xD9, + /* order */ + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x01, + 0x08, 0xA2, 0xE0, 0xCC, 0x0D, 0x99, 0xF8, 0xA5, 0xEF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} _EC_SECG_CHAR2_163R1 = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xC9, + /* a */ + 0x07, 0xB6, 0x88, 0x2C, 0xAA, 0xEF, 0xA8, 0x4F, 0x95, 0x54, 0xFF, 0x84, + 0x28, 0xBD, 0x88, 0xE2, 0x46, 0xD2, 0x78, 0x2A, 0xE2, + /* b */ + 0x07, 0x13, 0x61, 0x2D, 0xCD, 0xDC, 0xB4, 0x0A, 0xAB, 0x94, 0x6B, 0xDA, + 0x29, 0xCA, 0x91, 0xF7, 0x3A, 0xF9, 0x58, 0xAF, 0xD9, + /* x */ + 0x03, 0x69, 0x97, 0x96, 0x97, 0xAB, 0x43, 0x89, 0x77, 0x89, 0x56, 0x67, + 0x89, 0x56, 0x7F, 0x78, 0x7A, 0x78, 0x76, 0xA6, 0x54, + /* y */ + 0x00, 0x43, 0x5E, 0xDB, 0x42, 0xEF, 0xAF, 0xB2, 0x98, 0x9D, 0x51, 0xFE, + 0xFC, 0xE3, 0xC8, 0x09, 0x88, 0xF4, 0x1F, 0xF8, 0x83, + /* order */ + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x48, + 0xAA, 0xB6, 0x89, 0xC2, 0x9C, 0xA7, 0x10, 0x27, 0x9B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 21 * 6]; +} _EC_NIST_CHAR2_163B = { + { + NID_X9_62_characteristic_two_field, 0, 21, 2 + }, + { + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xC9, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x02, 0x0A, 0x60, 0x19, 0x07, 0xB8, 0xC9, 0x53, 0xCA, 0x14, 0x81, 0xEB, + 0x10, 0x51, 0x2F, 0x78, 0x74, 0x4A, 0x32, 0x05, 0xFD, + /* x */ + 0x03, 0xF0, 0xEB, 0xA1, 0x62, 0x86, 0xA2, 0xD5, 0x7E, 0xA0, 0x99, 0x11, + 0x68, 0xD4, 0x99, 0x46, 0x37, 0xE8, 0x34, 0x3E, 0x36, + /* y */ + 0x00, 0xD5, 0x1F, 0xBC, 0x6C, 0x71, 0xA0, 0x09, 0x4F, 0xA2, 0xCD, 0xD5, + 0x45, 0xB1, 0x1C, 0x5C, 0x0C, 0x79, 0x73, 0x24, 0xF1, + /* order */ + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x92, + 0xFE, 0x77, 0xE7, 0x0C, 0x12, 0xA4, 0x23, 0x4C, 0x33 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} _EC_SECG_CHAR2_193R1 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + /* seed */ + 0x10, 0x3F, 0xAE, 0xC7, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, + 0x75, 0x77, 0x7F, 0xC5, 0xB1, 0x91, 0xEF, 0x30, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0x01, + /* a */ + 0x00, 0x17, 0x85, 0x8F, 0xEB, 0x7A, 0x98, 0x97, 0x51, 0x69, 0xE1, 0x71, + 0xF7, 0x7B, 0x40, 0x87, 0xDE, 0x09, 0x8A, 0xC8, 0xA9, 0x11, 0xDF, 0x7B, + 0x01, + /* b */ + 0x00, 0xFD, 0xFB, 0x49, 0xBF, 0xE6, 0xC3, 0xA8, 0x9F, 0xAC, 0xAD, 0xAA, + 0x7A, 0x1E, 0x5B, 0xBC, 0x7C, 0xC1, 0xC2, 0xE5, 0xD8, 0x31, 0x47, 0x88, + 0x14, + /* x */ + 0x01, 0xF4, 0x81, 0xBC, 0x5F, 0x0F, 0xF8, 0x4A, 0x74, 0xAD, 0x6C, 0xDF, + 0x6F, 0xDE, 0xF4, 0xBF, 0x61, 0x79, 0x62, 0x53, 0x72, 0xD8, 0xC0, 0xC5, + 0xE1, + /* y */ + 0x00, 0x25, 0xE3, 0x99, 0xF2, 0x90, 0x37, 0x12, 0xCC, 0xF3, 0xEA, 0x9E, + 0x3A, 0x1A, 0xD1, 0x7F, 0xB0, 0xB3, 0x20, 0x1B, 0x6A, 0xF7, 0xCE, 0x1B, + 0x05, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0xC7, 0xF3, 0x4A, 0x77, 0x8F, 0x44, 0x3A, 0xCC, 0x92, 0x0E, 0xBA, + 0x49 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 25 * 6]; +} _EC_SECG_CHAR2_193R2 = { + { + NID_X9_62_characteristic_two_field, 20, 25, 2 + }, + { + /* seed */ + 0x10, 0xB7, 0xB4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x51, + 0x37, 0xC8, 0xA1, 0x6F, 0xD0, 0xDA, 0x22, 0x11, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0x01, + /* a */ + 0x01, 0x63, 0xF3, 0x5A, 0x51, 0x37, 0xC2, 0xCE, 0x3E, 0xA6, 0xED, 0x86, + 0x67, 0x19, 0x0B, 0x0B, 0xC4, 0x3E, 0xCD, 0x69, 0x97, 0x77, 0x02, 0x70, + 0x9B, + /* b */ + 0x00, 0xC9, 0xBB, 0x9E, 0x89, 0x27, 0xD4, 0xD6, 0x4C, 0x37, 0x7E, 0x2A, + 0xB2, 0x85, 0x6A, 0x5B, 0x16, 0xE3, 0xEF, 0xB7, 0xF6, 0x1D, 0x43, 0x16, + 0xAE, + /* x */ + 0x00, 0xD9, 0xB6, 0x7D, 0x19, 0x2E, 0x03, 0x67, 0xC8, 0x03, 0xF3, 0x9E, + 0x1A, 0x7E, 0x82, 0xCA, 0x14, 0xA6, 0x51, 0x35, 0x0A, 0xAE, 0x61, 0x7E, + 0x8F, + /* y */ + 0x01, 0xCE, 0x94, 0x33, 0x56, 0x07, 0xC3, 0x04, 0xAC, 0x29, 0xE7, 0xDE, + 0xFB, 0xD9, 0xCA, 0x01, 0xF5, 0x96, 0xF9, 0x27, 0x22, 0x4C, 0xDE, 0xCF, + 0x6C, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01, 0x5A, 0xAB, 0x56, 0x1B, 0x00, 0x54, 0x13, 0xCC, 0xD4, 0xEE, 0x99, + 0xD5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} _EC_NIST_CHAR2_233K = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { + /* no seed */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x01, 0x72, 0x32, 0xBA, 0x85, 0x3A, 0x7E, 0x73, 0x1A, 0xF1, 0x29, 0xF2, + 0x2F, 0xF4, 0x14, 0x95, 0x63, 0xA4, 0x19, 0xC2, 0x6B, 0xF5, 0x0A, 0x4C, + 0x9D, 0x6E, 0xEF, 0xAD, 0x61, 0x26, + /* y */ + 0x01, 0xDB, 0x53, 0x7D, 0xEC, 0xE8, 0x19, 0xB7, 0xF7, 0x0F, 0x55, 0x5A, + 0x67, 0xC4, 0x27, 0xA8, 0xCD, 0x9B, 0xF1, 0x8A, 0xEB, 0x9B, 0x56, 0xE0, + 0xC1, 0x10, 0x56, 0xFA, 0xE6, 0xA3, + /* order */ + 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x06, 0x9D, 0x5B, 0xB9, 0x15, 0xBC, 0xD4, 0x6E, 0xFB, + 0x1A, 0xD5, 0xF1, 0x73, 0xAB, 0xDF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_NIST_CHAR2_233B = { + { + NID_X9_62_characteristic_two_field, 20, 30, 2 + }, + { + /* seed */ + 0x74, 0xD5, 0x9F, 0xF0, 0x7F, 0x6B, 0x41, 0x3D, 0x0E, 0xA1, 0x4B, 0x34, + 0x4B, 0x20, 0xA2, 0xDB, 0x04, 0x9B, 0x50, 0xC3, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x00, 0x66, 0x64, 0x7E, 0xDE, 0x6C, 0x33, 0x2C, 0x7F, 0x8C, 0x09, 0x23, + 0xBB, 0x58, 0x21, 0x3B, 0x33, 0x3B, 0x20, 0xE9, 0xCE, 0x42, 0x81, 0xFE, + 0x11, 0x5F, 0x7D, 0x8F, 0x90, 0xAD, + /* x */ + 0x00, 0xFA, 0xC9, 0xDF, 0xCB, 0xAC, 0x83, 0x13, 0xBB, 0x21, 0x39, 0xF1, + 0xBB, 0x75, 0x5F, 0xEF, 0x65, 0xBC, 0x39, 0x1F, 0x8B, 0x36, 0xF8, 0xF8, + 0xEB, 0x73, 0x71, 0xFD, 0x55, 0x8B, + /* y */ + 0x01, 0x00, 0x6A, 0x08, 0xA4, 0x19, 0x03, 0x35, 0x06, 0x78, 0xE5, 0x85, + 0x28, 0xBE, 0xBF, 0x8A, 0x0B, 0xEF, 0xF8, 0x67, 0xA7, 0xCA, 0x36, 0x71, + 0x6F, 0x7E, 0x01, 0xF8, 0x10, 0x52, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x13, 0xE9, 0x74, 0xE7, 0x2F, 0x8A, 0x69, 0x22, 0x03, + 0x1D, 0x26, 0x03, 0xCF, 0xE0, 0xD7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 30 * 6]; +} _EC_SECG_CHAR2_239K1 = { + { + NID_X9_62_characteristic_two_field, 0, 30, 4 + }, + { + /* no seed */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x40, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x29, 0xA0, 0xB6, 0xA8, 0x87, 0xA9, 0x83, 0xE9, 0x73, 0x09, 0x88, 0xA6, + 0x87, 0x27, 0xA8, 0xB2, 0xD1, 0x26, 0xC4, 0x4C, 0xC2, 0xCC, 0x7B, 0x2A, + 0x65, 0x55, 0x19, 0x30, 0x35, 0xDC, + /* y */ + 0x76, 0x31, 0x08, 0x04, 0xF1, 0x2E, 0x54, 0x9B, 0xDB, 0x01, 0x1C, 0x10, + 0x30, 0x89, 0xE7, 0x35, 0x10, 0xAC, 0xB2, 0x75, 0xFC, 0x31, 0x2A, 0x5D, + 0xC6, 0xB7, 0x65, 0x53, 0xF0, 0xCA, + /* order */ + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x5A, 0x79, 0xFE, 0xC6, 0x7C, 0xB6, 0xE9, 0x1F, 0x1C, + 0x1D, 0xA8, 0x00, 0xE4, 0x78, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 36 * 6]; +} _EC_NIST_CHAR2_283K = { + { + NID_X9_62_characteristic_two_field, 0, 36, 4 + }, + { + /* no seed */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x05, 0x03, 0x21, 0x3F, 0x78, 0xCA, 0x44, 0x88, 0x3F, 0x1A, 0x3B, 0x81, + 0x62, 0xF1, 0x88, 0xE5, 0x53, 0xCD, 0x26, 0x5F, 0x23, 0xC1, 0x56, 0x7A, + 0x16, 0x87, 0x69, 0x13, 0xB0, 0xC2, 0xAC, 0x24, 0x58, 0x49, 0x28, 0x36, + /* y */ + 0x01, 0xCC, 0xDA, 0x38, 0x0F, 0x1C, 0x9E, 0x31, 0x8D, 0x90, 0xF9, 0x5D, + 0x07, 0xE5, 0x42, 0x6F, 0xE8, 0x7E, 0x45, 0xC0, 0xE8, 0x18, 0x46, 0x98, + 0xE4, 0x59, 0x62, 0x36, 0x4E, 0x34, 0x11, 0x61, 0x77, 0xDD, 0x22, 0x59, + /* order */ + 0x01, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xE9, 0xAE, 0x2E, 0xD0, 0x75, 0x77, + 0x26, 0x5D, 0xFF, 0x7F, 0x94, 0x45, 0x1E, 0x06, 0x1E, 0x16, 0x3C, 0x61 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 36 * 6]; +} _EC_NIST_CHAR2_283B = { + { + NID_X9_62_characteristic_two_field, 20, 36, 2 + }, + { + /* no seed */ + 0x77, 0xE2, 0xB0, 0x73, 0x70, 0xEB, 0x0F, 0x83, 0x2A, 0x6D, 0xD5, 0xB6, + 0x2D, 0xFC, 0x88, 0xCD, 0x06, 0xBB, 0x84, 0xBE, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0xA1, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x02, 0x7B, 0x68, 0x0A, 0xC8, 0xB8, 0x59, 0x6D, 0xA5, 0xA4, 0xAF, 0x8A, + 0x19, 0xA0, 0x30, 0x3F, 0xCA, 0x97, 0xFD, 0x76, 0x45, 0x30, 0x9F, 0xA2, + 0xA5, 0x81, 0x48, 0x5A, 0xF6, 0x26, 0x3E, 0x31, 0x3B, 0x79, 0xA2, 0xF5, + /* x */ + 0x05, 0xF9, 0x39, 0x25, 0x8D, 0xB7, 0xDD, 0x90, 0xE1, 0x93, 0x4F, 0x8C, + 0x70, 0xB0, 0xDF, 0xEC, 0x2E, 0xED, 0x25, 0xB8, 0x55, 0x7E, 0xAC, 0x9C, + 0x80, 0xE2, 0xE1, 0x98, 0xF8, 0xCD, 0xBE, 0xCD, 0x86, 0xB1, 0x20, 0x53, + /* y */ + 0x03, 0x67, 0x68, 0x54, 0xFE, 0x24, 0x14, 0x1C, 0xB9, 0x8F, 0xE6, 0xD4, + 0xB2, 0x0D, 0x02, 0xB4, 0x51, 0x6F, 0xF7, 0x02, 0x35, 0x0E, 0xDD, 0xB0, + 0x82, 0x67, 0x79, 0xC8, 0x13, 0xF0, 0xDF, 0x45, 0xBE, 0x81, 0x12, 0xF4, + /* order */ + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xEF, 0x90, 0x39, 0x96, 0x60, 0xFC, + 0x93, 0x8A, 0x90, 0x16, 0x5B, 0x04, 0x2A, 0x7C, 0xEF, 0xAD, 0xB3, 0x07 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 52 * 6]; +} _EC_NIST_CHAR2_409K = { + { + NID_X9_62_characteristic_two_field, 0, 52, 4 + }, + { + /* no seed */ + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x00, 0x60, 0xF0, 0x5F, 0x65, 0x8F, 0x49, 0xC1, 0xAD, 0x3A, 0xB1, 0x89, + 0x0F, 0x71, 0x84, 0x21, 0x0E, 0xFD, 0x09, 0x87, 0xE3, 0x07, 0xC8, 0x4C, + 0x27, 0xAC, 0xCF, 0xB8, 0xF9, 0xF6, 0x7C, 0xC2, 0xC4, 0x60, 0x18, 0x9E, + 0xB5, 0xAA, 0xAA, 0x62, 0xEE, 0x22, 0x2E, 0xB1, 0xB3, 0x55, 0x40, 0xCF, + 0xE9, 0x02, 0x37, 0x46, + /* y */ + 0x01, 0xE3, 0x69, 0x05, 0x0B, 0x7C, 0x4E, 0x42, 0xAC, 0xBA, 0x1D, 0xAC, + 0xBF, 0x04, 0x29, 0x9C, 0x34, 0x60, 0x78, 0x2F, 0x91, 0x8E, 0xA4, 0x27, + 0xE6, 0x32, 0x51, 0x65, 0xE9, 0xEA, 0x10, 0xE3, 0xDA, 0x5F, 0x6C, 0x42, + 0xE9, 0xC5, 0x52, 0x15, 0xAA, 0x9C, 0xA2, 0x7A, 0x58, 0x63, 0xEC, 0x48, + 0xD8, 0xE0, 0x28, 0x6B, + /* order */ + 0x00, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFE, 0x5F, 0x83, 0xB2, 0xD4, 0xEA, 0x20, 0x40, 0x0E, 0xC4, + 0x55, 0x7D, 0x5E, 0xD3, 0xE3, 0xE7, 0xCA, 0x5B, 0x4B, 0x5C, 0x83, 0xB8, + 0xE0, 0x1E, 0x5F, 0xCF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 52 * 6]; +} _EC_NIST_CHAR2_409B = { + { + NID_X9_62_characteristic_two_field, 20, 52, 2 + }, + { + /* seed */ + 0x40, 0x99, 0xB5, 0xA4, 0x57, 0xF9, 0xD6, 0x9F, 0x79, 0x21, 0x3D, 0x09, + 0x4C, 0x4B, 0xCD, 0x4D, 0x42, 0x62, 0x21, 0x0B, + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x00, 0x21, 0xA5, 0xC2, 0xC8, 0xEE, 0x9F, 0xEB, 0x5C, 0x4B, 0x9A, 0x75, + 0x3B, 0x7B, 0x47, 0x6B, 0x7F, 0xD6, 0x42, 0x2E, 0xF1, 0xF3, 0xDD, 0x67, + 0x47, 0x61, 0xFA, 0x99, 0xD6, 0xAC, 0x27, 0xC8, 0xA9, 0xA1, 0x97, 0xB2, + 0x72, 0x82, 0x2F, 0x6C, 0xD5, 0x7A, 0x55, 0xAA, 0x4F, 0x50, 0xAE, 0x31, + 0x7B, 0x13, 0x54, 0x5F, + /* x */ + 0x01, 0x5D, 0x48, 0x60, 0xD0, 0x88, 0xDD, 0xB3, 0x49, 0x6B, 0x0C, 0x60, + 0x64, 0x75, 0x62, 0x60, 0x44, 0x1C, 0xDE, 0x4A, 0xF1, 0x77, 0x1D, 0x4D, + 0xB0, 0x1F, 0xFE, 0x5B, 0x34, 0xE5, 0x97, 0x03, 0xDC, 0x25, 0x5A, 0x86, + 0x8A, 0x11, 0x80, 0x51, 0x56, 0x03, 0xAE, 0xAB, 0x60, 0x79, 0x4E, 0x54, + 0xBB, 0x79, 0x96, 0xA7, + /* y */ + 0x00, 0x61, 0xB1, 0xCF, 0xAB, 0x6B, 0xE5, 0xF3, 0x2B, 0xBF, 0xA7, 0x83, + 0x24, 0xED, 0x10, 0x6A, 0x76, 0x36, 0xB9, 0xC5, 0xA7, 0xBD, 0x19, 0x8D, + 0x01, 0x58, 0xAA, 0x4F, 0x54, 0x88, 0xD0, 0x8F, 0x38, 0x51, 0x4F, 0x1F, + 0xDF, 0x4B, 0x4F, 0x40, 0xD2, 0x18, 0x1B, 0x36, 0x81, 0xC3, 0x64, 0xBA, + 0x02, 0x73, 0xC7, 0x06, + /* order */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, 0xE2, 0xAA, 0xD6, 0xA6, 0x12, 0xF3, 0x33, 0x07, 0xBE, + 0x5F, 0xA4, 0x7C, 0x3C, 0x9E, 0x05, 0x2F, 0x83, 0x81, 0x64, 0xCD, 0x37, + 0xD9, 0xA2, 0x11, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 72 * 6]; +} _EC_NIST_CHAR2_571K = { + { + NID_X9_62_characteristic_two_field, 0, 72, 4 + }, + { + /* no seed */ + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, 0x25, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* x */ + 0x02, 0x6E, 0xB7, 0xA8, 0x59, 0x92, 0x3F, 0xBC, 0x82, 0x18, 0x96, 0x31, + 0xF8, 0x10, 0x3F, 0xE4, 0xAC, 0x9C, 0xA2, 0x97, 0x00, 0x12, 0xD5, 0xD4, + 0x60, 0x24, 0x80, 0x48, 0x01, 0x84, 0x1C, 0xA4, 0x43, 0x70, 0x95, 0x84, + 0x93, 0xB2, 0x05, 0xE6, 0x47, 0xDA, 0x30, 0x4D, 0xB4, 0xCE, 0xB0, 0x8C, + 0xBB, 0xD1, 0xBA, 0x39, 0x49, 0x47, 0x76, 0xFB, 0x98, 0x8B, 0x47, 0x17, + 0x4D, 0xCA, 0x88, 0xC7, 0xE2, 0x94, 0x52, 0x83, 0xA0, 0x1C, 0x89, 0x72, + /* y */ + 0x03, 0x49, 0xDC, 0x80, 0x7F, 0x4F, 0xBF, 0x37, 0x4F, 0x4A, 0xEA, 0xDE, + 0x3B, 0xCA, 0x95, 0x31, 0x4D, 0xD5, 0x8C, 0xEC, 0x9F, 0x30, 0x7A, 0x54, + 0xFF, 0xC6, 0x1E, 0xFC, 0x00, 0x6D, 0x8A, 0x2C, 0x9D, 0x49, 0x79, 0xC0, + 0xAC, 0x44, 0xAE, 0xA7, 0x4F, 0xBE, 0xBB, 0xB9, 0xF7, 0x72, 0xAE, 0xDC, + 0xB6, 0x20, 0xB0, 0x1A, 0x7B, 0xA7, 0xAF, 0x1B, 0x32, 0x04, 0x30, 0xC8, + 0x59, 0x19, 0x84, 0xF6, 0x01, 0xCD, 0x4C, 0x14, 0x3E, 0xF1, 0xC7, 0xA3, + /* order */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x13, 0x18, 0x50, 0xE1, 0xF1, 0x9A, 0x63, 0xE4, 0xB3, 0x91, 0xA8, 0xDB, + 0x91, 0x7F, 0x41, 0x38, 0xB6, 0x30, 0xD8, 0x4B, 0xE5, 0xD6, 0x39, 0x38, + 0x1E, 0x91, 0xDE, 0xB4, 0x5C, 0xFE, 0x77, 0x8F, 0x63, 0x7C, 0x10, 0x01 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 72 * 6]; +} _EC_NIST_CHAR2_571B = { + { + NID_X9_62_characteristic_two_field, 20, 72, 2 + }, + { + /* seed */ + 0x2A, 0xA0, 0x58, 0xF7, 0x3A, 0x0E, 0x33, 0xAB, 0x48, 0x6B, 0x0F, 0x61, + 0x04, 0x10, 0xC5, 0x3A, 0x7F, 0x13, 0x23, 0x10, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, 0x25, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* b */ + 0x02, 0xF4, 0x0E, 0x7E, 0x22, 0x21, 0xF2, 0x95, 0xDE, 0x29, 0x71, 0x17, + 0xB7, 0xF3, 0xD6, 0x2F, 0x5C, 0x6A, 0x97, 0xFF, 0xCB, 0x8C, 0xEF, 0xF1, + 0xCD, 0x6B, 0xA8, 0xCE, 0x4A, 0x9A, 0x18, 0xAD, 0x84, 0xFF, 0xAB, 0xBD, + 0x8E, 0xFA, 0x59, 0x33, 0x2B, 0xE7, 0xAD, 0x67, 0x56, 0xA6, 0x6E, 0x29, + 0x4A, 0xFD, 0x18, 0x5A, 0x78, 0xFF, 0x12, 0xAA, 0x52, 0x0E, 0x4D, 0xE7, + 0x39, 0xBA, 0xCA, 0x0C, 0x7F, 0xFE, 0xFF, 0x7F, 0x29, 0x55, 0x72, 0x7A, + /* x */ + 0x03, 0x03, 0x00, 0x1D, 0x34, 0xB8, 0x56, 0x29, 0x6C, 0x16, 0xC0, 0xD4, + 0x0D, 0x3C, 0xD7, 0x75, 0x0A, 0x93, 0xD1, 0xD2, 0x95, 0x5F, 0xA8, 0x0A, + 0xA5, 0xF4, 0x0F, 0xC8, 0xDB, 0x7B, 0x2A, 0xBD, 0xBD, 0xE5, 0x39, 0x50, + 0xF4, 0xC0, 0xD2, 0x93, 0xCD, 0xD7, 0x11, 0xA3, 0x5B, 0x67, 0xFB, 0x14, + 0x99, 0xAE, 0x60, 0x03, 0x86, 0x14, 0xF1, 0x39, 0x4A, 0xBF, 0xA3, 0xB4, + 0xC8, 0x50, 0xD9, 0x27, 0xE1, 0xE7, 0x76, 0x9C, 0x8E, 0xEC, 0x2D, 0x19, + /* y */ + 0x03, 0x7B, 0xF2, 0x73, 0x42, 0xDA, 0x63, 0x9B, 0x6D, 0xCC, 0xFF, 0xFE, + 0xB7, 0x3D, 0x69, 0xD7, 0x8C, 0x6C, 0x27, 0xA6, 0x00, 0x9C, 0xBB, 0xCA, + 0x19, 0x80, 0xF8, 0x53, 0x39, 0x21, 0xE8, 0xA6, 0x84, 0x42, 0x3E, 0x43, + 0xBA, 0xB0, 0x8A, 0x57, 0x62, 0x91, 0xAF, 0x8F, 0x46, 0x1B, 0xB2, 0xA8, + 0xB3, 0x53, 0x1D, 0x2F, 0x04, 0x85, 0xC1, 0x9B, 0x16, 0xE2, 0xF1, 0x51, + 0x6E, 0x23, 0xDD, 0x3C, 0x1A, 0x48, 0x27, 0xAF, 0x1B, 0x8A, 0xC1, 0x5B, + /* order */ + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xE6, 0x61, 0xCE, 0x18, 0xFF, 0x55, 0x98, 0x73, 0x08, 0x05, 0x9B, 0x18, + 0x68, 0x23, 0x85, 0x1E, 0xC7, 0xDD, 0x9C, 0xA1, 0x16, 0x1D, 0xE9, 0x3D, + 0x51, 0x74, 0xD6, 0x6E, 0x83, 0x82, 0xE9, 0xBB, 0x2F, 0xE8, 0x4E, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} _EC_X9_62_CHAR2_163V1 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + /* seed */ + 0xD2, 0xC0, 0xFB, 0x15, 0x76, 0x08, 0x60, 0xDE, 0xF1, 0xEE, 0xF4, 0xD6, + 0x96, 0xE6, 0x76, 0x87, 0x56, 0x15, 0x17, 0x54, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x07, + /* a */ + 0x07, 0x25, 0x46, 0xB5, 0x43, 0x52, 0x34, 0xA4, 0x22, 0xE0, 0x78, 0x96, + 0x75, 0xF4, 0x32, 0xC8, 0x94, 0x35, 0xDE, 0x52, 0x42, + /* b */ + 0x00, 0xC9, 0x51, 0x7D, 0x06, 0xD5, 0x24, 0x0D, 0x3C, 0xFF, 0x38, 0xC7, + 0x4B, 0x20, 0xB6, 0xCD, 0x4D, 0x6F, 0x9D, 0xD4, 0xD9, + /* x */ + 0x07, 0xAF, 0x69, 0x98, 0x95, 0x46, 0x10, 0x3D, 0x79, 0x32, 0x9F, 0xCC, + 0x3D, 0x74, 0x88, 0x0F, 0x33, 0xBB, 0xE8, 0x03, 0xCB, + /* y */ + 0x01, 0xEC, 0x23, 0x21, 0x1B, 0x59, 0x66, 0xAD, 0xEA, 0x1D, 0x3F, 0x87, + 0xF7, 0xEA, 0x58, 0x48, 0xAE, 0xF0, 0xB7, 0xCA, 0x9F, + /* order */ + 0x04, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xE6, + 0x0F, 0xC8, 0x82, 0x1C, 0xC7, 0x4D, 0xAE, 0xAF, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} _EC_X9_62_CHAR2_163V2 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + /* seed */ + 0x53, 0x81, 0x4C, 0x05, 0x0D, 0x44, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x58, 0x0C, 0xA4, 0xE2, 0x9F, 0xFD, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x07, + /* a */ + 0x01, 0x08, 0xB3, 0x9E, 0x77, 0xC4, 0xB1, 0x08, 0xBE, 0xD9, 0x81, 0xED, + 0x0E, 0x89, 0x0E, 0x11, 0x7C, 0x51, 0x1C, 0xF0, 0x72, + /* b */ + 0x06, 0x67, 0xAC, 0xEB, 0x38, 0xAF, 0x4E, 0x48, 0x8C, 0x40, 0x74, 0x33, + 0xFF, 0xAE, 0x4F, 0x1C, 0x81, 0x16, 0x38, 0xDF, 0x20, + /* x */ + 0x00, 0x24, 0x26, 0x6E, 0x4E, 0xB5, 0x10, 0x6D, 0x0A, 0x96, 0x4D, 0x92, + 0xC4, 0x86, 0x0E, 0x26, 0x71, 0xDB, 0x9B, 0x6C, 0xC5, + /* y */ + 0x07, 0x9F, 0x68, 0x4D, 0xDF, 0x66, 0x84, 0xC5, 0xCD, 0x25, 0x8B, 0x38, + 0x90, 0x02, 0x1B, 0x23, 0x86, 0xDF, 0xD1, 0x9F, 0xC5, + /* order */ + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFD, 0xF6, + 0x4D, 0xE1, 0x15, 0x1A, 0xDB, 0xB7, 0x8F, 0x10, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 21 * 6]; +} _EC_X9_62_CHAR2_163V3 = { + { + NID_X9_62_characteristic_two_field, 20, 21, 2 + }, + { + /* seed */ + 0x50, 0xCB, 0xF1, 0xD9, 0x5C, 0xA9, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, + 0x61, 0x51, 0x75, 0xF1, 0x6A, 0x36, 0xA3, 0xB8, + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0x07, + /* a */ + 0x07, 0xA5, 0x26, 0xC6, 0x3D, 0x3E, 0x25, 0xA2, 0x56, 0xA0, 0x07, 0x69, + 0x9F, 0x54, 0x47, 0xE3, 0x2A, 0xE4, 0x56, 0xB5, 0x0E, + /* b */ + 0x03, 0xF7, 0x06, 0x17, 0x98, 0xEB, 0x99, 0xE2, 0x38, 0xFD, 0x6F, 0x1B, + 0xF9, 0x5B, 0x48, 0xFE, 0xEB, 0x48, 0x54, 0x25, 0x2B, + /* x */ + 0x02, 0xF9, 0xF8, 0x7B, 0x7C, 0x57, 0x4D, 0x0B, 0xDE, 0xCF, 0x8A, 0x22, + 0xE6, 0x52, 0x47, 0x75, 0xF9, 0x8C, 0xDE, 0xBD, 0xCB, + /* y */ + 0x05, 0xB9, 0x35, 0x59, 0x0C, 0x15, 0x5E, 0x17, 0xEA, 0x48, 0xEB, 0x3F, + 0xF3, 0x71, 0x8B, 0x89, 0x3D, 0xF5, 0x9A, 0x05, 0xD0, + /* order */ + 0x03, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0x1A, + 0xEE, 0x14, 0x0F, 0x11, 0x0A, 0xFF, 0x96, 0x13, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 23 * 6]; +} _EC_X9_62_CHAR2_176V1 = { + { + NID_X9_62_characteristic_two_field, 0, 23, 0xFF6E + }, + { + /* no seed */ + /* p */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, 0x00, 0x00, 0x07, + /* a */ + 0x00, 0xE4, 0xE6, 0xDB, 0x29, 0x95, 0x06, 0x5C, 0x40, 0x7D, 0x9D, 0x39, + 0xB8, 0xD0, 0x96, 0x7B, 0x96, 0x70, 0x4B, 0xA8, 0xE9, 0xC9, 0x0B, + /* b */ + 0x00, 0x5D, 0xDA, 0x47, 0x0A, 0xBE, 0x64, 0x14, 0xDE, 0x8E, 0xC1, 0x33, + 0xAE, 0x28, 0xE9, 0xBB, 0xD7, 0xFC, 0xEC, 0x0A, 0xE0, 0xFF, 0xF2, + /* x */ + 0x00, 0x8D, 0x16, 0xC2, 0x86, 0x67, 0x98, 0xB6, 0x00, 0xF9, 0xF0, 0x8B, + 0xB4, 0xA8, 0xE8, 0x60, 0xF3, 0x29, 0x8C, 0xE0, 0x4A, 0x57, 0x98, + /* y */ + 0x00, 0x6F, 0xA4, 0x53, 0x9C, 0x2D, 0xAD, 0xDD, 0xD6, 0xBA, 0xB5, 0x16, + 0x7D, 0x61, 0xB4, 0x36, 0xE1, 0xD9, 0x2B, 0xB1, 0x6A, 0x56, 0x2C, + /* order */ + 0x00, 0x00, 0x01, 0x00, 0x92, 0x53, 0x73, 0x97, 0xEC, 0xA4, 0xF6, 0x14, + 0x57, 0x99, 0xD6, 0x2B, 0x0A, 0x19, 0xCE, 0x06, 0xFE, 0x26, 0xAD + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_X9_62_CHAR2_191V1 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 2 + }, + { + /* seed */ + 0x4E, 0x13, 0xCA, 0x54, 0x27, 0x44, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x55, 0x2F, 0x27, 0x9A, 0x8C, 0x84, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x01, + /* a */ + 0x28, 0x66, 0x53, 0x7B, 0x67, 0x67, 0x52, 0x63, 0x6A, 0x68, 0xF5, 0x65, + 0x54, 0xE1, 0x26, 0x40, 0x27, 0x6B, 0x64, 0x9E, 0xF7, 0x52, 0x62, 0x67, + /* b */ + 0x2E, 0x45, 0xEF, 0x57, 0x1F, 0x00, 0x78, 0x6F, 0x67, 0xB0, 0x08, 0x1B, + 0x94, 0x95, 0xA3, 0xD9, 0x54, 0x62, 0xF5, 0xDE, 0x0A, 0xA1, 0x85, 0xEC, + /* x */ + 0x36, 0xB3, 0xDA, 0xF8, 0xA2, 0x32, 0x06, 0xF9, 0xC4, 0xF2, 0x99, 0xD7, + 0xB2, 0x1A, 0x9C, 0x36, 0x91, 0x37, 0xF2, 0xC8, 0x4A, 0xE1, 0xAA, 0x0D, + /* y */ + 0x76, 0x5B, 0xE7, 0x34, 0x33, 0xB3, 0xF9, 0x5E, 0x33, 0x29, 0x32, 0xE7, + 0x0E, 0xA2, 0x45, 0xCA, 0x24, 0x18, 0xEA, 0x0E, 0xF9, 0x80, 0x18, 0xFB, + /* order */ + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x04, 0xA2, 0x0E, 0x90, 0xC3, 0x90, 0x67, 0xC8, 0x93, 0xBB, 0xB9, 0xA5 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_X9_62_CHAR2_191V2 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 4 + }, + { + /* seed */ + 0x08, 0x71, 0xEF, 0x2F, 0xEF, 0x24, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x58, 0xBE, 0xE0, 0xD9, 0x5C, 0x15, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x01, + /* a */ + 0x40, 0x10, 0x28, 0x77, 0x4D, 0x77, 0x77, 0xC7, 0xB7, 0x66, 0x6D, 0x13, + 0x66, 0xEA, 0x43, 0x20, 0x71, 0x27, 0x4F, 0x89, 0xFF, 0x01, 0xE7, 0x18, + /* b */ + 0x06, 0x20, 0x04, 0x8D, 0x28, 0xBC, 0xBD, 0x03, 0xB6, 0x24, 0x9C, 0x99, + 0x18, 0x2B, 0x7C, 0x8C, 0xD1, 0x97, 0x00, 0xC3, 0x62, 0xC4, 0x6A, 0x01, + /* x */ + 0x38, 0x09, 0xB2, 0xB7, 0xCC, 0x1B, 0x28, 0xCC, 0x5A, 0x87, 0x92, 0x6A, + 0xAD, 0x83, 0xFD, 0x28, 0x78, 0x9E, 0x81, 0xE2, 0xC9, 0xE3, 0xBF, 0x10, + /* y */ + 0x17, 0x43, 0x43, 0x86, 0x62, 0x6D, 0x14, 0xF3, 0xDB, 0xF0, 0x17, 0x60, + 0xD9, 0x21, 0x3A, 0x3E, 0x1C, 0xF3, 0x7A, 0xEC, 0x43, 0x7D, 0x66, 0x8A, + /* order */ + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x50, 0x50, 0x8C, 0xB8, 0x9F, 0x65, 0x28, 0x24, 0xE0, 0x6B, 0x81, 0x73 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 24 * 6]; +} _EC_X9_62_CHAR2_191V3 = { + { + NID_X9_62_characteristic_two_field, 20, 24, 6 + }, + { + /* seed */ + 0xE0, 0x53, 0x51, 0x2D, 0xC6, 0x84, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x50, 0x67, 0xAE, 0x78, 0x6D, 0x1F, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02, 0x01, + /* a */ + 0x6C, 0x01, 0x07, 0x47, 0x56, 0x09, 0x91, 0x22, 0x22, 0x10, 0x56, 0x91, + 0x1C, 0x77, 0xD7, 0x7E, 0x77, 0xA7, 0x77, 0xE7, 0xE7, 0xE7, 0x7F, 0xCB, + /* b */ + 0x71, 0xFE, 0x1A, 0xF9, 0x26, 0xCF, 0x84, 0x79, 0x89, 0xEF, 0xEF, 0x8D, + 0xB4, 0x59, 0xF6, 0x63, 0x94, 0xD9, 0x0F, 0x32, 0xAD, 0x3F, 0x15, 0xE8, + /* x */ + 0x37, 0x5D, 0x4C, 0xE2, 0x4F, 0xDE, 0x43, 0x44, 0x89, 0xDE, 0x87, 0x46, + 0xE7, 0x17, 0x86, 0x01, 0x50, 0x09, 0xE6, 0x6E, 0x38, 0xA9, 0x26, 0xDD, + /* y */ + 0x54, 0x5A, 0x39, 0x17, 0x61, 0x96, 0x57, 0x5D, 0x98, 0x59, 0x99, 0x36, + 0x6E, 0x6A, 0xD3, 0x4C, 0xE0, 0xA7, 0x7C, 0xD7, 0x12, 0x7B, 0x06, 0xBE, + /* order */ + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, + 0x61, 0x0C, 0x0B, 0x19, 0x68, 0x12, 0xBF, 0xB6, 0x28, 0x8A, 0x3E, 0xA3 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 27 * 6]; +} _EC_X9_62_CHAR2_208W1 = { + { + NID_X9_62_characteristic_two_field, 0, 27, 0xFE48 + }, + { + /* no seed */ + /* p */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x07, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, + /* b */ + 0x00, 0xC8, 0x61, 0x9E, 0xD4, 0x5A, 0x62, 0xE6, 0x21, 0x2E, 0x11, 0x60, + 0x34, 0x9E, 0x2B, 0xFA, 0x84, 0x44, 0x39, 0xFA, 0xFC, 0x2A, 0x3F, 0xD1, + 0x63, 0x8F, 0x9E, + /* x */ + 0x00, 0x89, 0xFD, 0xFB, 0xE4, 0xAB, 0xE1, 0x93, 0xDF, 0x95, 0x59, 0xEC, + 0xF0, 0x7A, 0xC0, 0xCE, 0x78, 0x55, 0x4E, 0x27, 0x84, 0xEB, 0x8C, 0x1E, + 0xD1, 0xA5, 0x7A, + /* y */ + 0x00, 0x0F, 0x55, 0xB5, 0x1A, 0x06, 0xE7, 0x8E, 0x9A, 0xC3, 0x8A, 0x03, + 0x5F, 0xF5, 0x20, 0xD8, 0xB0, 0x17, 0x81, 0xBE, 0xB1, 0xA6, 0xBB, 0x08, + 0x61, 0x7D, 0xE3, + /* order */ + 0x00, 0x00, 0x01, 0x01, 0xBA, 0xF9, 0x5C, 0x97, 0x23, 0xC5, 0x7B, 0x6C, + 0x21, 0xDA, 0x2E, 0xFF, 0x2D, 0x5E, 0xD5, 0x88, 0xBD, 0xD5, 0x71, 0x7E, + 0x21, 0x2F, 0x9D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_CHAR2_239V1 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 4 + }, + { + /* seed */ + 0xD3, 0x4B, 0x9A, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, + 0xCA, 0x71, 0xB9, 0x20, 0xBF, 0xEF, 0xB0, 0x5D, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x32, 0x01, 0x08, 0x57, 0x07, 0x7C, 0x54, 0x31, 0x12, 0x3A, 0x46, 0xB8, + 0x08, 0x90, 0x67, 0x56, 0xF5, 0x43, 0x42, 0x3E, 0x8D, 0x27, 0x87, 0x75, + 0x78, 0x12, 0x57, 0x78, 0xAC, 0x76, + /* b */ + 0x79, 0x04, 0x08, 0xF2, 0xEE, 0xDA, 0xF3, 0x92, 0xB0, 0x12, 0xED, 0xEF, + 0xB3, 0x39, 0x2F, 0x30, 0xF4, 0x32, 0x7C, 0x0C, 0xA3, 0xF3, 0x1F, 0xC3, + 0x83, 0xC4, 0x22, 0xAA, 0x8C, 0x16, + /* x */ + 0x57, 0x92, 0x70, 0x98, 0xFA, 0x93, 0x2E, 0x7C, 0x0A, 0x96, 0xD3, 0xFD, + 0x5B, 0x70, 0x6E, 0xF7, 0xE5, 0xF5, 0xC1, 0x56, 0xE1, 0x6B, 0x7E, 0x7C, + 0x86, 0x03, 0x85, 0x52, 0xE9, 0x1D, + /* y */ + 0x61, 0xD8, 0xEE, 0x50, 0x77, 0xC3, 0x3F, 0xEC, 0xF6, 0xF1, 0xA1, 0x6B, + 0x26, 0x8D, 0xE4, 0x69, 0xC3, 0xC7, 0x74, 0x4E, 0xA9, 0xA9, 0x71, 0x64, + 0x9F, 0xC7, 0xA9, 0x61, 0x63, 0x05, + /* order */ + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x0F, 0x4D, 0x42, 0xFF, 0xE1, 0x49, 0x2A, 0x49, 0x93, + 0xF1, 0xCA, 0xD6, 0x66, 0xE4, 0x47 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_CHAR2_239V2 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 6 + }, + { + /* seed */ + 0x2A, 0xA6, 0x98, 0x2F, 0xDF, 0xA4, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x5D, 0x26, 0x67, 0x27, 0x27, 0x7D, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x42, 0x30, 0x01, 0x77, 0x57, 0xA7, 0x67, 0xFA, 0xE4, 0x23, 0x98, 0x56, + 0x9B, 0x74, 0x63, 0x25, 0xD4, 0x53, 0x13, 0xAF, 0x07, 0x66, 0x26, 0x64, + 0x79, 0xB7, 0x56, 0x54, 0xE6, 0x5F, + /* b */ + 0x50, 0x37, 0xEA, 0x65, 0x41, 0x96, 0xCF, 0xF0, 0xCD, 0x82, 0xB2, 0xC1, + 0x4A, 0x2F, 0xCF, 0x2E, 0x3F, 0xF8, 0x77, 0x52, 0x85, 0xB5, 0x45, 0x72, + 0x2F, 0x03, 0xEA, 0xCD, 0xB7, 0x4B, + /* x */ + 0x28, 0xF9, 0xD0, 0x4E, 0x90, 0x00, 0x69, 0xC8, 0xDC, 0x47, 0xA0, 0x85, + 0x34, 0xFE, 0x76, 0xD2, 0xB9, 0x00, 0xB7, 0xD7, 0xEF, 0x31, 0xF5, 0x70, + 0x9F, 0x20, 0x0C, 0x4C, 0xA2, 0x05, + /* y */ + 0x56, 0x67, 0x33, 0x4C, 0x45, 0xAF, 0xF3, 0xB5, 0xA0, 0x3B, 0xAD, 0x9D, + 0xD7, 0x5E, 0x2C, 0x71, 0xA9, 0x93, 0x62, 0x56, 0x7D, 0x54, 0x53, 0xF7, + 0xFA, 0x6E, 0x22, 0x7E, 0xC8, 0x33, + /* order */ + 0x15, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, 0x55, + 0x55, 0x55, 0x55, 0x3C, 0x6F, 0x28, 0x85, 0x25, 0x9C, 0x31, 0xE3, 0xFC, + 0xDF, 0x15, 0x46, 0x24, 0x52, 0x2D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 30 * 6]; +} _EC_X9_62_CHAR2_239V3 = { + { + NID_X9_62_characteristic_two_field, 20, 30, 0xA + }, + { + /* seed */ + 0x9E, 0x07, 0x6F, 0x4D, 0x69, 0x6E, 0x67, 0x68, 0x75, 0x61, 0x51, 0x75, + 0xE1, 0x1E, 0x9F, 0xDD, 0x77, 0xF9, 0x20, 0x41, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x01, 0x23, 0x87, 0x74, 0x66, 0x6A, 0x67, 0x76, 0x6D, 0x66, 0x76, 0xF7, + 0x78, 0xE6, 0x76, 0xB6, 0x69, 0x99, 0x17, 0x66, 0x66, 0xE6, 0x87, 0x66, + 0x6D, 0x87, 0x66, 0xC6, 0x6A, 0x9F, + /* b */ + 0x6A, 0x94, 0x19, 0x77, 0xBA, 0x9F, 0x6A, 0x43, 0x51, 0x99, 0xAC, 0xFC, + 0x51, 0x06, 0x7E, 0xD5, 0x87, 0xF5, 0x19, 0xC5, 0xEC, 0xB5, 0x41, 0xB8, + 0xE4, 0x41, 0x11, 0xDE, 0x1D, 0x40, + /* x */ + 0x70, 0xF6, 0xE9, 0xD0, 0x4D, 0x28, 0x9C, 0x4E, 0x89, 0x91, 0x3C, 0xE3, + 0x53, 0x0B, 0xFD, 0xE9, 0x03, 0x97, 0x7D, 0x42, 0xB1, 0x46, 0xD5, 0x39, + 0xBF, 0x1B, 0xDE, 0x4E, 0x9C, 0x92, + /* y */ + 0x2E, 0x5A, 0x0E, 0xAF, 0x6E, 0x5E, 0x13, 0x05, 0xB9, 0x00, 0x4D, 0xCE, + 0x5C, 0x0E, 0xD7, 0xFE, 0x59, 0xA3, 0x56, 0x08, 0xF3, 0x38, 0x37, 0xC8, + 0x16, 0xD8, 0x0B, 0x79, 0xF4, 0x61, + /* order */ + 0x0C, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, 0xCC, + 0xCC, 0xCC, 0xCC, 0xAC, 0x49, 0x12, 0xD2, 0xD9, 0xDF, 0x90, 0x3E, 0xF9, + 0x88, 0x8B, 0x8A, 0x0E, 0x4C, 0xFF + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 35 * 6]; +} _EC_X9_62_CHAR2_272W1 = { + { + NID_X9_62_characteristic_two_field, 0, 35, 0xFF06 + }, + { + /* no seed */ + /* p */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0B, + /* a */ + 0x00, 0x91, 0xA0, 0x91, 0xF0, 0x3B, 0x5F, 0xBA, 0x4A, 0xB2, 0xCC, 0xF4, + 0x9C, 0x4E, 0xDD, 0x22, 0x0F, 0xB0, 0x28, 0x71, 0x2D, 0x42, 0xBE, 0x75, + 0x2B, 0x2C, 0x40, 0x09, 0x4D, 0xBA, 0xCD, 0xB5, 0x86, 0xFB, 0x20, + /* b */ + 0x00, 0x71, 0x67, 0xEF, 0xC9, 0x2B, 0xB2, 0xE3, 0xCE, 0x7C, 0x8A, 0xAA, + 0xFF, 0x34, 0xE1, 0x2A, 0x9C, 0x55, 0x70, 0x03, 0xD7, 0xC7, 0x3A, 0x6F, + 0xAF, 0x00, 0x3F, 0x99, 0xF6, 0xCC, 0x84, 0x82, 0xE5, 0x40, 0xF7, + /* x */ + 0x00, 0x61, 0x08, 0xBA, 0xBB, 0x2C, 0xEE, 0xBC, 0xF7, 0x87, 0x05, 0x8A, + 0x05, 0x6C, 0xBE, 0x0C, 0xFE, 0x62, 0x2D, 0x77, 0x23, 0xA2, 0x89, 0xE0, + 0x8A, 0x07, 0xAE, 0x13, 0xEF, 0x0D, 0x10, 0xD1, 0x71, 0xDD, 0x8D, + /* y */ + 0x00, 0x10, 0xC7, 0x69, 0x57, 0x16, 0x85, 0x1E, 0xEF, 0x6B, 0xA7, 0xF6, + 0x87, 0x2E, 0x61, 0x42, 0xFB, 0xD2, 0x41, 0xB8, 0x30, 0xFF, 0x5E, 0xFC, + 0xAC, 0xEC, 0xCA, 0xB0, 0x5E, 0x02, 0x00, 0x5D, 0xDE, 0x9D, 0x23, + /* order */ + 0x00, 0x00, 0x01, 0x00, 0xFA, 0xF5, 0x13, 0x54, 0xE0, 0xE3, 0x9E, 0x48, + 0x92, 0xDF, 0x6E, 0x31, 0x9C, 0x72, 0xC8, 0x16, 0x16, 0x03, 0xFA, 0x45, + 0xAA, 0x7B, 0x99, 0x8A, 0x16, 0x7B, 0x8F, 0x1E, 0x62, 0x95, 0x21 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 39 * 6]; +} _EC_X9_62_CHAR2_304W1 = { + { + NID_X9_62_characteristic_two_field, 0, 39, 0xFE2E + }, + { + /* no seed */ + /* p */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x08, 0x07, + /* a */ + 0x00, 0xFD, 0x0D, 0x69, 0x31, 0x49, 0xA1, 0x18, 0xF6, 0x51, 0xE6, 0xDC, + 0xE6, 0x80, 0x20, 0x85, 0x37, 0x7E, 0x5F, 0x88, 0x2D, 0x1B, 0x51, 0x0B, + 0x44, 0x16, 0x00, 0x74, 0xC1, 0x28, 0x80, 0x78, 0x36, 0x5A, 0x03, 0x96, + 0xC8, 0xE6, 0x81, + /* b */ + 0x00, 0xBD, 0xDB, 0x97, 0xE5, 0x55, 0xA5, 0x0A, 0x90, 0x8E, 0x43, 0xB0, + 0x1C, 0x79, 0x8E, 0xA5, 0xDA, 0xA6, 0x78, 0x8F, 0x1E, 0xA2, 0x79, 0x4E, + 0xFC, 0xF5, 0x71, 0x66, 0xB8, 0xC1, 0x40, 0x39, 0x60, 0x1E, 0x55, 0x82, + 0x73, 0x40, 0xBE, + /* x */ + 0x00, 0x19, 0x7B, 0x07, 0x84, 0x5E, 0x9B, 0xE2, 0xD9, 0x6A, 0xDB, 0x0F, + 0x5F, 0x3C, 0x7F, 0x2C, 0xFF, 0xBD, 0x7A, 0x3E, 0xB8, 0xB6, 0xFE, 0xC3, + 0x5C, 0x7F, 0xD6, 0x7F, 0x26, 0xDD, 0xF6, 0x28, 0x5A, 0x64, 0x4F, 0x74, + 0x0A, 0x26, 0x14, + /* y */ + 0x00, 0xE1, 0x9F, 0xBE, 0xB7, 0x6E, 0x0D, 0xA1, 0x71, 0x51, 0x7E, 0xCF, + 0x40, 0x1B, 0x50, 0x28, 0x9B, 0xF0, 0x14, 0x10, 0x32, 0x88, 0x52, 0x7A, + 0x9B, 0x41, 0x6A, 0x10, 0x5E, 0x80, 0x26, 0x0B, 0x54, 0x9F, 0xDC, 0x1B, + 0x92, 0xC0, 0x3B, + /* order */ + 0x00, 0x00, 0x01, 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, 0x80, 0x01, + 0x01, 0xD5, 0x56, 0x57, 0x2A, 0xAB, 0xAC, 0x80, 0x01, 0x02, 0x2D, 0x5C, + 0x91, 0xDD, 0x17, 0x3F, 0x8F, 0xB5, 0x61, 0xDA, 0x68, 0x99, 0x16, 0x44, + 0x43, 0x05, 0x1D + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[20 + 45 * 6]; +} _EC_X9_62_CHAR2_359V1 = { + { + NID_X9_62_characteristic_two_field, 20, 45, 0x4C + }, + { + /* seed */ + 0x2B, 0x35, 0x49, 0x20, 0xB7, 0x24, 0xD6, 0x96, 0xE6, 0x76, 0x87, 0x56, + 0x15, 0x17, 0x58, 0x5B, 0xA1, 0x33, 0x2D, 0xC6, + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x56, 0x67, 0x67, 0x6A, 0x65, 0x4B, 0x20, 0x75, 0x4F, 0x35, 0x6E, 0xA9, + 0x20, 0x17, 0xD9, 0x46, 0x56, 0x7C, 0x46, 0x67, 0x55, 0x56, 0xF1, 0x95, + 0x56, 0xA0, 0x46, 0x16, 0xB5, 0x67, 0xD2, 0x23, 0xA5, 0xE0, 0x56, 0x56, + 0xFB, 0x54, 0x90, 0x16, 0xA9, 0x66, 0x56, 0xA5, 0x57, + /* b */ + 0x24, 0x72, 0xE2, 0xD0, 0x19, 0x7C, 0x49, 0x36, 0x3F, 0x1F, 0xE7, 0xF5, + 0xB6, 0xDB, 0x07, 0x5D, 0x52, 0xB6, 0x94, 0x7D, 0x13, 0x5D, 0x8C, 0xA4, + 0x45, 0x80, 0x5D, 0x39, 0xBC, 0x34, 0x56, 0x26, 0x08, 0x96, 0x87, 0x74, + 0x2B, 0x63, 0x29, 0xE7, 0x06, 0x80, 0x23, 0x19, 0x88, + /* x */ + 0x3C, 0x25, 0x8E, 0xF3, 0x04, 0x77, 0x67, 0xE7, 0xED, 0xE0, 0xF1, 0xFD, + 0xAA, 0x79, 0xDA, 0xEE, 0x38, 0x41, 0x36, 0x6A, 0x13, 0x2E, 0x16, 0x3A, + 0xCE, 0xD4, 0xED, 0x24, 0x01, 0xDF, 0x9C, 0x6B, 0xDC, 0xDE, 0x98, 0xE8, + 0xE7, 0x07, 0xC0, 0x7A, 0x22, 0x39, 0xB1, 0xB0, 0x97, + /* y */ + 0x53, 0xD7, 0xE0, 0x85, 0x29, 0x54, 0x70, 0x48, 0x12, 0x1E, 0x9C, 0x95, + 0xF3, 0x79, 0x1D, 0xD8, 0x04, 0x96, 0x39, 0x48, 0xF3, 0x4F, 0xAE, 0x7B, + 0xF4, 0x4E, 0xA8, 0x23, 0x65, 0xDC, 0x78, 0x68, 0xFE, 0x57, 0xE4, 0xAE, + 0x2D, 0xE2, 0x11, 0x30, 0x5A, 0x40, 0x71, 0x04, 0xBD, + /* order */ + 0x01, 0xAF, 0x28, 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, 0xAF, 0x28, + 0x6B, 0xCA, 0x1A, 0xF2, 0x86, 0xBC, 0xA1, 0xAF, 0x28, 0x6B, 0xC9, 0xFB, + 0x8F, 0x6B, 0x85, 0xC5, 0x56, 0x89, 0x2C, 0x20, 0xA7, 0xEB, 0x96, 0x4F, + 0xE7, 0x71, 0x9E, 0x74, 0xF4, 0x90, 0x75, 0x8D, 0x3B + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 47 * 6]; +} _EC_X9_62_CHAR2_368W1 = { + { + NID_X9_62_characteristic_two_field, 0, 47, 0xFF70 + }, + { + /* no seed */ + /* p */ + 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, + /* a */ + 0x00, 0xE0, 0xD2, 0xEE, 0x25, 0x09, 0x52, 0x06, 0xF5, 0xE2, 0xA4, 0xF9, + 0xED, 0x22, 0x9F, 0x1F, 0x25, 0x6E, 0x79, 0xA0, 0xE2, 0xB4, 0x55, 0x97, + 0x0D, 0x8D, 0x0D, 0x86, 0x5B, 0xD9, 0x47, 0x78, 0xC5, 0x76, 0xD6, 0x2F, + 0x0A, 0xB7, 0x51, 0x9C, 0xCD, 0x2A, 0x1A, 0x90, 0x6A, 0xE3, 0x0D, + /* b */ + 0x00, 0xFC, 0x12, 0x17, 0xD4, 0x32, 0x0A, 0x90, 0x45, 0x2C, 0x76, 0x0A, + 0x58, 0xED, 0xCD, 0x30, 0xC8, 0xDD, 0x06, 0x9B, 0x3C, 0x34, 0x45, 0x38, + 0x37, 0xA3, 0x4E, 0xD5, 0x0C, 0xB5, 0x49, 0x17, 0xE1, 0xC2, 0x11, 0x2D, + 0x84, 0xD1, 0x64, 0xF4, 0x44, 0xF8, 0xF7, 0x47, 0x86, 0x04, 0x6A, + /* x */ + 0x00, 0x10, 0x85, 0xE2, 0x75, 0x53, 0x81, 0xDC, 0xCC, 0xE3, 0xC1, 0x55, + 0x7A, 0xFA, 0x10, 0xC2, 0xF0, 0xC0, 0xC2, 0x82, 0x56, 0x46, 0xC5, 0xB3, + 0x4A, 0x39, 0x4C, 0xBC, 0xFA, 0x8B, 0xC1, 0x6B, 0x22, 0xE7, 0xE7, 0x89, + 0xE9, 0x27, 0xBE, 0x21, 0x6F, 0x02, 0xE1, 0xFB, 0x13, 0x6A, 0x5F, + /* y */ + 0x00, 0x7B, 0x3E, 0xB1, 0xBD, 0xDC, 0xBA, 0x62, 0xD5, 0xD8, 0xB2, 0x05, + 0x9B, 0x52, 0x57, 0x97, 0xFC, 0x73, 0x82, 0x2C, 0x59, 0x05, 0x9C, 0x62, + 0x3A, 0x45, 0xFF, 0x38, 0x43, 0xCE, 0xE8, 0xF8, 0x7C, 0xD1, 0x85, 0x5A, + 0xDA, 0xA8, 0x1E, 0x2A, 0x07, 0x50, 0xB8, 0x0F, 0xDA, 0x23, 0x10, + /* order */ + 0x00, 0x00, 0x01, 0x00, 0x90, 0x51, 0x2D, 0xA9, 0xAF, 0x72, 0xB0, 0x83, + 0x49, 0xD9, 0x8A, 0x5D, 0xD4, 0xC7, 0xB0, 0x53, 0x2E, 0xCA, 0x51, 0xCE, + 0x03, 0xE2, 0xD1, 0x0F, 0x3B, 0x7A, 0xC5, 0x79, 0xBD, 0x87, 0xE9, 0x09, + 0xAE, 0x40, 0xA6, 0xF1, 0x31, 0xE9, 0xCF, 0xCE, 0x5B, 0xD9, 0x67 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 54 * 6]; +} _EC_X9_62_CHAR2_431R1 = { + { + NID_X9_62_characteristic_two_field, 0, 54, 0x2760 + }, + { + /* no seed */ + /* p */ + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x1A, 0x82, 0x7E, 0xF0, 0x0D, 0xD6, 0xFC, 0x0E, 0x23, 0x4C, 0xAF, 0x04, + 0x6C, 0x6A, 0x5D, 0x8A, 0x85, 0x39, 0x5B, 0x23, 0x6C, 0xC4, 0xAD, 0x2C, + 0xF3, 0x2A, 0x0C, 0xAD, 0xBD, 0xC9, 0xDD, 0xF6, 0x20, 0xB0, 0xEB, 0x99, + 0x06, 0xD0, 0x95, 0x7F, 0x6C, 0x6F, 0xEA, 0xCD, 0x61, 0x54, 0x68, 0xDF, + 0x10, 0x4D, 0xE2, 0x96, 0xCD, 0x8F, + /* b */ + 0x10, 0xD9, 0xB4, 0xA3, 0xD9, 0x04, 0x7D, 0x8B, 0x15, 0x43, 0x59, 0xAB, + 0xFB, 0x1B, 0x7F, 0x54, 0x85, 0xB0, 0x4C, 0xEB, 0x86, 0x82, 0x37, 0xDD, + 0xC9, 0xDE, 0xDA, 0x98, 0x2A, 0x67, 0x9A, 0x5A, 0x91, 0x9B, 0x62, 0x6D, + 0x4E, 0x50, 0xA8, 0xDD, 0x73, 0x1B, 0x10, 0x7A, 0x99, 0x62, 0x38, 0x1F, + 0xB5, 0xD8, 0x07, 0xBF, 0x26, 0x18, + /* x */ + 0x12, 0x0F, 0xC0, 0x5D, 0x3C, 0x67, 0xA9, 0x9D, 0xE1, 0x61, 0xD2, 0xF4, + 0x09, 0x26, 0x22, 0xFE, 0xCA, 0x70, 0x1B, 0xE4, 0xF5, 0x0F, 0x47, 0x58, + 0x71, 0x4E, 0x8A, 0x87, 0xBB, 0xF2, 0xA6, 0x58, 0xEF, 0x8C, 0x21, 0xE7, + 0xC5, 0xEF, 0xE9, 0x65, 0x36, 0x1F, 0x6C, 0x29, 0x99, 0xC0, 0xC2, 0x47, + 0xB0, 0xDB, 0xD7, 0x0C, 0xE6, 0xB7, + /* y */ + 0x20, 0xD0, 0xAF, 0x89, 0x03, 0xA9, 0x6F, 0x8D, 0x5F, 0xA2, 0xC2, 0x55, + 0x74, 0x5D, 0x3C, 0x45, 0x1B, 0x30, 0x2C, 0x93, 0x46, 0xD9, 0xB7, 0xE4, + 0x85, 0xE7, 0xBC, 0xE4, 0x1F, 0x6B, 0x59, 0x1F, 0x3E, 0x8F, 0x6A, 0xDD, + 0xCB, 0xB0, 0xBC, 0x4C, 0x2F, 0x94, 0x7A, 0x7D, 0xE1, 0xA8, 0x9B, 0x62, + 0x5D, 0x6A, 0x59, 0x8B, 0x37, 0x60, + /* order */ + 0x00, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, + 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, 0x34, 0x03, 0x40, + 0x34, 0x03, 0x40, 0x34, 0x03, 0x23, 0xC3, 0x13, 0xFA, 0xB5, 0x05, 0x89, + 0x70, 0x3B, 0x5E, 0xC6, 0x8D, 0x35, 0x87, 0xFE, 0xC6, 0x0D, 0x16, 0x1C, + 0xC1, 0x49, 0xC1, 0xAD, 0x4A, 0x91 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 15 * 6]; +} _EC_WTLS_1 = { + { + NID_X9_62_characteristic_two_field, 0, 15, 2 + }, + { + /* no seed */ + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x02, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x01, + /* x */ + 0x01, 0x66, 0x79, 0x79, 0xA4, 0x0B, 0xA4, 0x97, 0xE5, 0xD5, 0xC2, 0x70, + 0x78, 0x06, 0x17, + /* y */ + 0x00, 0xF4, 0x4B, 0x4A, 0xF1, 0xEC, 0xC2, 0x63, 0x0E, 0x08, 0x78, 0x5C, + 0xEB, 0xCC, 0x15, + /* order */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFD, 0xBF, 0x91, 0xAF, + 0x6D, 0xEA, 0x73 + } +}; + +/* IPSec curves */ +/* + * NOTE: The of curves over a extension field of non prime degree is not + * recommended (Weil-descent). As the group order is not a prime this curve + * is not suitable for ECDSA. + */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} _EC_IPSEC_155_ID3 = { + { + NID_X9_62_characteristic_two_field, 0, 20, 3 + }, + { + /* no seed */ + /* p */ + 0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x07, 0x33, 0x8f, + /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7b, + /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xc8, + /* order */ + 0x02, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xAA, 0xC7, 0xF3, + 0xC7, 0x88, 0x1B, 0xD0, 0x86, 0x8F, 0xA8, 0x6C + } +}; + +/* + * NOTE: The of curves over a extension field of non prime degree is not + * recommended (Weil-descent). As the group order is not a prime this curve + * is not suitable for ECDSA. + */ +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} _EC_IPSEC_185_ID4 = { + { + NID_X9_62_characteristic_two_field, 0, 24, 2 + }, + { + /* no seed */ + /* p */ + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x20, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + /* a */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + /* b */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x1e, 0xe9, + /* x */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x18, + /* y */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x0d, + /* order */ + 0x00, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xED, 0xF9, 0x7C, 0x44, 0xDB, 0x9F, 0x24, 0x20, 0xBA, 0xFC, 0xA7, 0x5E + } +}; + +#endif + +/* + * These curves were added by Annie Yousar <a.yousar@informatik.hu-berlin.de> + * For the definition of RFC 5639 curves see + * http://www.ietf.org/rfc/rfc5639.txt These curves are generated verifiable + * at random, nevertheless the seed is omitted as parameter because the + * generation mechanism is different from those defined in ANSI X9.62. + */ + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} _EC_brainpoolP160r1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { + /* no seed */ + /* p */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, 0xC7, 0xAD, + 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + /* a */ + 0x34, 0x0E, 0x7B, 0xE2, 0xA2, 0x80, 0xEB, 0x74, 0xE2, 0xBE, 0x61, 0xBA, + 0xDA, 0x74, 0x5D, 0x97, 0xE8, 0xF7, 0xC3, 0x00, + /* b */ + 0x1E, 0x58, 0x9A, 0x85, 0x95, 0x42, 0x34, 0x12, 0x13, 0x4F, 0xAA, 0x2D, + 0xBD, 0xEC, 0x95, 0xC8, 0xD8, 0x67, 0x5E, 0x58, + /* x */ + 0xBE, 0xD5, 0xAF, 0x16, 0xEA, 0x3F, 0x6A, 0x4F, 0x62, 0x93, 0x8C, 0x46, + 0x31, 0xEB, 0x5A, 0xF7, 0xBD, 0xBC, 0xDB, 0xC3, + /* y */ + 0x16, 0x67, 0xCB, 0x47, 0x7A, 0x1A, 0x8E, 0xC3, 0x38, 0xF9, 0x47, 0x41, + 0x66, 0x9C, 0x97, 0x63, 0x16, 0xDA, 0x63, 0x21, + /* order */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, 0x59, 0x91, + 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 20 * 6]; +} _EC_brainpoolP160t1 = { + { + NID_X9_62_prime_field, 0, 20, 1 + }, + { + /* no seed */ + /* p */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, 0xC7, 0xAD, + 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0F, + /* a */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, 0xC7, 0xAD, + 0x95, 0xB3, 0xD8, 0x13, 0x95, 0x15, 0x62, 0x0C, + /* b */ + 0x7A, 0x55, 0x6B, 0x6D, 0xAE, 0x53, 0x5B, 0x7B, 0x51, 0xED, 0x2C, 0x4D, + 0x7D, 0xAA, 0x7A, 0x0B, 0x5C, 0x55, 0xF3, 0x80, + /* x */ + 0xB1, 0x99, 0xB1, 0x3B, 0x9B, 0x34, 0xEF, 0xC1, 0x39, 0x7E, 0x64, 0xBA, + 0xEB, 0x05, 0xAC, 0xC2, 0x65, 0xFF, 0x23, 0x78, + /* y */ + 0xAD, 0xD6, 0x71, 0x8B, 0x7C, 0x7C, 0x19, 0x61, 0xF0, 0x99, 0x1B, 0x84, + 0x24, 0x43, 0x77, 0x21, 0x52, 0xC9, 0xE0, 0xAD, + /* order */ + 0xE9, 0x5E, 0x4A, 0x5F, 0x73, 0x70, 0x59, 0xDC, 0x60, 0xDF, 0x59, 0x91, + 0xD4, 0x50, 0x29, 0x40, 0x9E, 0x60, 0xFC, 0x09 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} _EC_brainpoolP192r1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { + /* no seed */ + /* p */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, 0x46, 0x30, + 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, 0xE1, 0xA8, 0x62, 0x97, + /* a */ + 0x6A, 0x91, 0x17, 0x40, 0x76, 0xB1, 0xE0, 0xE1, 0x9C, 0x39, 0xC0, 0x31, + 0xFE, 0x86, 0x85, 0xC1, 0xCA, 0xE0, 0x40, 0xE5, 0xC6, 0x9A, 0x28, 0xEF, + /* b */ + 0x46, 0x9A, 0x28, 0xEF, 0x7C, 0x28, 0xCC, 0xA3, 0xDC, 0x72, 0x1D, 0x04, + 0x4F, 0x44, 0x96, 0xBC, 0xCA, 0x7E, 0xF4, 0x14, 0x6F, 0xBF, 0x25, 0xC9, + /* x */ + 0xC0, 0xA0, 0x64, 0x7E, 0xAA, 0xB6, 0xA4, 0x87, 0x53, 0xB0, 0x33, 0xC5, + 0x6C, 0xB0, 0xF0, 0x90, 0x0A, 0x2F, 0x5C, 0x48, 0x53, 0x37, 0x5F, 0xD6, + /* y */ + 0x14, 0xB6, 0x90, 0x86, 0x6A, 0xBD, 0x5B, 0xB8, 0x8B, 0x5F, 0x48, 0x28, + 0xC1, 0x49, 0x00, 0x02, 0xE6, 0x77, 0x3F, 0xA2, 0xFA, 0x29, 0x9B, 0x8F, + /* order */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, 0x46, 0x2F, + 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 24 * 6]; +} _EC_brainpoolP192t1 = { + { + NID_X9_62_prime_field, 0, 24, 1 + }, + { + /* no seed */ + /* p */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, 0x46, 0x30, + 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, 0xE1, 0xA8, 0x62, 0x97, + /* a */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, 0x46, 0x30, + 0x93, 0xD1, 0x8D, 0xB7, 0x8F, 0xCE, 0x47, 0x6D, 0xE1, 0xA8, 0x62, 0x94, + /* b */ + 0x13, 0xD5, 0x6F, 0xFA, 0xEC, 0x78, 0x68, 0x1E, 0x68, 0xF9, 0xDE, 0xB4, + 0x3B, 0x35, 0xBE, 0xC2, 0xFB, 0x68, 0x54, 0x2E, 0x27, 0x89, 0x7B, 0x79, + /* x */ + 0x3A, 0xE9, 0xE5, 0x8C, 0x82, 0xF6, 0x3C, 0x30, 0x28, 0x2E, 0x1F, 0xE7, + 0xBB, 0xF4, 0x3F, 0xA7, 0x2C, 0x44, 0x6A, 0xF6, 0xF4, 0x61, 0x81, 0x29, + /* y */ + 0x09, 0x7E, 0x2C, 0x56, 0x67, 0xC2, 0x22, 0x3A, 0x90, 0x2A, 0xB5, 0xCA, + 0x44, 0x9D, 0x00, 0x84, 0xB7, 0xE5, 0xB3, 0xDE, 0x7C, 0xCC, 0x01, 0xC9, + /* order */ + 0xC3, 0x02, 0xF4, 0x1D, 0x93, 0x2A, 0x36, 0xCD, 0xA7, 0xA3, 0x46, 0x2F, + 0x9E, 0x9E, 0x91, 0x6B, 0x5B, 0xE8, 0xF1, 0x02, 0x9A, 0xC4, 0xAC, 0xC1 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} _EC_brainpoolP224r1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { + /* no seed */ + /* p */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, 0x30, 0x25, + 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, 0x97, 0xDA, 0x89, 0xF5, + 0x7E, 0xC8, 0xC0, 0xFF, + /* a */ + 0x68, 0xA5, 0xE6, 0x2C, 0xA9, 0xCE, 0x6C, 0x1C, 0x29, 0x98, 0x03, 0xA6, + 0xC1, 0x53, 0x0B, 0x51, 0x4E, 0x18, 0x2A, 0xD8, 0xB0, 0x04, 0x2A, 0x59, + 0xCA, 0xD2, 0x9F, 0x43, + /* b */ + 0x25, 0x80, 0xF6, 0x3C, 0xCF, 0xE4, 0x41, 0x38, 0x87, 0x07, 0x13, 0xB1, + 0xA9, 0x23, 0x69, 0xE3, 0x3E, 0x21, 0x35, 0xD2, 0x66, 0xDB, 0xB3, 0x72, + 0x38, 0x6C, 0x40, 0x0B, + /* x */ + 0x0D, 0x90, 0x29, 0xAD, 0x2C, 0x7E, 0x5C, 0xF4, 0x34, 0x08, 0x23, 0xB2, + 0xA8, 0x7D, 0xC6, 0x8C, 0x9E, 0x4C, 0xE3, 0x17, 0x4C, 0x1E, 0x6E, 0xFD, + 0xEE, 0x12, 0xC0, 0x7D, + /* y */ + 0x58, 0xAA, 0x56, 0xF7, 0x72, 0xC0, 0x72, 0x6F, 0x24, 0xC6, 0xB8, 0x9E, + 0x4E, 0xCD, 0xAC, 0x24, 0x35, 0x4B, 0x9E, 0x99, 0xCA, 0xA3, 0xF6, 0xD3, + 0x76, 0x14, 0x02, 0xCD, + /* order */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, 0x30, 0x25, + 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, 0x6D, 0xDE, 0xBC, 0xA3, + 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 28 * 6]; +} _EC_brainpoolP224t1 = { + { + NID_X9_62_prime_field, 0, 28, 1 + }, + { + /* no seed */ + /* p */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, 0x30, 0x25, + 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, 0x97, 0xDA, 0x89, 0xF5, + 0x7E, 0xC8, 0xC0, 0xFF, + /* a */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, 0x30, 0x25, + 0x75, 0xD1, 0xD7, 0x87, 0xB0, 0x9F, 0x07, 0x57, 0x97, 0xDA, 0x89, 0xF5, + 0x7E, 0xC8, 0xC0, 0xFC, + /* b */ + 0x4B, 0x33, 0x7D, 0x93, 0x41, 0x04, 0xCD, 0x7B, 0xEF, 0x27, 0x1B, 0xF6, + 0x0C, 0xED, 0x1E, 0xD2, 0x0D, 0xA1, 0x4C, 0x08, 0xB3, 0xBB, 0x64, 0xF1, + 0x8A, 0x60, 0x88, 0x8D, + /* x */ + 0x6A, 0xB1, 0xE3, 0x44, 0xCE, 0x25, 0xFF, 0x38, 0x96, 0x42, 0x4E, 0x7F, + 0xFE, 0x14, 0x76, 0x2E, 0xCB, 0x49, 0xF8, 0x92, 0x8A, 0xC0, 0xC7, 0x60, + 0x29, 0xB4, 0xD5, 0x80, + /* y */ + 0x03, 0x74, 0xE9, 0xF5, 0x14, 0x3E, 0x56, 0x8C, 0xD2, 0x3F, 0x3F, 0x4D, + 0x7C, 0x0D, 0x4B, 0x1E, 0x41, 0xC8, 0xCC, 0x0D, 0x1C, 0x6A, 0xBD, 0x5F, + 0x1A, 0x46, 0xDB, 0x4C, + /* order */ + 0xD7, 0xC1, 0x34, 0xAA, 0x26, 0x43, 0x66, 0x86, 0x2A, 0x18, 0x30, 0x25, + 0x75, 0xD0, 0xFB, 0x98, 0xD1, 0x16, 0xBC, 0x4B, 0x6D, 0xDE, 0xBC, 0xA3, + 0xA5, 0xA7, 0x93, 0x9F + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} _EC_brainpoolP256r1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { + /* no seed */ + /* p */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, + 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, 0xD5, 0x26, 0x20, 0x28, + 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, 0x53, 0x77, + /* a */ + 0x7D, 0x5A, 0x09, 0x75, 0xFC, 0x2C, 0x30, 0x57, 0xEE, 0xF6, 0x75, 0x30, + 0x41, 0x7A, 0xFF, 0xE7, 0xFB, 0x80, 0x55, 0xC1, 0x26, 0xDC, 0x5C, 0x6C, + 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9, + /* b */ + 0x26, 0xDC, 0x5C, 0x6C, 0xE9, 0x4A, 0x4B, 0x44, 0xF3, 0x30, 0xB5, 0xD9, + 0xBB, 0xD7, 0x7C, 0xBF, 0x95, 0x84, 0x16, 0x29, 0x5C, 0xF7, 0xE1, 0xCE, + 0x6B, 0xCC, 0xDC, 0x18, 0xFF, 0x8C, 0x07, 0xB6, + /* x */ + 0x8B, 0xD2, 0xAE, 0xB9, 0xCB, 0x7E, 0x57, 0xCB, 0x2C, 0x4B, 0x48, 0x2F, + 0xFC, 0x81, 0xB7, 0xAF, 0xB9, 0xDE, 0x27, 0xE1, 0xE3, 0xBD, 0x23, 0xC2, + 0x3A, 0x44, 0x53, 0xBD, 0x9A, 0xCE, 0x32, 0x62, + /* y */ + 0x54, 0x7E, 0xF8, 0x35, 0xC3, 0xDA, 0xC4, 0xFD, 0x97, 0xF8, 0x46, 0x1A, + 0x14, 0x61, 0x1D, 0xC9, 0xC2, 0x77, 0x45, 0x13, 0x2D, 0xED, 0x8E, 0x54, + 0x5C, 0x1D, 0x54, 0xC7, 0x2F, 0x04, 0x69, 0x97, + /* order */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, + 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, 0xB5, 0x61, 0xA6, 0xF7, + 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 32 * 6]; +} _EC_brainpoolP256t1 = { + { + NID_X9_62_prime_field, 0, 32, 1 + }, + { + /* no seed */ + /* p */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, + 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, 0xD5, 0x26, 0x20, 0x28, + 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, 0x53, 0x77, + /* a */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, + 0x9D, 0x83, 0x8D, 0x72, 0x6E, 0x3B, 0xF6, 0x23, 0xD5, 0x26, 0x20, 0x28, + 0x20, 0x13, 0x48, 0x1D, 0x1F, 0x6E, 0x53, 0x74, + /* b */ + 0x66, 0x2C, 0x61, 0xC4, 0x30, 0xD8, 0x4E, 0xA4, 0xFE, 0x66, 0xA7, 0x73, + 0x3D, 0x0B, 0x76, 0xB7, 0xBF, 0x93, 0xEB, 0xC4, 0xAF, 0x2F, 0x49, 0x25, + 0x6A, 0xE5, 0x81, 0x01, 0xFE, 0xE9, 0x2B, 0x04, + /* x */ + 0xA3, 0xE8, 0xEB, 0x3C, 0xC1, 0xCF, 0xE7, 0xB7, 0x73, 0x22, 0x13, 0xB2, + 0x3A, 0x65, 0x61, 0x49, 0xAF, 0xA1, 0x42, 0xC4, 0x7A, 0xAF, 0xBC, 0x2B, + 0x79, 0xA1, 0x91, 0x56, 0x2E, 0x13, 0x05, 0xF4, + /* y */ + 0x2D, 0x99, 0x6C, 0x82, 0x34, 0x39, 0xC5, 0x6D, 0x7F, 0x7B, 0x22, 0xE1, + 0x46, 0x44, 0x41, 0x7E, 0x69, 0xBC, 0xB6, 0xDE, 0x39, 0xD0, 0x27, 0x00, + 0x1D, 0xAB, 0xE8, 0xF3, 0x5B, 0x25, 0xC9, 0xBE, + /* order */ + 0xA9, 0xFB, 0x57, 0xDB, 0xA1, 0xEE, 0xA9, 0xBC, 0x3E, 0x66, 0x0A, 0x90, + 0x9D, 0x83, 0x8D, 0x71, 0x8C, 0x39, 0x7A, 0xA3, 0xB5, 0x61, 0xA6, 0xF7, + 0x90, 0x1E, 0x0E, 0x82, 0x97, 0x48, 0x56, 0xA7 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} _EC_brainpoolP320r1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { + /* no seed */ + /* p */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, 0x78, 0x5E, + 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, 0xF6, 0xF4, 0x0D, 0xEF, + 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, + 0xF1, 0xB3, 0x2E, 0x27, + /* a */ + 0x3E, 0xE3, 0x0B, 0x56, 0x8F, 0xBA, 0xB0, 0xF8, 0x83, 0xCC, 0xEB, 0xD4, + 0x6D, 0x3F, 0x3B, 0xB8, 0xA2, 0xA7, 0x35, 0x13, 0xF5, 0xEB, 0x79, 0xDA, + 0x66, 0x19, 0x0E, 0xB0, 0x85, 0xFF, 0xA9, 0xF4, 0x92, 0xF3, 0x75, 0xA9, + 0x7D, 0x86, 0x0E, 0xB4, + /* b */ + 0x52, 0x08, 0x83, 0x94, 0x9D, 0xFD, 0xBC, 0x42, 0xD3, 0xAD, 0x19, 0x86, + 0x40, 0x68, 0x8A, 0x6F, 0xE1, 0x3F, 0x41, 0x34, 0x95, 0x54, 0xB4, 0x9A, + 0xCC, 0x31, 0xDC, 0xCD, 0x88, 0x45, 0x39, 0x81, 0x6F, 0x5E, 0xB4, 0xAC, + 0x8F, 0xB1, 0xF1, 0xA6, + /* x */ + 0x43, 0xBD, 0x7E, 0x9A, 0xFB, 0x53, 0xD8, 0xB8, 0x52, 0x89, 0xBC, 0xC4, + 0x8E, 0xE5, 0xBF, 0xE6, 0xF2, 0x01, 0x37, 0xD1, 0x0A, 0x08, 0x7E, 0xB6, + 0xE7, 0x87, 0x1E, 0x2A, 0x10, 0xA5, 0x99, 0xC7, 0x10, 0xAF, 0x8D, 0x0D, + 0x39, 0xE2, 0x06, 0x11, + /* y */ + 0x14, 0xFD, 0xD0, 0x55, 0x45, 0xEC, 0x1C, 0xC8, 0xAB, 0x40, 0x93, 0x24, + 0x7F, 0x77, 0x27, 0x5E, 0x07, 0x43, 0xFF, 0xED, 0x11, 0x71, 0x82, 0xEA, + 0xA9, 0xC7, 0x78, 0x77, 0xAA, 0xAC, 0x6A, 0xC7, 0xD3, 0x52, 0x45, 0xD1, + 0x69, 0x2E, 0x8E, 0xE1, + /* order */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, 0x78, 0x5E, + 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, 0xB6, 0x8F, 0x12, 0xA3, + 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, + 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 40 * 6]; +} _EC_brainpoolP320t1 = { + { + NID_X9_62_prime_field, 0, 40, 1 + }, + { + /* no seed */ + /* p */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, 0x78, 0x5E, + 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, 0xF6, 0xF4, 0x0D, 0xEF, + 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, + 0xF1, 0xB3, 0x2E, 0x27, + /* a */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, 0x78, 0x5E, + 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA6, 0xF6, 0xF4, 0x0D, 0xEF, + 0x4F, 0x92, 0xB9, 0xEC, 0x78, 0x93, 0xEC, 0x28, 0xFC, 0xD4, 0x12, 0xB1, + 0xF1, 0xB3, 0x2E, 0x24, + /* b */ + 0xA7, 0xF5, 0x61, 0xE0, 0x38, 0xEB, 0x1E, 0xD5, 0x60, 0xB3, 0xD1, 0x47, + 0xDB, 0x78, 0x20, 0x13, 0x06, 0x4C, 0x19, 0xF2, 0x7E, 0xD2, 0x7C, 0x67, + 0x80, 0xAA, 0xF7, 0x7F, 0xB8, 0xA5, 0x47, 0xCE, 0xB5, 0xB4, 0xFE, 0xF4, + 0x22, 0x34, 0x03, 0x53, + /* x */ + 0x92, 0x5B, 0xE9, 0xFB, 0x01, 0xAF, 0xC6, 0xFB, 0x4D, 0x3E, 0x7D, 0x49, + 0x90, 0x01, 0x0F, 0x81, 0x34, 0x08, 0xAB, 0x10, 0x6C, 0x4F, 0x09, 0xCB, + 0x7E, 0xE0, 0x78, 0x68, 0xCC, 0x13, 0x6F, 0xFF, 0x33, 0x57, 0xF6, 0x24, + 0xA2, 0x1B, 0xED, 0x52, + /* y */ + 0x63, 0xBA, 0x3A, 0x7A, 0x27, 0x48, 0x3E, 0xBF, 0x66, 0x71, 0xDB, 0xEF, + 0x7A, 0xBB, 0x30, 0xEB, 0xEE, 0x08, 0x4E, 0x58, 0xA0, 0xB0, 0x77, 0xAD, + 0x42, 0xA5, 0xA0, 0x98, 0x9D, 0x1E, 0xE7, 0x1B, 0x1B, 0x9B, 0xC0, 0x45, + 0x5F, 0xB0, 0xD2, 0xC3, + /* order */ + 0xD3, 0x5E, 0x47, 0x20, 0x36, 0xBC, 0x4F, 0xB7, 0xE1, 0x3C, 0x78, 0x5E, + 0xD2, 0x01, 0xE0, 0x65, 0xF9, 0x8F, 0xCF, 0xA5, 0xB6, 0x8F, 0x12, 0xA3, + 0x2D, 0x48, 0x2E, 0xC7, 0xEE, 0x86, 0x58, 0xE9, 0x86, 0x91, 0x55, 0x5B, + 0x44, 0xC5, 0x93, 0x11 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} _EC_brainpoolP384r1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { + /* no seed */ + /* p */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, + 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB4, + 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, + 0x90, 0x1D, 0x1A, 0x71, 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + /* a */ + 0x7B, 0xC3, 0x82, 0xC6, 0x3D, 0x8C, 0x15, 0x0C, 0x3C, 0x72, 0x08, 0x0A, + 0xCE, 0x05, 0xAF, 0xA0, 0xC2, 0xBE, 0xA2, 0x8E, 0x4F, 0xB2, 0x27, 0x87, + 0x13, 0x91, 0x65, 0xEF, 0xBA, 0x91, 0xF9, 0x0F, 0x8A, 0xA5, 0x81, 0x4A, + 0x50, 0x3A, 0xD4, 0xEB, 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, + /* b */ + 0x04, 0xA8, 0xC7, 0xDD, 0x22, 0xCE, 0x28, 0x26, 0x8B, 0x39, 0xB5, 0x54, + 0x16, 0xF0, 0x44, 0x7C, 0x2F, 0xB7, 0x7D, 0xE1, 0x07, 0xDC, 0xD2, 0xA6, + 0x2E, 0x88, 0x0E, 0xA5, 0x3E, 0xEB, 0x62, 0xD5, 0x7C, 0xB4, 0x39, 0x02, + 0x95, 0xDB, 0xC9, 0x94, 0x3A, 0xB7, 0x86, 0x96, 0xFA, 0x50, 0x4C, 0x11, + /* x */ + 0x1D, 0x1C, 0x64, 0xF0, 0x68, 0xCF, 0x45, 0xFF, 0xA2, 0xA6, 0x3A, 0x81, + 0xB7, 0xC1, 0x3F, 0x6B, 0x88, 0x47, 0xA3, 0xE7, 0x7E, 0xF1, 0x4F, 0xE3, + 0xDB, 0x7F, 0xCA, 0xFE, 0x0C, 0xBD, 0x10, 0xE8, 0xE8, 0x26, 0xE0, 0x34, + 0x36, 0xD6, 0x46, 0xAA, 0xEF, 0x87, 0xB2, 0xE2, 0x47, 0xD4, 0xAF, 0x1E, + /* y */ + 0x8A, 0xBE, 0x1D, 0x75, 0x20, 0xF9, 0xC2, 0xA4, 0x5C, 0xB1, 0xEB, 0x8E, + 0x95, 0xCF, 0xD5, 0x52, 0x62, 0xB7, 0x0B, 0x29, 0xFE, 0xEC, 0x58, 0x64, + 0xE1, 0x9C, 0x05, 0x4F, 0xF9, 0x91, 0x29, 0x28, 0x0E, 0x46, 0x46, 0x21, + 0x77, 0x91, 0x81, 0x11, 0x42, 0x82, 0x03, 0x41, 0x26, 0x3C, 0x53, 0x15, + /* order */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, + 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB3, + 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, + 0x6B, 0x7F, 0xC3, 0x10, 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 48 * 6]; +} _EC_brainpoolP384t1 = { + { + NID_X9_62_prime_field, 0, 48, 1 + }, + { + /* no seed */ + /* p */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, + 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB4, + 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, + 0x90, 0x1D, 0x1A, 0x71, 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x53, + /* a */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, + 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB4, + 0x12, 0xB1, 0xDA, 0x19, 0x7F, 0xB7, 0x11, 0x23, 0xAC, 0xD3, 0xA7, 0x29, + 0x90, 0x1D, 0x1A, 0x71, 0x87, 0x47, 0x00, 0x13, 0x31, 0x07, 0xEC, 0x50, + /* b */ + 0x7F, 0x51, 0x9E, 0xAD, 0xA7, 0xBD, 0xA8, 0x1B, 0xD8, 0x26, 0xDB, 0xA6, + 0x47, 0x91, 0x0F, 0x8C, 0x4B, 0x93, 0x46, 0xED, 0x8C, 0xCD, 0xC6, 0x4E, + 0x4B, 0x1A, 0xBD, 0x11, 0x75, 0x6D, 0xCE, 0x1D, 0x20, 0x74, 0xAA, 0x26, + 0x3B, 0x88, 0x80, 0x5C, 0xED, 0x70, 0x35, 0x5A, 0x33, 0xB4, 0x71, 0xEE, + /* x */ + 0x18, 0xDE, 0x98, 0xB0, 0x2D, 0xB9, 0xA3, 0x06, 0xF2, 0xAF, 0xCD, 0x72, + 0x35, 0xF7, 0x2A, 0x81, 0x9B, 0x80, 0xAB, 0x12, 0xEB, 0xD6, 0x53, 0x17, + 0x24, 0x76, 0xFE, 0xCD, 0x46, 0x2A, 0xAB, 0xFF, 0xC4, 0xFF, 0x19, 0x1B, + 0x94, 0x6A, 0x5F, 0x54, 0xD8, 0xD0, 0xAA, 0x2F, 0x41, 0x88, 0x08, 0xCC, + /* y */ + 0x25, 0xAB, 0x05, 0x69, 0x62, 0xD3, 0x06, 0x51, 0xA1, 0x14, 0xAF, 0xD2, + 0x75, 0x5A, 0xD3, 0x36, 0x74, 0x7F, 0x93, 0x47, 0x5B, 0x7A, 0x1F, 0xCA, + 0x3B, 0x88, 0xF2, 0xB6, 0xA2, 0x08, 0xCC, 0xFE, 0x46, 0x94, 0x08, 0x58, + 0x4D, 0xC2, 0xB2, 0x91, 0x26, 0x75, 0xBF, 0x5B, 0x9E, 0x58, 0x29, 0x28, + /* order */ + 0x8C, 0xB9, 0x1E, 0x82, 0xA3, 0x38, 0x6D, 0x28, 0x0F, 0x5D, 0x6F, 0x7E, + 0x50, 0xE6, 0x41, 0xDF, 0x15, 0x2F, 0x71, 0x09, 0xED, 0x54, 0x56, 0xB3, + 0x1F, 0x16, 0x6E, 0x6C, 0xAC, 0x04, 0x25, 0xA7, 0xCF, 0x3A, 0xB6, 0xAF, + 0x6B, 0x7F, 0xC3, 0x10, 0x3B, 0x88, 0x32, 0x02, 0xE9, 0x04, 0x65, 0x65 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} _EC_brainpoolP512r1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { + /* no seed */ + /* p */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, + 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, + 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, + 0x9B, 0xC6, 0x68, 0x42, 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, + 0x28, 0x81, 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + /* a */ + 0x78, 0x30, 0xA3, 0x31, 0x8B, 0x60, 0x3B, 0x89, 0xE2, 0x32, 0x71, 0x45, + 0xAC, 0x23, 0x4C, 0xC5, 0x94, 0xCB, 0xDD, 0x8D, 0x3D, 0xF9, 0x16, 0x10, + 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, 0x63, 0xBC, 0x2D, 0xED, 0x5D, 0x5A, + 0xA8, 0x25, 0x3A, 0xA1, 0x0A, 0x2E, 0xF1, 0xC9, 0x8B, 0x9A, 0xC8, 0xB5, + 0x7F, 0x11, 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, 0xE7, 0xC1, 0xAC, 0x4D, + 0x77, 0xFC, 0x94, 0xCA, + /* b */ + 0x3D, 0xF9, 0x16, 0x10, 0xA8, 0x34, 0x41, 0xCA, 0xEA, 0x98, 0x63, 0xBC, + 0x2D, 0xED, 0x5D, 0x5A, 0xA8, 0x25, 0x3A, 0xA1, 0x0A, 0x2E, 0xF1, 0xC9, + 0x8B, 0x9A, 0xC8, 0xB5, 0x7F, 0x11, 0x17, 0xA7, 0x2B, 0xF2, 0xC7, 0xB9, + 0xE7, 0xC1, 0xAC, 0x4D, 0x77, 0xFC, 0x94, 0xCA, 0xDC, 0x08, 0x3E, 0x67, + 0x98, 0x40, 0x50, 0xB7, 0x5E, 0xBA, 0xE5, 0xDD, 0x28, 0x09, 0xBD, 0x63, + 0x80, 0x16, 0xF7, 0x23, + /* x */ + 0x81, 0xAE, 0xE4, 0xBD, 0xD8, 0x2E, 0xD9, 0x64, 0x5A, 0x21, 0x32, 0x2E, + 0x9C, 0x4C, 0x6A, 0x93, 0x85, 0xED, 0x9F, 0x70, 0xB5, 0xD9, 0x16, 0xC1, + 0xB4, 0x3B, 0x62, 0xEE, 0xF4, 0xD0, 0x09, 0x8E, 0xFF, 0x3B, 0x1F, 0x78, + 0xE2, 0xD0, 0xD4, 0x8D, 0x50, 0xD1, 0x68, 0x7B, 0x93, 0xB9, 0x7D, 0x5F, + 0x7C, 0x6D, 0x50, 0x47, 0x40, 0x6A, 0x5E, 0x68, 0x8B, 0x35, 0x22, 0x09, + 0xBC, 0xB9, 0xF8, 0x22, + /* y */ + 0x7D, 0xDE, 0x38, 0x5D, 0x56, 0x63, 0x32, 0xEC, 0xC0, 0xEA, 0xBF, 0xA9, + 0xCF, 0x78, 0x22, 0xFD, 0xF2, 0x09, 0xF7, 0x00, 0x24, 0xA5, 0x7B, 0x1A, + 0xA0, 0x00, 0xC5, 0x5B, 0x88, 0x1F, 0x81, 0x11, 0xB2, 0xDC, 0xDE, 0x49, + 0x4A, 0x5F, 0x48, 0x5E, 0x5B, 0xCA, 0x4B, 0xD8, 0x8A, 0x27, 0x63, 0xAE, + 0xD1, 0xCA, 0x2B, 0x2F, 0xA8, 0xF0, 0x54, 0x06, 0x78, 0xCD, 0x1E, 0x0F, + 0x3A, 0xD8, 0x08, 0x92, + /* order */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, + 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, + 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, + 0x4C, 0xA9, 0x26, 0x19, 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, + 0x1D, 0xB1, 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +static const struct { + EC_CURVE_DATA h; + unsigned char data[0 + 64 * 6]; +} _EC_brainpoolP512t1 = { + { + NID_X9_62_prime_field, 0, 64, 1 + }, + { + /* no seed */ + /* p */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, + 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, + 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, + 0x9B, 0xC6, 0x68, 0x42, 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, + 0x28, 0x81, 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF3, + /* a */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, + 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, + 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x71, 0x7D, 0x4D, 0x9B, 0x00, + 0x9B, 0xC6, 0x68, 0x42, 0xAE, 0xCD, 0xA1, 0x2A, 0xE6, 0xA3, 0x80, 0xE6, + 0x28, 0x81, 0xFF, 0x2F, 0x2D, 0x82, 0xC6, 0x85, 0x28, 0xAA, 0x60, 0x56, + 0x58, 0x3A, 0x48, 0xF0, + /* b */ + 0x7C, 0xBB, 0xBC, 0xF9, 0x44, 0x1C, 0xFA, 0xB7, 0x6E, 0x18, 0x90, 0xE4, + 0x68, 0x84, 0xEA, 0xE3, 0x21, 0xF7, 0x0C, 0x0B, 0xCB, 0x49, 0x81, 0x52, + 0x78, 0x97, 0x50, 0x4B, 0xEC, 0x3E, 0x36, 0xA6, 0x2B, 0xCD, 0xFA, 0x23, + 0x04, 0x97, 0x65, 0x40, 0xF6, 0x45, 0x00, 0x85, 0xF2, 0xDA, 0xE1, 0x45, + 0xC2, 0x25, 0x53, 0xB4, 0x65, 0x76, 0x36, 0x89, 0x18, 0x0E, 0xA2, 0x57, + 0x18, 0x67, 0x42, 0x3E, + /* x */ + 0x64, 0x0E, 0xCE, 0x5C, 0x12, 0x78, 0x87, 0x17, 0xB9, 0xC1, 0xBA, 0x06, + 0xCB, 0xC2, 0xA6, 0xFE, 0xBA, 0x85, 0x84, 0x24, 0x58, 0xC5, 0x6D, 0xDE, + 0x9D, 0xB1, 0x75, 0x8D, 0x39, 0xC0, 0x31, 0x3D, 0x82, 0xBA, 0x51, 0x73, + 0x5C, 0xDB, 0x3E, 0xA4, 0x99, 0xAA, 0x77, 0xA7, 0xD6, 0x94, 0x3A, 0x64, + 0xF7, 0xA3, 0xF2, 0x5F, 0xE2, 0x6F, 0x06, 0xB5, 0x1B, 0xAA, 0x26, 0x96, + 0xFA, 0x90, 0x35, 0xDA, + /* y */ + 0x5B, 0x53, 0x4B, 0xD5, 0x95, 0xF5, 0xAF, 0x0F, 0xA2, 0xC8, 0x92, 0x37, + 0x6C, 0x84, 0xAC, 0xE1, 0xBB, 0x4E, 0x30, 0x19, 0xB7, 0x16, 0x34, 0xC0, + 0x11, 0x31, 0x15, 0x9C, 0xAE, 0x03, 0xCE, 0xE9, 0xD9, 0x93, 0x21, 0x84, + 0xBE, 0xEF, 0x21, 0x6B, 0xD7, 0x1D, 0xF2, 0xDA, 0xDF, 0x86, 0xA6, 0x27, + 0x30, 0x6E, 0xCF, 0xF9, 0x6D, 0xBB, 0x8B, 0xAC, 0xE1, 0x98, 0xB6, 0x1E, + 0x00, 0xF8, 0xB3, 0x32, + /* order */ + 0xAA, 0xDD, 0x9D, 0xB8, 0xDB, 0xE9, 0xC4, 0x8B, 0x3F, 0xD4, 0xE6, 0xAE, + 0x33, 0xC9, 0xFC, 0x07, 0xCB, 0x30, 0x8D, 0xB3, 0xB3, 0xC9, 0xD2, 0x0E, + 0xD6, 0x63, 0x9C, 0xCA, 0x70, 0x33, 0x08, 0x70, 0x55, 0x3E, 0x5C, 0x41, + 0x4C, 0xA9, 0x26, 0x19, 0x41, 0x86, 0x61, 0x19, 0x7F, 0xAC, 0x10, 0x47, + 0x1D, 0xB1, 0xD3, 0x81, 0x08, 0x5D, 0xDA, 0xDD, 0xB5, 0x87, 0x96, 0x82, + 0x9C, 0xA9, 0x00, 0x69 + } +}; + +typedef struct _ec_list_element_st { + int nid; + const EC_CURVE_DATA *data; + const EC_METHOD *(*meth) (void); + const char *comment; +} ec_list_element; + +static const ec_list_element curve_list[] = { + /* prime field curves */ + /* secg curves */ + {NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, + "SECG/WTLS curve over a 112 bit prime field"}, + {NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, + "SECG curve over a 112 bit prime field"}, + {NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, + "SECG curve over a 128 bit prime field"}, + {NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, + "SECG curve over a 128 bit prime field"}, + {NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, + "SECG curve over a 160 bit prime field"}, + {NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, + "SECG curve over a 160 bit prime field"}, + {NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, + "SECG/WTLS curve over a 160 bit prime field"}, + /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ + {NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, + "SECG curve over a 192 bit prime field"}, + {NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, + "SECG curve over a 224 bit prime field"}, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + {NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, + "NIST/SECG curve over a 224 bit prime field"}, +#else + {NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, + "NIST/SECG curve over a 224 bit prime field"}, +#endif + {NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, + "SECG curve over a 256 bit prime field"}, + /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ + {NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, + "NIST/SECG curve over a 384 bit prime field"}, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + {NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, + "NIST/SECG curve over a 521 bit prime field"}, +#else + {NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, + "NIST/SECG curve over a 521 bit prime field"}, +#endif + /* X9.62 curves */ + {NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, + "NIST/X9.62/SECG curve over a 192 bit prime field"}, + {NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, + "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, + "X9.62 curve over a 192 bit prime field"}, + {NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, + "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, + "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, + "X9.62 curve over a 239 bit prime field"}, + {NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, +#if defined(ECP_NISTZ256_ASM) + EC_GFp_nistz256_method, +#elif !defined(OPENSSL_NO_EC_NISTP_64_GCC_128) + EC_GFp_nistp256_method, +#else + 0, +#endif + "X9.62/SECG curve over a 256 bit prime field"}, +#ifndef OPENSSL_NO_EC2M + /* characteristic two field curves */ + /* NIST/SECG curves */ + {NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, + "SECG curve over a 113 bit binary field"}, + {NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, + "SECG curve over a 113 bit binary field"}, + {NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, + "SECG/WTLS curve over a 131 bit binary field"}, + {NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, + "SECG curve over a 131 bit binary field"}, + {NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, + "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, + "SECG curve over a 163 bit binary field"}, + {NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, + "NIST/SECG curve over a 163 bit binary field"}, + {NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, + "SECG curve over a 193 bit binary field"}, + {NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, + "SECG curve over a 193 bit binary field"}, + {NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, + "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, + "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, + "SECG curve over a 239 bit binary field"}, + {NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, + "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, + "NIST/SECG curve over a 283 bit binary field"}, + {NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, + "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, + "NIST/SECG curve over a 409 bit binary field"}, + {NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, + "NIST/SECG curve over a 571 bit binary field"}, + {NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, + "NIST/SECG curve over a 571 bit binary field"}, + /* X9.62 curves */ + {NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, + "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, + "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, + "X9.62 curve over a 163 bit binary field"}, + {NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, + "X9.62 curve over a 176 bit binary field"}, + {NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, + "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, + "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, + "X9.62 curve over a 191 bit binary field"}, + {NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, + "X9.62 curve over a 208 bit binary field"}, + {NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, + "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, + "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, + "X9.62 curve over a 239 bit binary field"}, + {NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, + "X9.62 curve over a 272 bit binary field"}, + {NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, + "X9.62 curve over a 304 bit binary field"}, + {NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, + "X9.62 curve over a 359 bit binary field"}, + {NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, + "X9.62 curve over a 368 bit binary field"}, + {NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, + "X9.62 curve over a 431 bit binary field"}, + /* + * the WAP/WTLS curves [unlike SECG, spec has its own OIDs for curves + * from X9.62] + */ + {NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, + "WTLS curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, + "NIST/SECG/WTLS curve over a 163 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, + "SECG curve over a 113 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, + "X9.62 curve over a 163 bit binary field"}, +#endif + {NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, + "SECG/WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, + "SECG/WTLS curve over a 160 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, + "WTLS curve over a 112 bit prime field"}, + {NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, + "WTLS curve over a 160 bit prime field"}, +#ifndef OPENSSL_NO_EC2M + {NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, + "NIST/SECG/WTLS curve over a 233 bit binary field"}, + {NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, + "NIST/SECG/WTLS curve over a 233 bit binary field"}, +#endif + {NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, + "WTLS curve over a 224 bit prime field"}, +#ifndef OPENSSL_NO_EC2M + /* IPSec curves */ + {NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, + "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, + {NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, + "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, +#endif + /* brainpool curves */ + {NID_brainpoolP160r1, &_EC_brainpoolP160r1.h, 0, + "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP160t1, &_EC_brainpoolP160t1.h, 0, + "RFC 5639 curve over a 160 bit prime field"}, + {NID_brainpoolP192r1, &_EC_brainpoolP192r1.h, 0, + "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP192t1, &_EC_brainpoolP192t1.h, 0, + "RFC 5639 curve over a 192 bit prime field"}, + {NID_brainpoolP224r1, &_EC_brainpoolP224r1.h, 0, + "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP224t1, &_EC_brainpoolP224t1.h, 0, + "RFC 5639 curve over a 224 bit prime field"}, + {NID_brainpoolP256r1, &_EC_brainpoolP256r1.h, 0, + "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP256t1, &_EC_brainpoolP256t1.h, 0, + "RFC 5639 curve over a 256 bit prime field"}, + {NID_brainpoolP320r1, &_EC_brainpoolP320r1.h, 0, + "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP320t1, &_EC_brainpoolP320t1.h, 0, + "RFC 5639 curve over a 320 bit prime field"}, + {NID_brainpoolP384r1, &_EC_brainpoolP384r1.h, 0, + "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP384t1, &_EC_brainpoolP384t1.h, 0, + "RFC 5639 curve over a 384 bit prime field"}, + {NID_brainpoolP512r1, &_EC_brainpoolP512r1.h, 0, + "RFC 5639 curve over a 512 bit prime field"}, + {NID_brainpoolP512t1, &_EC_brainpoolP512t1.h, 0, + "RFC 5639 curve over a 512 bit prime field"}, +}; + +#define curve_list_length OSSL_NELEM(curve_list) + +static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) +{ + EC_GROUP *group = NULL; + EC_POINT *P = NULL; + BN_CTX *ctx = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *x = NULL, *y = NULL, *order = + NULL; + int ok = 0; + int seed_len, param_len; + const EC_METHOD *meth; + const EC_CURVE_DATA *data; + const unsigned char *params; + + /* If no curve data curve method must handle everything */ + if (curve.data == NULL) + return EC_GROUP_new(curve.meth != NULL ? curve.meth() : NULL); + + if ((ctx = BN_CTX_new()) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE); + goto err; + } + + data = curve.data; + seed_len = data->seed_len; + param_len = data->param_len; + params = (const unsigned char *)(data + 1); /* skip header */ + params += seed_len; /* skip seed */ + + if ((p = BN_bin2bn(params + 0 * param_len, param_len, NULL)) == NULL + || (a = BN_bin2bn(params + 1 * param_len, param_len, NULL)) == NULL + || (b = BN_bin2bn(params + 2 * param_len, param_len, NULL)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); + goto err; + } + + if (curve.meth != 0) { + meth = curve.meth(); + if (((group = EC_GROUP_new(meth)) == NULL) || + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } else if (data->field_type == NID_X9_62_prime_field) { + if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } +#ifndef OPENSSL_NO_EC2M + else { /* field_type == + * NID_X9_62_characteristic_two_field */ + + if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } +#endif + + if ((P = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + + if ((x = BN_bin2bn(params + 3 * param_len, param_len, NULL)) == NULL + || (y = BN_bin2bn(params + 4 * param_len, param_len, NULL)) == NULL) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + if ((order = BN_bin2bn(params + 5 * param_len, param_len, NULL)) == NULL + || !BN_set_word(x, (BN_ULONG)data->cofactor)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); + goto err; + } + if (!EC_GROUP_set_generator(group, P, order, x)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + if (seed_len) { + if (!EC_GROUP_set_seed(group, params - seed_len, seed_len)) { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } + ok = 1; + err: + if (!ok) { + EC_GROUP_free(group); + group = NULL; + } + EC_POINT_free(P); + BN_CTX_free(ctx); + BN_free(p); + BN_free(a); + BN_free(b); + BN_free(order); + BN_free(x); + BN_free(y); + return group; +} + +EC_GROUP *EC_GROUP_new_by_curve_name(int nid) +{ + size_t i; + EC_GROUP *ret = NULL; + + if (nid <= 0) + return NULL; + + for (i = 0; i < curve_list_length; i++) + if (curve_list[i].nid == nid) { + ret = ec_group_new_from_data(curve_list[i]); + break; + } + + if (ret == NULL) { + ECerr(EC_F_EC_GROUP_NEW_BY_CURVE_NAME, EC_R_UNKNOWN_GROUP); + return NULL; + } + + EC_GROUP_set_curve_name(ret, nid); + + return ret; +} + +size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems) +{ + size_t i, min; + + if (r == NULL || nitems == 0) + return curve_list_length; + + min = nitems < curve_list_length ? nitems : curve_list_length; + + for (i = 0; i < min; i++) { + r[i].nid = curve_list[i].nid; + r[i].comment = curve_list[i].comment; + } + + return curve_list_length; +} + +/* Functions to translate between common NIST curve names and NIDs */ + +typedef struct { + const char *name; /* NIST Name of curve */ + int nid; /* Curve NID */ +} EC_NIST_NAME; + +static EC_NIST_NAME nist_curves[] = { + {"B-163", NID_sect163r2}, + {"B-233", NID_sect233r1}, + {"B-283", NID_sect283r1}, + {"B-409", NID_sect409r1}, + {"B-571", NID_sect571r1}, + {"K-163", NID_sect163k1}, + {"K-233", NID_sect233k1}, + {"K-283", NID_sect283k1}, + {"K-409", NID_sect409k1}, + {"K-571", NID_sect571k1}, + {"P-192", NID_X9_62_prime192v1}, + {"P-224", NID_secp224r1}, + {"P-256", NID_X9_62_prime256v1}, + {"P-384", NID_secp384r1}, + {"P-521", NID_secp521r1} +}; + +const char *EC_curve_nid2nist(int nid) +{ + size_t i; + for (i = 0; i < OSSL_NELEM(nist_curves); i++) { + if (nist_curves[i].nid == nid) + return nist_curves[i].name; + } + return NULL; +} + +int EC_curve_nist2nid(const char *name) +{ + size_t i; + for (i = 0; i < OSSL_NELEM(nist_curves); i++) { + if (strcmp(nist_curves[i].name, name) == 0) + return nist_curves[i].nid; + } + return NID_undef; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_cvt.c b/openssl-1.1.0h/crypto/ec/ec_cvt.c new file mode 100644 index 0000000..bfff6d6 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_cvt.c @@ -0,0 +1,95 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * Portions of the attached software ("Contribution") are developed by + * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. + * + * The Contribution is licensed pursuant to the OpenSSL open source + * license provided above. + * + * The elliptic curve binary polynomial software is originally written by + * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <openssl/err.h> +#include "ec_lcl.h" + +EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + const EC_METHOD *meth; + EC_GROUP *ret; + +#if defined(OPENSSL_BN_ASM_MONT) + /* + * This might appear controversial, but the fact is that generic + * prime method was observed to deliver better performance even + * for NIST primes on a range of platforms, e.g.: 60%-15% + * improvement on IA-64, ~25% on ARM, 30%-90% on P4, 20%-25% + * in 32-bit build and 35%--12% in 64-bit build on Core2... + * Coefficients are relative to optimized bn_nist.c for most + * intensive ECDSA verify and ECDH operations for 192- and 521- + * bit keys respectively. Choice of these boundary values is + * arguable, because the dependency of improvement coefficient + * from key length is not a "monotone" curve. For example while + * 571-bit result is 23% on ARM, 384-bit one is -1%. But it's + * generally faster, sometimes "respectfully" faster, sometimes + * "tolerably" slower... What effectively happens is that loop + * with bn_mul_add_words is put against bn_mul_mont, and the + * latter "wins" on short vectors. Correct solution should be + * implementing dedicated NxN multiplication subroutines for + * small N. But till it materializes, let's stick to generic + * prime method... + * <appro> + */ + meth = EC_GFp_mont_method(); +#else + if (BN_nist_mod_func(p)) + meth = EC_GFp_nist_method(); + else + meth = EC_GFp_mont_method(); +#endif + + ret = EC_GROUP_new(meth); + if (ret == NULL) + return NULL; + + if (!EC_GROUP_set_curve_GFp(ret, p, a, b, ctx)) { + EC_GROUP_clear_free(ret); + return NULL; + } + + return ret; +} + +#ifndef OPENSSL_NO_EC2M +EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + const EC_METHOD *meth; + EC_GROUP *ret; + + meth = EC_GF2m_simple_method(); + + ret = EC_GROUP_new(meth); + if (ret == NULL) + return NULL; + + if (!EC_GROUP_set_curve_GF2m(ret, p, a, b, ctx)) { + EC_GROUP_clear_free(ret); + return NULL; + } + + return ret; +} +#endif diff --git a/openssl-1.1.0h/crypto/ec/ec_err.c b/openssl-1.1.0h/crypto/ec/ec_err.c new file mode 100644 index 0000000..e4c2c1c --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_err.c @@ -0,0 +1,290 @@ +/* + * Generated by util/mkerr.pl DO NOT EDIT + * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <stdio.h> +#include <openssl/err.h> +#include <openssl/ec.h> + +/* BEGIN ERROR CODES */ +#ifndef OPENSSL_NO_ERR + +# define ERR_FUNC(func) ERR_PACK(ERR_LIB_EC,func,0) +# define ERR_REASON(reason) ERR_PACK(ERR_LIB_EC,0,reason) + +static ERR_STRING_DATA EC_str_functs[] = { + {ERR_FUNC(EC_F_BN_TO_FELEM), "BN_to_felem"}, + {ERR_FUNC(EC_F_D2I_ECPARAMETERS), "d2i_ECParameters"}, + {ERR_FUNC(EC_F_D2I_ECPKPARAMETERS), "d2i_ECPKParameters"}, + {ERR_FUNC(EC_F_D2I_ECPRIVATEKEY), "d2i_ECPrivateKey"}, + {ERR_FUNC(EC_F_DO_EC_KEY_PRINT), "do_EC_KEY_print"}, + {ERR_FUNC(EC_F_ECDH_CMS_DECRYPT), "ecdh_cms_decrypt"}, + {ERR_FUNC(EC_F_ECDH_CMS_SET_SHARED_INFO), "ecdh_cms_set_shared_info"}, + {ERR_FUNC(EC_F_ECDH_COMPUTE_KEY), "ECDH_compute_key"}, + {ERR_FUNC(EC_F_ECDH_SIMPLE_COMPUTE_KEY), "ecdh_simple_compute_key"}, + {ERR_FUNC(EC_F_ECDSA_DO_SIGN_EX), "ECDSA_do_sign_ex"}, + {ERR_FUNC(EC_F_ECDSA_DO_VERIFY), "ECDSA_do_verify"}, + {ERR_FUNC(EC_F_ECDSA_SIGN_EX), "ECDSA_sign_ex"}, + {ERR_FUNC(EC_F_ECDSA_SIGN_SETUP), "ECDSA_sign_setup"}, + {ERR_FUNC(EC_F_ECDSA_SIG_NEW), "ECDSA_SIG_new"}, + {ERR_FUNC(EC_F_ECDSA_VERIFY), "ECDSA_verify"}, + {ERR_FUNC(EC_F_ECKEY_PARAM2TYPE), "eckey_param2type"}, + {ERR_FUNC(EC_F_ECKEY_PARAM_DECODE), "eckey_param_decode"}, + {ERR_FUNC(EC_F_ECKEY_PRIV_DECODE), "eckey_priv_decode"}, + {ERR_FUNC(EC_F_ECKEY_PRIV_ENCODE), "eckey_priv_encode"}, + {ERR_FUNC(EC_F_ECKEY_PUB_DECODE), "eckey_pub_decode"}, + {ERR_FUNC(EC_F_ECKEY_PUB_ENCODE), "eckey_pub_encode"}, + {ERR_FUNC(EC_F_ECKEY_TYPE2PARAM), "eckey_type2param"}, + {ERR_FUNC(EC_F_ECPARAMETERS_PRINT), "ECParameters_print"}, + {ERR_FUNC(EC_F_ECPARAMETERS_PRINT_FP), "ECParameters_print_fp"}, + {ERR_FUNC(EC_F_ECPKPARAMETERS_PRINT), "ECPKParameters_print"}, + {ERR_FUNC(EC_F_ECPKPARAMETERS_PRINT_FP), "ECPKParameters_print_fp"}, + {ERR_FUNC(EC_F_ECP_NISTZ256_GET_AFFINE), "ecp_nistz256_get_affine"}, + {ERR_FUNC(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE), + "ecp_nistz256_mult_precompute"}, + {ERR_FUNC(EC_F_ECP_NISTZ256_POINTS_MUL), "ecp_nistz256_points_mul"}, + {ERR_FUNC(EC_F_ECP_NISTZ256_PRE_COMP_NEW), "ecp_nistz256_pre_comp_new"}, + {ERR_FUNC(EC_F_ECP_NISTZ256_WINDOWED_MUL), "ecp_nistz256_windowed_mul"}, + {ERR_FUNC(EC_F_ECX_KEY_OP), "ecx_key_op"}, + {ERR_FUNC(EC_F_ECX_PRIV_ENCODE), "ecx_priv_encode"}, + {ERR_FUNC(EC_F_ECX_PUB_ENCODE), "ecx_pub_encode"}, + {ERR_FUNC(EC_F_EC_ASN1_GROUP2CURVE), "ec_asn1_group2curve"}, + {ERR_FUNC(EC_F_EC_ASN1_GROUP2FIELDID), "ec_asn1_group2fieldid"}, + {ERR_FUNC(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY), + "ec_GF2m_montgomery_point_multiply"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_GROUP_CHECK_DISCRIMINANT), + "ec_GF2m_simple_group_check_discriminant"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE), + "ec_GF2m_simple_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_OCT2POINT), "ec_GF2m_simple_oct2point"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_POINT2OCT), "ec_GF2m_simple_point2oct"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_POINT_GET_AFFINE_COORDINATES), + "ec_GF2m_simple_point_get_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_POINT_SET_AFFINE_COORDINATES), + "ec_GF2m_simple_point_set_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES), + "ec_GF2m_simple_set_compressed_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_DECODE), "ec_GFp_mont_field_decode"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_ENCODE), "ec_GFp_mont_field_encode"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_MUL), "ec_GFp_mont_field_mul"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE), + "ec_GFp_mont_field_set_to_one"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_SQR), "ec_GFp_mont_field_sqr"}, + {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE), + "ec_GFp_mont_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE), + "ec_GFp_nistp224_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL), "ec_GFp_nistp224_points_mul"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES), + "ec_GFp_nistp224_point_get_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE), + "ec_GFp_nistp256_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP256_POINTS_MUL), "ec_GFp_nistp256_points_mul"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES), + "ec_GFp_nistp256_point_get_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE), + "ec_GFp_nistp521_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP521_POINTS_MUL), "ec_GFp_nistp521_points_mul"}, + {ERR_FUNC(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES), + "ec_GFp_nistp521_point_get_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"}, + {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"}, + {ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE), + "ec_GFp_nist_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT), + "ec_GFp_simple_group_check_discriminant"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE), + "ec_GFp_simple_group_set_curve"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE), "ec_GFp_simple_make_affine"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_OCT2POINT), "ec_GFp_simple_oct2point"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_POINT2OCT), "ec_GFp_simple_point2oct"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE), + "ec_GFp_simple_points_make_affine"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES), + "ec_GFp_simple_point_get_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES), + "ec_GFp_simple_point_set_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES), + "ec_GFp_simple_set_compressed_coordinates"}, + {ERR_FUNC(EC_F_EC_GROUP_CHECK), "EC_GROUP_check"}, + {ERR_FUNC(EC_F_EC_GROUP_CHECK_DISCRIMINANT), + "EC_GROUP_check_discriminant"}, + {ERR_FUNC(EC_F_EC_GROUP_COPY), "EC_GROUP_copy"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_CURVE_GF2M), "EC_GROUP_get_curve_GF2m"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_CURVE_GFP), "EC_GROUP_get_curve_GFp"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_DEGREE), "EC_GROUP_get_degree"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_ECPARAMETERS), "EC_GROUP_get_ecparameters"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_ECPKPARAMETERS), + "EC_GROUP_get_ecpkparameters"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_PENTANOMIAL_BASIS), + "EC_GROUP_get_pentanomial_basis"}, + {ERR_FUNC(EC_F_EC_GROUP_GET_TRINOMIAL_BASIS), + "EC_GROUP_get_trinomial_basis"}, + {ERR_FUNC(EC_F_EC_GROUP_NEW), "EC_GROUP_new"}, + {ERR_FUNC(EC_F_EC_GROUP_NEW_BY_CURVE_NAME), "EC_GROUP_new_by_curve_name"}, + {ERR_FUNC(EC_F_EC_GROUP_NEW_FROM_DATA), "ec_group_new_from_data"}, + {ERR_FUNC(EC_F_EC_GROUP_NEW_FROM_ECPARAMETERS), + "EC_GROUP_new_from_ecparameters"}, + {ERR_FUNC(EC_F_EC_GROUP_NEW_FROM_ECPKPARAMETERS), + "EC_GROUP_new_from_ecpkparameters"}, + {ERR_FUNC(EC_F_EC_GROUP_SET_CURVE_GF2M), "EC_GROUP_set_curve_GF2m"}, + {ERR_FUNC(EC_F_EC_GROUP_SET_CURVE_GFP), "EC_GROUP_set_curve_GFp"}, + {ERR_FUNC(EC_F_EC_GROUP_SET_GENERATOR), "EC_GROUP_set_generator"}, + {ERR_FUNC(EC_F_EC_KEY_CHECK_KEY), "EC_KEY_check_key"}, + {ERR_FUNC(EC_F_EC_KEY_COPY), "EC_KEY_copy"}, + {ERR_FUNC(EC_F_EC_KEY_GENERATE_KEY), "EC_KEY_generate_key"}, + {ERR_FUNC(EC_F_EC_KEY_NEW), "EC_KEY_new"}, + {ERR_FUNC(EC_F_EC_KEY_NEW_METHOD), "EC_KEY_new_method"}, + {ERR_FUNC(EC_F_EC_KEY_OCT2PRIV), "EC_KEY_oct2priv"}, + {ERR_FUNC(EC_F_EC_KEY_PRINT), "EC_KEY_print"}, + {ERR_FUNC(EC_F_EC_KEY_PRINT_FP), "EC_KEY_print_fp"}, + {ERR_FUNC(EC_F_EC_KEY_PRIV2OCT), "EC_KEY_priv2oct"}, + {ERR_FUNC(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES), + "EC_KEY_set_public_key_affine_coordinates"}, + {ERR_FUNC(EC_F_EC_KEY_SIMPLE_CHECK_KEY), "ec_key_simple_check_key"}, + {ERR_FUNC(EC_F_EC_KEY_SIMPLE_OCT2PRIV), "ec_key_simple_oct2priv"}, + {ERR_FUNC(EC_F_EC_KEY_SIMPLE_PRIV2OCT), "ec_key_simple_priv2oct"}, + {ERR_FUNC(EC_F_EC_POINTS_MAKE_AFFINE), "EC_POINTs_make_affine"}, + {ERR_FUNC(EC_F_EC_POINT_ADD), "EC_POINT_add"}, + {ERR_FUNC(EC_F_EC_POINT_CMP), "EC_POINT_cmp"}, + {ERR_FUNC(EC_F_EC_POINT_COPY), "EC_POINT_copy"}, + {ERR_FUNC(EC_F_EC_POINT_DBL), "EC_POINT_dbl"}, + {ERR_FUNC(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M), + "EC_POINT_get_affine_coordinates_GF2m"}, + {ERR_FUNC(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP), + "EC_POINT_get_affine_coordinates_GFp"}, + {ERR_FUNC(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP), + "EC_POINT_get_Jprojective_coordinates_GFp"}, + {ERR_FUNC(EC_F_EC_POINT_INVERT), "EC_POINT_invert"}, + {ERR_FUNC(EC_F_EC_POINT_IS_AT_INFINITY), "EC_POINT_is_at_infinity"}, + {ERR_FUNC(EC_F_EC_POINT_IS_ON_CURVE), "EC_POINT_is_on_curve"}, + {ERR_FUNC(EC_F_EC_POINT_MAKE_AFFINE), "EC_POINT_make_affine"}, + {ERR_FUNC(EC_F_EC_POINT_NEW), "EC_POINT_new"}, + {ERR_FUNC(EC_F_EC_POINT_OCT2POINT), "EC_POINT_oct2point"}, + {ERR_FUNC(EC_F_EC_POINT_POINT2OCT), "EC_POINT_point2oct"}, + {ERR_FUNC(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M), + "EC_POINT_set_affine_coordinates_GF2m"}, + {ERR_FUNC(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP), + "EC_POINT_set_affine_coordinates_GFp"}, + {ERR_FUNC(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M), + "EC_POINT_set_compressed_coordinates_GF2m"}, + {ERR_FUNC(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP), + "EC_POINT_set_compressed_coordinates_GFp"}, + {ERR_FUNC(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP), + "EC_POINT_set_Jprojective_coordinates_GFp"}, + {ERR_FUNC(EC_F_EC_POINT_SET_TO_INFINITY), "EC_POINT_set_to_infinity"}, + {ERR_FUNC(EC_F_EC_PRE_COMP_NEW), "ec_pre_comp_new"}, + {ERR_FUNC(EC_F_EC_WNAF_MUL), "ec_wNAF_mul"}, + {ERR_FUNC(EC_F_EC_WNAF_PRECOMPUTE_MULT), "ec_wNAF_precompute_mult"}, + {ERR_FUNC(EC_F_I2D_ECPARAMETERS), "i2d_ECParameters"}, + {ERR_FUNC(EC_F_I2D_ECPKPARAMETERS), "i2d_ECPKParameters"}, + {ERR_FUNC(EC_F_I2D_ECPRIVATEKEY), "i2d_ECPrivateKey"}, + {ERR_FUNC(EC_F_I2O_ECPUBLICKEY), "i2o_ECPublicKey"}, + {ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "nistp224_pre_comp_new"}, + {ERR_FUNC(EC_F_NISTP256_PRE_COMP_NEW), "nistp256_pre_comp_new"}, + {ERR_FUNC(EC_F_NISTP521_PRE_COMP_NEW), "nistp521_pre_comp_new"}, + {ERR_FUNC(EC_F_O2I_ECPUBLICKEY), "o2i_ECPublicKey"}, + {ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE), "old_ec_priv_decode"}, + {ERR_FUNC(EC_F_OSSL_ECDH_COMPUTE_KEY), "ossl_ecdh_compute_key"}, + {ERR_FUNC(EC_F_OSSL_ECDSA_SIGN_SIG), "ossl_ecdsa_sign_sig"}, + {ERR_FUNC(EC_F_OSSL_ECDSA_VERIFY_SIG), "ossl_ecdsa_verify_sig"}, + {ERR_FUNC(EC_F_PKEY_ECX_DERIVE), "pkey_ecx_derive"}, + {ERR_FUNC(EC_F_PKEY_EC_CTRL), "pkey_ec_ctrl"}, + {ERR_FUNC(EC_F_PKEY_EC_CTRL_STR), "pkey_ec_ctrl_str"}, + {ERR_FUNC(EC_F_PKEY_EC_DERIVE), "pkey_ec_derive"}, + {ERR_FUNC(EC_F_PKEY_EC_KEYGEN), "pkey_ec_keygen"}, + {ERR_FUNC(EC_F_PKEY_EC_PARAMGEN), "pkey_ec_paramgen"}, + {ERR_FUNC(EC_F_PKEY_EC_SIGN), "pkey_ec_sign"}, + {0, NULL} +}; + +static ERR_STRING_DATA EC_str_reasons[] = { + {ERR_REASON(EC_R_ASN1_ERROR), "asn1 error"}, + {ERR_REASON(EC_R_BAD_SIGNATURE), "bad signature"}, + {ERR_REASON(EC_R_BIGNUM_OUT_OF_RANGE), "bignum out of range"}, + {ERR_REASON(EC_R_BUFFER_TOO_SMALL), "buffer too small"}, + {ERR_REASON(EC_R_COORDINATES_OUT_OF_RANGE), "coordinates out of range"}, + {ERR_REASON(EC_R_CURVE_DOES_NOT_SUPPORT_ECDH), + "curve does not support ecdh"}, + {ERR_REASON(EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING), + "curve does not support signing"}, + {ERR_REASON(EC_R_D2I_ECPKPARAMETERS_FAILURE), + "d2i ecpkparameters failure"}, + {ERR_REASON(EC_R_DECODE_ERROR), "decode error"}, + {ERR_REASON(EC_R_DISCRIMINANT_IS_ZERO), "discriminant is zero"}, + {ERR_REASON(EC_R_EC_GROUP_NEW_BY_NAME_FAILURE), + "ec group new by name failure"}, + {ERR_REASON(EC_R_FIELD_TOO_LARGE), "field too large"}, + {ERR_REASON(EC_R_GF2M_NOT_SUPPORTED), "gf2m not supported"}, + {ERR_REASON(EC_R_GROUP2PKPARAMETERS_FAILURE), + "group2pkparameters failure"}, + {ERR_REASON(EC_R_I2D_ECPKPARAMETERS_FAILURE), + "i2d ecpkparameters failure"}, + {ERR_REASON(EC_R_INCOMPATIBLE_OBJECTS), "incompatible objects"}, + {ERR_REASON(EC_R_INVALID_ARGUMENT), "invalid argument"}, + {ERR_REASON(EC_R_INVALID_COMPRESSED_POINT), "invalid compressed point"}, + {ERR_REASON(EC_R_INVALID_COMPRESSION_BIT), "invalid compression bit"}, + {ERR_REASON(EC_R_INVALID_CURVE), "invalid curve"}, + {ERR_REASON(EC_R_INVALID_DIGEST), "invalid digest"}, + {ERR_REASON(EC_R_INVALID_DIGEST_TYPE), "invalid digest type"}, + {ERR_REASON(EC_R_INVALID_ENCODING), "invalid encoding"}, + {ERR_REASON(EC_R_INVALID_FIELD), "invalid field"}, + {ERR_REASON(EC_R_INVALID_FORM), "invalid form"}, + {ERR_REASON(EC_R_INVALID_GROUP_ORDER), "invalid group order"}, + {ERR_REASON(EC_R_INVALID_KEY), "invalid key"}, + {ERR_REASON(EC_R_INVALID_OUTPUT_LENGTH), "invalid output length"}, + {ERR_REASON(EC_R_INVALID_PEER_KEY), "invalid peer key"}, + {ERR_REASON(EC_R_INVALID_PENTANOMIAL_BASIS), "invalid pentanomial basis"}, + {ERR_REASON(EC_R_INVALID_PRIVATE_KEY), "invalid private key"}, + {ERR_REASON(EC_R_INVALID_TRINOMIAL_BASIS), "invalid trinomial basis"}, + {ERR_REASON(EC_R_KDF_PARAMETER_ERROR), "kdf parameter error"}, + {ERR_REASON(EC_R_KEYS_NOT_SET), "keys not set"}, + {ERR_REASON(EC_R_MISSING_PARAMETERS), "missing parameters"}, + {ERR_REASON(EC_R_MISSING_PRIVATE_KEY), "missing private key"}, + {ERR_REASON(EC_R_NEED_NEW_SETUP_VALUES), "need new setup values"}, + {ERR_REASON(EC_R_NOT_A_NIST_PRIME), "not a NIST prime"}, + {ERR_REASON(EC_R_NOT_IMPLEMENTED), "not implemented"}, + {ERR_REASON(EC_R_NOT_INITIALIZED), "not initialized"}, + {ERR_REASON(EC_R_NO_PARAMETERS_SET), "no parameters set"}, + {ERR_REASON(EC_R_NO_PRIVATE_VALUE), "no private value"}, + {ERR_REASON(EC_R_OPERATION_NOT_SUPPORTED), "operation not supported"}, + {ERR_REASON(EC_R_PASSED_NULL_PARAMETER), "passed null parameter"}, + {ERR_REASON(EC_R_PEER_KEY_ERROR), "peer key error"}, + {ERR_REASON(EC_R_PKPARAMETERS2GROUP_FAILURE), + "pkparameters2group failure"}, + {ERR_REASON(EC_R_POINT_ARITHMETIC_FAILURE), "point arithmetic failure"}, + {ERR_REASON(EC_R_POINT_AT_INFINITY), "point at infinity"}, + {ERR_REASON(EC_R_POINT_IS_NOT_ON_CURVE), "point is not on curve"}, + {ERR_REASON(EC_R_RANDOM_NUMBER_GENERATION_FAILED), + "random number generation failed"}, + {ERR_REASON(EC_R_SHARED_INFO_ERROR), "shared info error"}, + {ERR_REASON(EC_R_SLOT_FULL), "slot full"}, + {ERR_REASON(EC_R_UNDEFINED_GENERATOR), "undefined generator"}, + {ERR_REASON(EC_R_UNDEFINED_ORDER), "undefined order"}, + {ERR_REASON(EC_R_UNKNOWN_GROUP), "unknown group"}, + {ERR_REASON(EC_R_UNKNOWN_ORDER), "unknown order"}, + {ERR_REASON(EC_R_UNSUPPORTED_FIELD), "unsupported field"}, + {ERR_REASON(EC_R_WRONG_CURVE_PARAMETERS), "wrong curve parameters"}, + {ERR_REASON(EC_R_WRONG_ORDER), "wrong order"}, + {0, NULL} +}; + +#endif + +int ERR_load_EC_strings(void) +{ +#ifndef OPENSSL_NO_ERR + + if (ERR_func_error_string(EC_str_functs[0].error) == NULL) { + ERR_load_strings(0, EC_str_functs); + ERR_load_strings(0, EC_str_reasons); + } +#endif + return 1; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_key.c b/openssl-1.1.0h/crypto/ec/ec_key.c new file mode 100644 index 0000000..f1f0afb --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_key.c @@ -0,0 +1,637 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions originally developed by SUN MICROSYSTEMS, INC., and + * contributed to the OpenSSL project. + */ + +#include <internal/cryptlib.h> +#include <string.h> +#include "ec_lcl.h" +#include <openssl/err.h> +#include <openssl/engine.h> + +EC_KEY *EC_KEY_new(void) +{ + return EC_KEY_new_method(NULL); +} + +EC_KEY *EC_KEY_new_by_curve_name(int nid) +{ + EC_KEY *ret = EC_KEY_new(); + if (ret == NULL) + return NULL; + ret->group = EC_GROUP_new_by_curve_name(nid); + if (ret->group == NULL) { + EC_KEY_free(ret); + return NULL; + } + if (ret->meth->set_group != NULL + && ret->meth->set_group(ret, ret->group) == 0) { + EC_KEY_free(ret); + return NULL; + } + return ret; +} + +void EC_KEY_free(EC_KEY *r) +{ + int i; + + if (r == NULL) + return; + + CRYPTO_atomic_add(&r->references, -1, &i, r->lock); + REF_PRINT_COUNT("EC_KEY", r); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + if (r->meth->finish != NULL) + r->meth->finish(r); + +#ifndef OPENSSL_NO_ENGINE + ENGINE_finish(r->engine); +#endif + + if (r->group && r->group->meth->keyfinish) + r->group->meth->keyfinish(r); + + CRYPTO_free_ex_data(CRYPTO_EX_INDEX_EC_KEY, r, &r->ex_data); + CRYPTO_THREAD_lock_free(r->lock); + EC_GROUP_free(r->group); + EC_POINT_free(r->pub_key); + BN_clear_free(r->priv_key); + + OPENSSL_clear_free((void *)r, sizeof(EC_KEY)); +} + +EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) +{ + if (dest == NULL || src == NULL) { + ECerr(EC_F_EC_KEY_COPY, ERR_R_PASSED_NULL_PARAMETER); + return NULL; + } + if (src->meth != dest->meth) { + if (dest->meth->finish != NULL) + dest->meth->finish(dest); + if (dest->group && dest->group->meth->keyfinish) + dest->group->meth->keyfinish(dest); +#ifndef OPENSSL_NO_ENGINE + if (ENGINE_finish(dest->engine) == 0) + return 0; + dest->engine = NULL; +#endif + } + /* copy the parameters */ + if (src->group != NULL) { + const EC_METHOD *meth = EC_GROUP_method_of(src->group); + /* clear the old group */ + EC_GROUP_free(dest->group); + dest->group = EC_GROUP_new(meth); + if (dest->group == NULL) + return NULL; + if (!EC_GROUP_copy(dest->group, src->group)) + return NULL; + + /* copy the public key */ + if (src->pub_key != NULL) { + EC_POINT_free(dest->pub_key); + dest->pub_key = EC_POINT_new(src->group); + if (dest->pub_key == NULL) + return NULL; + if (!EC_POINT_copy(dest->pub_key, src->pub_key)) + return NULL; + } + /* copy the private key */ + if (src->priv_key != NULL) { + if (dest->priv_key == NULL) { + dest->priv_key = BN_new(); + if (dest->priv_key == NULL) + return NULL; + } + if (!BN_copy(dest->priv_key, src->priv_key)) + return NULL; + if (src->group->meth->keycopy + && src->group->meth->keycopy(dest, src) == 0) + return NULL; + } + } + + + /* copy the rest */ + dest->enc_flag = src->enc_flag; + dest->conv_form = src->conv_form; + dest->version = src->version; + dest->flags = src->flags; + if (!CRYPTO_dup_ex_data(CRYPTO_EX_INDEX_EC_KEY, + &dest->ex_data, &src->ex_data)) + return NULL; + + if (src->meth != dest->meth) { +#ifndef OPENSSL_NO_ENGINE + if (src->engine != NULL && ENGINE_init(src->engine) == 0) + return NULL; + dest->engine = src->engine; +#endif + dest->meth = src->meth; + } + + if (src->meth->copy != NULL && src->meth->copy(dest, src) == 0) + return NULL; + + return dest; +} + +EC_KEY *EC_KEY_dup(const EC_KEY *ec_key) +{ + EC_KEY *ret = EC_KEY_new_method(ec_key->engine); + + if (ret == NULL) + return NULL; + + if (EC_KEY_copy(ret, ec_key) == NULL) { + EC_KEY_free(ret); + return NULL; + } + return ret; +} + +int EC_KEY_up_ref(EC_KEY *r) +{ + int i; + + if (CRYPTO_atomic_add(&r->references, 1, &i, r->lock) <= 0) + return 0; + + REF_PRINT_COUNT("EC_KEY", r); + REF_ASSERT_ISNT(i < 2); + return ((i > 1) ? 1 : 0); +} + +int EC_KEY_generate_key(EC_KEY *eckey) +{ + if (eckey == NULL || eckey->group == NULL) { + ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + if (eckey->meth->keygen != NULL) + return eckey->meth->keygen(eckey); + ECerr(EC_F_EC_KEY_GENERATE_KEY, EC_R_OPERATION_NOT_SUPPORTED); + return 0; +} + +int ossl_ec_key_gen(EC_KEY *eckey) +{ + OPENSSL_assert(eckey->group->meth->keygen != NULL); + return eckey->group->meth->keygen(eckey); +} + +int ec_key_simple_generate_key(EC_KEY *eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + BIGNUM *priv_key = NULL; + const BIGNUM *order = NULL; + EC_POINT *pub_key = NULL; + + if ((ctx = BN_CTX_new()) == NULL) + goto err; + + if (eckey->priv_key == NULL) { + priv_key = BN_new(); + if (priv_key == NULL) + goto err; + } else + priv_key = eckey->priv_key; + + order = EC_GROUP_get0_order(eckey->group); + if (order == NULL) + goto err; + + do + if (!BN_rand_range(priv_key, order)) + goto err; + while (BN_is_zero(priv_key)) ; + + if (eckey->pub_key == NULL) { + pub_key = EC_POINT_new(eckey->group); + if (pub_key == NULL) + goto err; + } else + pub_key = eckey->pub_key; + + if (!EC_POINT_mul(eckey->group, pub_key, priv_key, NULL, NULL, ctx)) + goto err; + + eckey->priv_key = priv_key; + eckey->pub_key = pub_key; + + ok = 1; + + err: + if (eckey->pub_key == NULL) + EC_POINT_free(pub_key); + if (eckey->priv_key != priv_key) + BN_free(priv_key); + BN_CTX_free(ctx); + return ok; +} + +int ec_key_simple_generate_public_key(EC_KEY *eckey) +{ + return EC_POINT_mul(eckey->group, eckey->pub_key, eckey->priv_key, NULL, + NULL, NULL); +} + +int EC_KEY_check_key(const EC_KEY *eckey) +{ + if (eckey == NULL || eckey->group == NULL || eckey->pub_key == NULL) { + ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (eckey->group->meth->keycheck == NULL) { + ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + + return eckey->group->meth->keycheck(eckey); +} + +int ec_key_simple_check_key(const EC_KEY *eckey) +{ + int ok = 0; + BN_CTX *ctx = NULL; + const BIGNUM *order = NULL; + EC_POINT *point = NULL; + + if (eckey == NULL || eckey->group == NULL || eckey->pub_key == NULL) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_POINT_AT_INFINITY); + goto err; + } + + if ((ctx = BN_CTX_new()) == NULL) + goto err; + if ((point = EC_POINT_new(eckey->group)) == NULL) + goto err; + + /* testing whether the pub_key is on the elliptic curve */ + if (EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx) <= 0) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + /* testing whether pub_key * order is the point at infinity */ + order = eckey->group->order; + if (BN_is_zero(order)) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_INVALID_GROUP_ORDER); + goto err; + } + if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_EC_LIB); + goto err; + } + if (!EC_POINT_is_at_infinity(eckey->group, point)) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_WRONG_ORDER); + goto err; + } + /* + * in case the priv_key is present : check if generator * priv_key == + * pub_key + */ + if (eckey->priv_key != NULL) { + if (BN_cmp(eckey->priv_key, order) >= 0) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_WRONG_ORDER); + goto err; + } + if (!EC_POINT_mul(eckey->group, point, eckey->priv_key, + NULL, NULL, ctx)) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_EC_LIB); + goto err; + } + if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, ctx) != 0) { + ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY); + goto err; + } + } + ok = 1; + err: + BN_CTX_free(ctx); + EC_POINT_free(point); + return ok; +} + +int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, + BIGNUM *y) +{ + BN_CTX *ctx = NULL; + BIGNUM *tx, *ty; + EC_POINT *point = NULL; + int ok = 0; +#ifndef OPENSSL_NO_EC2M + int tmp_nid, is_char_two = 0; +#endif + + if (key == NULL || key->group == NULL || x == NULL || y == NULL) { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + + BN_CTX_start(ctx); + point = EC_POINT_new(key->group); + + if (point == NULL) + goto err; + + tx = BN_CTX_get(ctx); + ty = BN_CTX_get(ctx); + if (ty == NULL) + goto err; + +#ifndef OPENSSL_NO_EC2M + tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(key->group)); + + if (tmp_nid == NID_X9_62_characteristic_two_field) + is_char_two = 1; + + if (is_char_two) { + if (!EC_POINT_set_affine_coordinates_GF2m(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(key->group, point, + tx, ty, ctx)) + goto err; + } else +#endif + { + if (!EC_POINT_set_affine_coordinates_GFp(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GFp(key->group, point, + tx, ty, ctx)) + goto err; + } + /* + * Check if retrieved coordinates match originals and are less than field + * order: if not values are out of range. + */ + if (BN_cmp(x, tx) || BN_cmp(y, ty) + || (BN_cmp(x, key->group->field) >= 0) + || (BN_cmp(y, key->group->field) >= 0)) { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + if (!EC_KEY_set_public_key(key, point)) + goto err; + + if (EC_KEY_check_key(key) == 0) + goto err; + + ok = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(ctx); + EC_POINT_free(point); + return ok; + +} + +const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key) +{ + return key->group; +} + +int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group) +{ + if (key->meth->set_group != NULL && key->meth->set_group(key, group) == 0) + return 0; + EC_GROUP_free(key->group); + key->group = EC_GROUP_dup(group); + return (key->group == NULL) ? 0 : 1; +} + +const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key) +{ + return key->priv_key; +} + +int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *priv_key) +{ + if (key->group == NULL || key->group->meth == NULL) + return 0; + if (key->group->meth->set_private != NULL + && key->group->meth->set_private(key, priv_key) == 0) + return 0; + if (key->meth->set_private != NULL + && key->meth->set_private(key, priv_key) == 0) + return 0; + BN_clear_free(key->priv_key); + key->priv_key = BN_dup(priv_key); + return (key->priv_key == NULL) ? 0 : 1; +} + +const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key) +{ + return key->pub_key; +} + +int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub_key) +{ + if (key->meth->set_public != NULL + && key->meth->set_public(key, pub_key) == 0) + return 0; + EC_POINT_free(key->pub_key); + key->pub_key = EC_POINT_dup(pub_key, key->group); + return (key->pub_key == NULL) ? 0 : 1; +} + +unsigned int EC_KEY_get_enc_flags(const EC_KEY *key) +{ + return key->enc_flag; +} + +void EC_KEY_set_enc_flags(EC_KEY *key, unsigned int flags) +{ + key->enc_flag = flags; +} + +point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key) +{ + return key->conv_form; +} + +void EC_KEY_set_conv_form(EC_KEY *key, point_conversion_form_t cform) +{ + key->conv_form = cform; + if (key->group != NULL) + EC_GROUP_set_point_conversion_form(key->group, cform); +} + +void EC_KEY_set_asn1_flag(EC_KEY *key, int flag) +{ + if (key->group != NULL) + EC_GROUP_set_asn1_flag(key->group, flag); +} + +int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx) +{ + if (key->group == NULL) + return 0; + return EC_GROUP_precompute_mult(key->group, ctx); +} + +int EC_KEY_get_flags(const EC_KEY *key) +{ + return key->flags; +} + +void EC_KEY_set_flags(EC_KEY *key, int flags) +{ + key->flags |= flags; +} + +void EC_KEY_clear_flags(EC_KEY *key, int flags) +{ + key->flags &= ~flags; +} + +size_t EC_KEY_key2buf(const EC_KEY *key, point_conversion_form_t form, + unsigned char **pbuf, BN_CTX *ctx) +{ + if (key == NULL || key->pub_key == NULL || key->group == NULL) + return 0; + return EC_POINT_point2buf(key->group, key->pub_key, form, pbuf, ctx); +} + +int EC_KEY_oct2key(EC_KEY *key, const unsigned char *buf, size_t len, + BN_CTX *ctx) +{ + if (key == NULL || key->group == NULL) + return 0; + if (key->pub_key == NULL) + key->pub_key = EC_POINT_new(key->group); + if (key->pub_key == NULL) + return 0; + if (EC_POINT_oct2point(key->group, key->pub_key, buf, len, ctx) == 0) + return 0; + /* + * Save the point conversion form. + * For non-custom curves the first octet of the buffer (excluding + * the last significant bit) contains the point conversion form. + * EC_POINT_oct2point() has already performed sanity checking of + * the buffer so we know it is valid. + */ + if ((key->group->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) + key->conv_form = (point_conversion_form_t)(buf[0] & ~0x01); + return 1; +} + +size_t EC_KEY_priv2oct(const EC_KEY *eckey, + unsigned char *buf, size_t len) +{ + if (eckey->group == NULL || eckey->group->meth == NULL) + return 0; + if (eckey->group->meth->priv2oct == NULL) { + ECerr(EC_F_EC_KEY_PRIV2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + + return eckey->group->meth->priv2oct(eckey, buf, len); +} + +size_t ec_key_simple_priv2oct(const EC_KEY *eckey, + unsigned char *buf, size_t len) +{ + size_t buf_len; + + buf_len = (EC_GROUP_order_bits(eckey->group) + 7) / 8; + if (eckey->priv_key == NULL) + return 0; + if (buf == NULL) + return buf_len; + else if (len < buf_len) + return 0; + + /* Octetstring may need leading zeros if BN is to short */ + + if (BN_bn2binpad(eckey->priv_key, buf, buf_len) == -1) { + ECerr(EC_F_EC_KEY_SIMPLE_PRIV2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + + return buf_len; +} + +int EC_KEY_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len) +{ + if (eckey->group == NULL || eckey->group->meth == NULL) + return 0; + if (eckey->group->meth->oct2priv == NULL) { + ECerr(EC_F_EC_KEY_OCT2PRIV, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return eckey->group->meth->oct2priv(eckey, buf, len); +} + +int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len) +{ + if (eckey->priv_key == NULL) + eckey->priv_key = BN_secure_new(); + if (eckey->priv_key == NULL) { + ECerr(EC_F_EC_KEY_SIMPLE_OCT2PRIV, ERR_R_MALLOC_FAILURE); + return 0; + } + eckey->priv_key = BN_bin2bn(buf, len, eckey->priv_key); + if (eckey->priv_key == NULL) { + ECerr(EC_F_EC_KEY_SIMPLE_OCT2PRIV, ERR_R_BN_LIB); + return 0; + } + return 1; +} + +size_t EC_KEY_priv2buf(const EC_KEY *eckey, unsigned char **pbuf) +{ + size_t len; + unsigned char *buf; + len = EC_KEY_priv2oct(eckey, NULL, 0); + if (len == 0) + return 0; + buf = OPENSSL_malloc(len); + if (buf == NULL) + return 0; + len = EC_KEY_priv2oct(eckey, buf, len); + if (len == 0) { + OPENSSL_free(buf); + return 0; + } + *pbuf = buf; + return len; +} + +int EC_KEY_can_sign(const EC_KEY *eckey) +{ + if (eckey->group == NULL || eckey->group->meth == NULL + || (eckey->group->meth->flags & EC_FLAGS_NO_SIGN)) + return 0; + return 1; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_kmeth.c b/openssl-1.1.0h/crypto/ec/ec_kmeth.c new file mode 100644 index 0000000..5e5d1ae --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_kmeth.c @@ -0,0 +1,317 @@ +/* + * Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <string.h> +#include <openssl/ec.h> +#include <openssl/engine.h> +#include <openssl/err.h> +#include "ec_lcl.h" + + +static const EC_KEY_METHOD openssl_ec_key_method = { + "OpenSSL EC_KEY method", + 0, + 0,0,0,0,0,0, + ossl_ec_key_gen, + ossl_ecdh_compute_key, + ossl_ecdsa_sign, + ossl_ecdsa_sign_setup, + ossl_ecdsa_sign_sig, + ossl_ecdsa_verify, + ossl_ecdsa_verify_sig +}; + +static const EC_KEY_METHOD *default_ec_key_meth = &openssl_ec_key_method; + +const EC_KEY_METHOD *EC_KEY_OpenSSL(void) +{ + return &openssl_ec_key_method; +} + +const EC_KEY_METHOD *EC_KEY_get_default_method(void) +{ + return default_ec_key_meth; +} + +void EC_KEY_set_default_method(const EC_KEY_METHOD *meth) +{ + if (meth == NULL) + default_ec_key_meth = &openssl_ec_key_method; + else + default_ec_key_meth = meth; +} + +const EC_KEY_METHOD *EC_KEY_get_method(const EC_KEY *key) +{ + return key->meth; +} + +int EC_KEY_set_method(EC_KEY *key, const EC_KEY_METHOD *meth) +{ + void (*finish)(EC_KEY *key) = key->meth->finish; + + if (finish != NULL) + finish(key); + +#ifndef OPENSSL_NO_ENGINE + ENGINE_finish(key->engine); + key->engine = NULL; +#endif + + key->meth = meth; + if (meth->init != NULL) + return meth->init(key); + return 1; +} + +EC_KEY *EC_KEY_new_method(ENGINE *engine) +{ + EC_KEY *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (ret == NULL) { + ECerr(EC_F_EC_KEY_NEW_METHOD, ERR_R_MALLOC_FAILURE); + return NULL; + } + + ret->references = 1; + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_EC_KEY_NEW_METHOD, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + + ret->meth = EC_KEY_get_default_method(); +#ifndef OPENSSL_NO_ENGINE + if (engine != NULL) { + if (!ENGINE_init(engine)) { + ECerr(EC_F_EC_KEY_NEW_METHOD, ERR_R_ENGINE_LIB); + goto err; + } + ret->engine = engine; + } else + ret->engine = ENGINE_get_default_EC(); + if (ret->engine != NULL) { + ret->meth = ENGINE_get_EC(ret->engine); + if (ret->meth == NULL) { + ECerr(EC_F_EC_KEY_NEW_METHOD, ERR_R_ENGINE_LIB); + goto err; + } + } +#endif + + ret->version = 1; + ret->conv_form = POINT_CONVERSION_UNCOMPRESSED; + + if (!CRYPTO_new_ex_data(CRYPTO_EX_INDEX_EC_KEY, ret, &ret->ex_data)) { + goto err; + } + + if (ret->meth->init != NULL && ret->meth->init(ret) == 0) { + ECerr(EC_F_EC_KEY_NEW_METHOD, ERR_R_INIT_FAIL); + goto err; + } + return ret; + +err: + EC_KEY_free(ret); + return NULL; +} + +int ECDH_compute_key(void *out, size_t outlen, const EC_POINT *pub_key, + const EC_KEY *eckey, + void *(*KDF) (const void *in, size_t inlen, void *out, + size_t *outlen)) +{ + unsigned char *sec = NULL; + size_t seclen; + if (eckey->meth->compute_key == NULL) { + ECerr(EC_F_ECDH_COMPUTE_KEY, EC_R_OPERATION_NOT_SUPPORTED); + return 0; + } + if (outlen > INT_MAX) { + ECerr(EC_F_ECDH_COMPUTE_KEY, EC_R_INVALID_OUTPUT_LENGTH); + return 0; + } + if (!eckey->meth->compute_key(&sec, &seclen, pub_key, eckey)) + return 0; + if (KDF != NULL) { + KDF(sec, seclen, out, &outlen); + } else { + if (outlen > seclen) + outlen = seclen; + memcpy(out, sec, outlen); + } + OPENSSL_clear_free(sec, seclen); + return outlen; +} + +EC_KEY_METHOD *EC_KEY_METHOD_new(const EC_KEY_METHOD *meth) +{ + EC_KEY_METHOD *ret = OPENSSL_zalloc(sizeof(*meth)); + + if (ret == NULL) + return NULL; + if (meth != NULL) + *ret = *meth; + ret->flags |= EC_KEY_METHOD_DYNAMIC; + return ret; +} + +void EC_KEY_METHOD_free(EC_KEY_METHOD *meth) +{ + if (meth->flags & EC_KEY_METHOD_DYNAMIC) + OPENSSL_free(meth); +} + +void EC_KEY_METHOD_set_init(EC_KEY_METHOD *meth, + int (*init)(EC_KEY *key), + void (*finish)(EC_KEY *key), + int (*copy)(EC_KEY *dest, const EC_KEY *src), + int (*set_group)(EC_KEY *key, const EC_GROUP *grp), + int (*set_private)(EC_KEY *key, + const BIGNUM *priv_key), + int (*set_public)(EC_KEY *key, + const EC_POINT *pub_key)) +{ + meth->init = init; + meth->finish = finish; + meth->copy = copy; + meth->set_group = set_group; + meth->set_private = set_private; + meth->set_public = set_public; +} + +void EC_KEY_METHOD_set_keygen(EC_KEY_METHOD *meth, + int (*keygen)(EC_KEY *key)) +{ + meth->keygen = keygen; +} + +void EC_KEY_METHOD_set_compute_key(EC_KEY_METHOD *meth, + int (*ckey)(unsigned char **psec, + size_t *pseclen, + const EC_POINT *pub_key, + const EC_KEY *ecdh)) +{ + meth->compute_key = ckey; +} + +void EC_KEY_METHOD_set_sign(EC_KEY_METHOD *meth, + int (*sign)(int type, const unsigned char *dgst, + int dlen, unsigned char *sig, + unsigned int *siglen, + const BIGNUM *kinv, const BIGNUM *r, + EC_KEY *eckey), + int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, + BIGNUM **kinvp, BIGNUM **rp), + ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, + int dgst_len, + const BIGNUM *in_kinv, + const BIGNUM *in_r, + EC_KEY *eckey)) +{ + meth->sign = sign; + meth->sign_setup = sign_setup; + meth->sign_sig = sign_sig; +} + +void EC_KEY_METHOD_set_verify(EC_KEY_METHOD *meth, + int (*verify)(int type, const unsigned + char *dgst, int dgst_len, + const unsigned char *sigbuf, + int sig_len, EC_KEY *eckey), + int (*verify_sig)(const unsigned char *dgst, + int dgst_len, + const ECDSA_SIG *sig, + EC_KEY *eckey)) +{ + meth->verify = verify; + meth->verify_sig = verify_sig; +} + +void EC_KEY_METHOD_get_init(const EC_KEY_METHOD *meth, + int (**pinit)(EC_KEY *key), + void (**pfinish)(EC_KEY *key), + int (**pcopy)(EC_KEY *dest, const EC_KEY *src), + int (**pset_group)(EC_KEY *key, + const EC_GROUP *grp), + int (**pset_private)(EC_KEY *key, + const BIGNUM *priv_key), + int (**pset_public)(EC_KEY *key, + const EC_POINT *pub_key)) +{ + if (pinit != NULL) + *pinit = meth->init; + if (pfinish != NULL) + *pfinish = meth->finish; + if (pcopy != NULL) + *pcopy = meth->copy; + if (pset_group != NULL) + *pset_group = meth->set_group; + if (pset_private != NULL) + *pset_private = meth->set_private; + if (pset_public != NULL) + *pset_public = meth->set_public; +} + +void EC_KEY_METHOD_get_keygen(const EC_KEY_METHOD *meth, + int (**pkeygen)(EC_KEY *key)) +{ + if (pkeygen != NULL) + *pkeygen = meth->keygen; +} + +void EC_KEY_METHOD_get_compute_key(const EC_KEY_METHOD *meth, + int (**pck)(unsigned char **pout, + size_t *poutlen, + const EC_POINT *pub_key, + const EC_KEY *ecdh)) +{ + if (pck != NULL) + *pck = meth->compute_key; +} + +void EC_KEY_METHOD_get_sign(const EC_KEY_METHOD *meth, + int (**psign)(int type, const unsigned char *dgst, + int dlen, unsigned char *sig, + unsigned int *siglen, + const BIGNUM *kinv, const BIGNUM *r, + EC_KEY *eckey), + int (**psign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, + BIGNUM **kinvp, BIGNUM **rp), + ECDSA_SIG *(**psign_sig)(const unsigned char *dgst, + int dgst_len, + const BIGNUM *in_kinv, + const BIGNUM *in_r, + EC_KEY *eckey)) +{ + if (psign != NULL) + *psign = meth->sign; + if (psign_setup != NULL) + *psign_setup = meth->sign_setup; + if (psign_sig != NULL) + *psign_sig = meth->sign_sig; +} + +void EC_KEY_METHOD_get_verify(const EC_KEY_METHOD *meth, + int (**pverify)(int type, const unsigned + char *dgst, int dgst_len, + const unsigned char *sigbuf, + int sig_len, EC_KEY *eckey), + int (**pverify_sig)(const unsigned char *dgst, + int dgst_len, + const ECDSA_SIG *sig, + EC_KEY *eckey)) +{ + if (pverify != NULL) + *pverify = meth->verify; + if (pverify_sig != NULL) + *pverify_sig = meth->verify_sig; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_lcl.h b/openssl-1.1.0h/crypto/ec/ec_lcl.h new file mode 100644 index 0000000..ded35a7 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_lcl.h @@ -0,0 +1,613 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * Portions of the attached software ("Contribution") are developed by + * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project. + * + * The Contribution is licensed pursuant to the OpenSSL open source + * license provided above. + * + * The elliptic curve binary polynomial software is originally written by + * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories. + * + */ + +#include <stdlib.h> + +#include <openssl/obj_mac.h> +#include <openssl/ec.h> +#include <openssl/bn.h> + +#include "e_os.h" + +#if defined(__SUNPRO_C) +# if __SUNPRO_C >= 0x520 +# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE) +# endif +#endif + +/* Use default functions for poin2oct, oct2point and compressed coordinates */ +#define EC_FLAGS_DEFAULT_OCT 0x1 + +/* Use custom formats for EC_GROUP, EC_POINT and EC_KEY */ +#define EC_FLAGS_CUSTOM_CURVE 0x2 + +/* Curve does not support signing operations */ +#define EC_FLAGS_NO_SIGN 0x4 + +/* + * Structure details are not part of the exported interface, so all this may + * change in future versions. + */ + +struct ec_method_st { + /* Various method flags */ + int flags; + /* used by EC_METHOD_get_field_type: */ + int field_type; /* a NID */ + /* + * used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, + * EC_GROUP_copy: + */ + int (*group_init) (EC_GROUP *); + void (*group_finish) (EC_GROUP *); + void (*group_clear_finish) (EC_GROUP *); + int (*group_copy) (EC_GROUP *, const EC_GROUP *); + /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */ + /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */ + int (*group_set_curve) (EC_GROUP *, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); + int (*group_get_curve) (const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, + BN_CTX *); + /* used by EC_GROUP_get_degree: */ + int (*group_get_degree) (const EC_GROUP *); + int (*group_order_bits) (const EC_GROUP *); + /* used by EC_GROUP_check: */ + int (*group_check_discriminant) (const EC_GROUP *, BN_CTX *); + /* + * used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, + * EC_POINT_copy: + */ + int (*point_init) (EC_POINT *); + void (*point_finish) (EC_POINT *); + void (*point_clear_finish) (EC_POINT *); + int (*point_copy) (EC_POINT *, const EC_POINT *); + /*- + * used by EC_POINT_set_to_infinity, + * EC_POINT_set_Jprojective_coordinates_GFp, + * EC_POINT_get_Jprojective_coordinates_GFp, + * EC_POINT_set_affine_coordinates_GFp, ..._GF2m, + * EC_POINT_get_affine_coordinates_GFp, ..._GF2m, + * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m: + */ + int (*point_set_to_infinity) (const EC_GROUP *, EC_POINT *); + int (*point_set_Jprojective_coordinates_GFp) (const EC_GROUP *, + EC_POINT *, const BIGNUM *x, + const BIGNUM *y, + const BIGNUM *z, BN_CTX *); + int (*point_get_Jprojective_coordinates_GFp) (const EC_GROUP *, + const EC_POINT *, BIGNUM *x, + BIGNUM *y, BIGNUM *z, + BN_CTX *); + int (*point_set_affine_coordinates) (const EC_GROUP *, EC_POINT *, + const BIGNUM *x, const BIGNUM *y, + BN_CTX *); + int (*point_get_affine_coordinates) (const EC_GROUP *, const EC_POINT *, + BIGNUM *x, BIGNUM *y, BN_CTX *); + int (*point_set_compressed_coordinates) (const EC_GROUP *, EC_POINT *, + const BIGNUM *x, int y_bit, + BN_CTX *); + /* used by EC_POINT_point2oct, EC_POINT_oct2point: */ + size_t (*point2oct) (const EC_GROUP *, const EC_POINT *, + point_conversion_form_t form, unsigned char *buf, + size_t len, BN_CTX *); + int (*oct2point) (const EC_GROUP *, EC_POINT *, const unsigned char *buf, + size_t len, BN_CTX *); + /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */ + int (*add) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *); + int (*dbl) (const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); + int (*invert) (const EC_GROUP *, EC_POINT *, BN_CTX *); + /* + * used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: + */ + int (*is_at_infinity) (const EC_GROUP *, const EC_POINT *); + int (*is_on_curve) (const EC_GROUP *, const EC_POINT *, BN_CTX *); + int (*point_cmp) (const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, + BN_CTX *); + /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */ + int (*make_affine) (const EC_GROUP *, EC_POINT *, BN_CTX *); + int (*points_make_affine) (const EC_GROUP *, size_t num, EC_POINT *[], + BN_CTX *); + /* + * used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, + * EC_POINT_have_precompute_mult (default implementations are used if the + * 'mul' pointer is 0): + */ + int (*mul) (const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); + int (*precompute_mult) (EC_GROUP *group, BN_CTX *); + int (*have_precompute_mult) (const EC_GROUP *group); + /* internal functions */ + /* + * 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and + * 'dbl' so that the same implementations of point operations can be used + * with different optimized implementations of expensive field + * operations: + */ + int (*field_mul) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); + int (*field_div) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); + /* e.g. to Montgomery */ + int (*field_encode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); + /* e.g. from Montgomery */ + int (*field_decode) (const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); + int (*field_set_to_one) (const EC_GROUP *, BIGNUM *r, BN_CTX *); + /* private key operations */ + size_t (*priv2oct)(const EC_KEY *eckey, unsigned char *buf, size_t len); + int (*oct2priv)(EC_KEY *eckey, const unsigned char *buf, size_t len); + int (*set_private)(EC_KEY *eckey, const BIGNUM *priv_key); + int (*keygen)(EC_KEY *eckey); + int (*keycheck)(const EC_KEY *eckey); + int (*keygenpub)(EC_KEY *eckey); + int (*keycopy)(EC_KEY *dst, const EC_KEY *src); + void (*keyfinish)(EC_KEY *eckey); + /* custom ECDH operation */ + int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen, + const EC_POINT *pub_key, const EC_KEY *ecdh); +}; + +/* + * Types and functions to manipulate pre-computed values. + */ +typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP; +typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP; +typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP; +typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP; +typedef struct ec_pre_comp_st EC_PRE_COMP; + +struct ec_group_st { + const EC_METHOD *meth; + EC_POINT *generator; /* optional */ + BIGNUM *order, *cofactor; + int curve_name; /* optional NID for named curve */ + int asn1_flag; /* flag to control the asn1 encoding */ + point_conversion_form_t asn1_form; + unsigned char *seed; /* optional seed for parameters (appears in + * ASN1) */ + size_t seed_len; + /* + * The following members are handled by the method functions, even if + * they appear generic + */ + /* + * Field specification. For curves over GF(p), this is the modulus; for + * curves over GF(2^m), this is the irreducible polynomial defining the + * field. + */ + BIGNUM *field; + /* + * Field specification for curves over GF(2^m). The irreducible f(t) is + * then of the form: t^poly[0] + t^poly[1] + ... + t^poly[k] where m = + * poly[0] > poly[1] > ... > poly[k] = 0. The array is terminated with + * poly[k+1]=-1. All elliptic curve irreducibles have at most 5 non-zero + * terms. + */ + int poly[6]; + /* + * Curve coefficients. (Here the assumption is that BIGNUMs can be used + * or abused for all kinds of fields, not just GF(p).) For characteristic + * > 3, the curve is defined by a Weierstrass equation of the form y^2 = + * x^3 + a*x + b. For characteristic 2, the curve is defined by an + * equation of the form y^2 + x*y = x^3 + a*x^2 + b. + */ + BIGNUM *a, *b; + /* enable optimized point arithmetics for special case */ + int a_is_minus3; + /* method-specific (e.g., Montgomery structure) */ + void *field_data1; + /* method-specific */ + void *field_data2; + /* method-specific */ + int (*field_mod_func) (BIGNUM *, const BIGNUM *, const BIGNUM *, + BN_CTX *); + /* data for ECDSA inverse */ + BN_MONT_CTX *mont_data; + + /* + * Precomputed values for speed. The PCT_xxx names match the + * pre_comp.xxx union names; see the SETPRECOMP and HAVEPRECOMP + * macros, below. + */ + enum { + PCT_none, + PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256, + PCT_ec + } pre_comp_type; + union { + NISTP224_PRE_COMP *nistp224; + NISTP256_PRE_COMP *nistp256; + NISTP521_PRE_COMP *nistp521; + NISTZ256_PRE_COMP *nistz256; + EC_PRE_COMP *ec; + } pre_comp; +}; + +#define SETPRECOMP(g, type, pre) \ + g->pre_comp_type = PCT_##type, g->pre_comp.type = pre +#define HAVEPRECOMP(g, type) \ + g->pre_comp_type == PCT_##type && g->pre_comp.type != NULL + +struct ec_key_st { + const EC_KEY_METHOD *meth; + ENGINE *engine; + int version; + EC_GROUP *group; + EC_POINT *pub_key; + BIGNUM *priv_key; + unsigned int enc_flag; + point_conversion_form_t conv_form; + int references; + int flags; + CRYPTO_EX_DATA ex_data; + CRYPTO_RWLOCK *lock; +}; + +struct ec_point_st { + const EC_METHOD *meth; + /* + * All members except 'meth' are handled by the method functions, even if + * they appear generic + */ + BIGNUM *X; + BIGNUM *Y; + BIGNUM *Z; /* Jacobian projective coordinates: * (X, Y, + * Z) represents (X/Z^2, Y/Z^3) if Z != 0 */ + int Z_is_one; /* enable optimized point arithmetics for + * special case */ +}; + +NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *); +NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); +NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *); +NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *); +NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); +EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *); + +void EC_pre_comp_free(EC_GROUP *group); +void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *); +void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *); +void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *); +void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *); +void EC_ec_pre_comp_free(EC_PRE_COMP *); + +/* + * method functions in ec_mult.c (ec_lib.c uses these as defaults if + * group->method->mul is 0) + */ +int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *); +int ec_wNAF_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_smpl.c */ +int ec_GFp_simple_group_init(EC_GROUP *); +void ec_GFp_simple_group_finish(EC_GROUP *); +void ec_GFp_simple_group_clear_finish(EC_GROUP *); +int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *); +int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *); +int ec_GFp_simple_group_get_degree(const EC_GROUP *); +int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); +int ec_GFp_simple_point_init(EC_POINT *); +void ec_GFp_simple_point_finish(EC_POINT *); +void ec_GFp_simple_point_clear_finish(EC_POINT *); +int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *); +int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); +int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, + EC_POINT *, const BIGNUM *x, + const BIGNUM *y, + const BIGNUM *z, BN_CTX *); +int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, + const EC_POINT *, BIGNUM *x, + BIGNUM *y, BIGNUM *z, + BN_CTX *); +int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, + const BIGNUM *x, + const BIGNUM *y, BN_CTX *); +int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, + const EC_POINT *, BIGNUM *x, + BIGNUM *y, BN_CTX *); +int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, + const BIGNUM *x, int y_bit, + BN_CTX *); +size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *); +int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *, + const unsigned char *buf, size_t len, BN_CTX *); +int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *); +int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, + BN_CTX *); +int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); +int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); +int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); +int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, + BN_CTX *); +int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); +int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, + EC_POINT *[], BN_CTX *); +int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); + +/* method functions in ecp_mont.c */ +int ec_GFp_mont_group_init(EC_GROUP *); +int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +void ec_GFp_mont_group_finish(EC_GROUP *); +void ec_GFp_mont_group_clear_finish(EC_GROUP *); +int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); +int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); +int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); +int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *); + +/* method functions in ecp_nist.c */ +int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src); +int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); + +/* method functions in ec2_smpl.c */ +int ec_GF2m_simple_group_init(EC_GROUP *); +void ec_GF2m_simple_group_finish(EC_GROUP *); +void ec_GF2m_simple_group_clear_finish(EC_GROUP *); +int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *); +int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *); +int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *); +int ec_GF2m_simple_group_get_degree(const EC_GROUP *); +int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *); +int ec_GF2m_simple_point_init(EC_POINT *); +void ec_GF2m_simple_point_finish(EC_POINT *); +void ec_GF2m_simple_point_clear_finish(EC_POINT *); +int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *); +int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *); +int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *, + const BIGNUM *x, + const BIGNUM *y, BN_CTX *); +int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, + const EC_POINT *, BIGNUM *x, + BIGNUM *y, BN_CTX *); +int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *, + const BIGNUM *x, int y_bit, + BN_CTX *); +size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *); +int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *, + const unsigned char *buf, size_t len, BN_CTX *); +int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *); +int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, + BN_CTX *); +int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); +int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *); +int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); +int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, + BN_CTX *); +int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); +int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, + EC_POINT *[], BN_CTX *); +int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); +int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + BN_CTX *); +int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *); + +/* method functions in ec2_mult.c */ +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 +/* method functions in ecp_nistp224.c */ +int ec_GFp_nistp224_group_init(EC_GROUP *group); +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *n, + BN_CTX *); +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx); +int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp256.c */ +int ec_GFp_nistp256_group_init(EC_GROUP *group); +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *n, + BN_CTX *); +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx); +int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp521.c */ +int ec_GFp_nistp521_group_init(EC_GROUP *group); +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *n, + BN_CTX *); +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx); +int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); + +/* utility functions in ecp_nistputil.c */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, + void *tmp_felems, + void (*felem_one) (void *out), + int (*felem_is_zero) (const void + *in), + void (*felem_assign) (void *out, + const void + *in), + void (*felem_square) (void *out, + const void + *in), + void (*felem_mul) (void *out, + const void + *in1, + const void + *in2), + void (*felem_inv) (void *out, + const void + *in), + void (*felem_contract) (void + *out, + const + void + *in)); +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, + unsigned char *digit, unsigned char in); +#endif +int ec_precompute_mont_data(EC_GROUP *); +int ec_group_simple_order_bits(const EC_GROUP *group); + +#ifdef ECP_NISTZ256_ASM +/** Returns GFp methods using montgomery multiplication, with x86-64 optimized + * P256. See http://eprint.iacr.org/2013/816. + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistz256_method(void); +#endif + +size_t ec_key_simple_priv2oct(const EC_KEY *eckey, + unsigned char *buf, size_t len); +int ec_key_simple_oct2priv(EC_KEY *eckey, const unsigned char *buf, size_t len); +int ec_key_simple_generate_key(EC_KEY *eckey); +int ec_key_simple_generate_public_key(EC_KEY *eckey); +int ec_key_simple_check_key(const EC_KEY *eckey); + +/* EC_METHOD definitions */ + +struct ec_key_method_st { + const char *name; + int32_t flags; + int (*init)(EC_KEY *key); + void (*finish)(EC_KEY *key); + int (*copy)(EC_KEY *dest, const EC_KEY *src); + int (*set_group)(EC_KEY *key, const EC_GROUP *grp); + int (*set_private)(EC_KEY *key, const BIGNUM *priv_key); + int (*set_public)(EC_KEY *key, const EC_POINT *pub_key); + int (*keygen)(EC_KEY *key); + int (*compute_key)(unsigned char **pout, size_t *poutlen, + const EC_POINT *pub_key, const EC_KEY *ecdh); + int (*sign)(int type, const unsigned char *dgst, int dlen, unsigned char + *sig, unsigned int *siglen, const BIGNUM *kinv, + const BIGNUM *r, EC_KEY *eckey); + int (*sign_setup)(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, + BIGNUM **rp); + ECDSA_SIG *(*sign_sig)(const unsigned char *dgst, int dgst_len, + const BIGNUM *in_kinv, const BIGNUM *in_r, + EC_KEY *eckey); + + int (*verify)(int type, const unsigned char *dgst, int dgst_len, + const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); + int (*verify_sig)(const unsigned char *dgst, int dgst_len, + const ECDSA_SIG *sig, EC_KEY *eckey); +}; + +#define EC_KEY_METHOD_DYNAMIC 1 + +int ossl_ec_key_gen(EC_KEY *eckey); +int ossl_ecdh_compute_key(unsigned char **pout, size_t *poutlen, + const EC_POINT *pub_key, const EC_KEY *ecdh); +int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen, + const EC_POINT *pub_key, const EC_KEY *ecdh); + +struct ECDSA_SIG_st { + BIGNUM *r; + BIGNUM *s; +}; + +int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, + BIGNUM **rp); +int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen, + unsigned char *sig, unsigned int *siglen, + const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey); +ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, + const BIGNUM *in_kinv, const BIGNUM *in_r, + EC_KEY *eckey); +int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len, + const unsigned char *sigbuf, int sig_len, EC_KEY *eckey); +int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len, + const ECDSA_SIG *sig, EC_KEY *eckey); + +int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], + const uint8_t peer_public_value[32]); +void X25519_public_from_private(uint8_t out_public_value[32], + const uint8_t private_key[32]); diff --git a/openssl-1.1.0h/crypto/ec/ec_lib.c b/openssl-1.1.0h/crypto/ec/ec_lib.c new file mode 100644 index 0000000..7cb4bfe --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_lib.c @@ -0,0 +1,1004 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Binary polynomial ECC support in OpenSSL originally developed by + * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. + */ + +#include <string.h> + +#include <openssl/err.h> +#include <openssl/opensslv.h> + +#include "ec_lcl.h" + +/* functions for EC_GROUP objects */ + +EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) +{ + EC_GROUP *ret; + + if (meth == NULL) { + ECerr(EC_F_EC_GROUP_NEW, EC_R_SLOT_FULL); + return NULL; + } + if (meth->group_init == 0) { + ECerr(EC_F_EC_GROUP_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return NULL; + } + + ret = OPENSSL_zalloc(sizeof(*ret)); + if (ret == NULL) { + ECerr(EC_F_EC_GROUP_NEW, ERR_R_MALLOC_FAILURE); + return NULL; + } + + ret->meth = meth; + if ((ret->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) { + ret->order = BN_new(); + if (ret->order == NULL) + goto err; + ret->cofactor = BN_new(); + if (ret->cofactor == NULL) + goto err; + } + ret->asn1_flag = OPENSSL_EC_NAMED_CURVE; + ret->asn1_form = POINT_CONVERSION_UNCOMPRESSED; + if (!meth->group_init(ret)) + goto err; + return ret; + + err: + BN_free(ret->order); + BN_free(ret->cofactor); + OPENSSL_free(ret); + return NULL; +} + +void EC_pre_comp_free(EC_GROUP *group) +{ + switch (group->pre_comp_type) { + default: + break; +#ifdef ECP_NISTZ256_REFERENCE_IMPLEMENTATION + case PCT_nistz256: + EC_nistz256_pre_comp_free(group->pre_comp.nistz256); + break; +#endif +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + case PCT_nistp224: + EC_nistp224_pre_comp_free(group->pre_comp.nistp224); + break; + case PCT_nistp256: + EC_nistp256_pre_comp_free(group->pre_comp.nistp256); + break; + case PCT_nistp521: + EC_nistp521_pre_comp_free(group->pre_comp.nistp521); + break; +#endif + case PCT_ec: + EC_ec_pre_comp_free(group->pre_comp.ec); + break; + } + group->pre_comp.ec = NULL; +} + +void EC_GROUP_free(EC_GROUP *group) +{ + if (!group) + return; + + if (group->meth->group_finish != 0) + group->meth->group_finish(group); + + EC_pre_comp_free(group); + BN_MONT_CTX_free(group->mont_data); + EC_POINT_free(group->generator); + BN_free(group->order); + BN_free(group->cofactor); + OPENSSL_free(group->seed); + OPENSSL_free(group); +} + +void EC_GROUP_clear_free(EC_GROUP *group) +{ + if (!group) + return; + + if (group->meth->group_clear_finish != 0) + group->meth->group_clear_finish(group); + else if (group->meth->group_finish != 0) + group->meth->group_finish(group); + + EC_pre_comp_free(group); + BN_MONT_CTX_free(group->mont_data); + EC_POINT_clear_free(group->generator); + BN_clear_free(group->order); + BN_clear_free(group->cofactor); + OPENSSL_clear_free(group->seed, group->seed_len); + OPENSSL_clear_free(group, sizeof(*group)); +} + +int EC_GROUP_copy(EC_GROUP *dest, const EC_GROUP *src) +{ + if (dest->meth->group_copy == 0) { + ECerr(EC_F_EC_GROUP_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (dest->meth != src->meth) { + ECerr(EC_F_EC_GROUP_COPY, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (dest == src) + return 1; + + /* Copy precomputed */ + dest->pre_comp_type = src->pre_comp_type; + switch (src->pre_comp_type) { + default: + dest->pre_comp.ec = NULL; + break; +#ifdef ECP_NISTZ256_REFERENCE_IMPLEMENTATION + case PCT_nistz256: + dest->pre_comp.nistz256 = EC_nistz256_pre_comp_dup(src->pre_comp.nistz256); + break; +#endif +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + case PCT_nistp224: + dest->pre_comp.nistp224 = EC_nistp224_pre_comp_dup(src->pre_comp.nistp224); + break; + case PCT_nistp256: + dest->pre_comp.nistp256 = EC_nistp256_pre_comp_dup(src->pre_comp.nistp256); + break; + case PCT_nistp521: + dest->pre_comp.nistp521 = EC_nistp521_pre_comp_dup(src->pre_comp.nistp521); + break; +#endif + case PCT_ec: + dest->pre_comp.ec = EC_ec_pre_comp_dup(src->pre_comp.ec); + break; + } + + if (src->mont_data != NULL) { + if (dest->mont_data == NULL) { + dest->mont_data = BN_MONT_CTX_new(); + if (dest->mont_data == NULL) + return 0; + } + if (!BN_MONT_CTX_copy(dest->mont_data, src->mont_data)) + return 0; + } else { + /* src->generator == NULL */ + BN_MONT_CTX_free(dest->mont_data); + dest->mont_data = NULL; + } + + if (src->generator != NULL) { + if (dest->generator == NULL) { + dest->generator = EC_POINT_new(dest); + if (dest->generator == NULL) + return 0; + } + if (!EC_POINT_copy(dest->generator, src->generator)) + return 0; + } else { + /* src->generator == NULL */ + EC_POINT_clear_free(dest->generator); + dest->generator = NULL; + } + + if ((src->meth->flags & EC_FLAGS_CUSTOM_CURVE) == 0) { + if (!BN_copy(dest->order, src->order)) + return 0; + if (!BN_copy(dest->cofactor, src->cofactor)) + return 0; + } + + dest->curve_name = src->curve_name; + dest->asn1_flag = src->asn1_flag; + dest->asn1_form = src->asn1_form; + + if (src->seed) { + OPENSSL_free(dest->seed); + dest->seed = OPENSSL_malloc(src->seed_len); + if (dest->seed == NULL) + return 0; + if (!memcpy(dest->seed, src->seed, src->seed_len)) + return 0; + dest->seed_len = src->seed_len; + } else { + OPENSSL_free(dest->seed); + dest->seed = NULL; + dest->seed_len = 0; + } + + return dest->meth->group_copy(dest, src); +} + +EC_GROUP *EC_GROUP_dup(const EC_GROUP *a) +{ + EC_GROUP *t = NULL; + int ok = 0; + + if (a == NULL) + return NULL; + + if ((t = EC_GROUP_new(a->meth)) == NULL) + return (NULL); + if (!EC_GROUP_copy(t, a)) + goto err; + + ok = 1; + + err: + if (!ok) { + EC_GROUP_free(t); + return NULL; + } + return t; +} + +const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group) +{ + return group->meth; +} + +int EC_METHOD_get_field_type(const EC_METHOD *meth) +{ + return meth->field_type; +} + +int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, + const BIGNUM *order, const BIGNUM *cofactor) +{ + if (generator == NULL) { + ECerr(EC_F_EC_GROUP_SET_GENERATOR, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (group->generator == NULL) { + group->generator = EC_POINT_new(group); + if (group->generator == NULL) + return 0; + } + if (!EC_POINT_copy(group->generator, generator)) + return 0; + + if (order != NULL) { + if (!BN_copy(group->order, order)) + return 0; + } else + BN_zero(group->order); + + if (cofactor != NULL) { + if (!BN_copy(group->cofactor, cofactor)) + return 0; + } else + BN_zero(group->cofactor); + + /* + * Some groups have an order with + * factors of two, which makes the Montgomery setup fail. + * |group->mont_data| will be NULL in this case. + */ + if (BN_is_odd(group->order)) { + return ec_precompute_mont_data(group); + } + + BN_MONT_CTX_free(group->mont_data); + group->mont_data = NULL; + return 1; +} + +const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group) +{ + return group->generator; +} + +BN_MONT_CTX *EC_GROUP_get_mont_data(const EC_GROUP *group) +{ + return group->mont_data; +} + +int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx) +{ + if (group->order == NULL) + return 0; + if (!BN_copy(order, group->order)) + return 0; + + return !BN_is_zero(order); +} + +const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group) +{ + return group->order; +} + +int EC_GROUP_order_bits(const EC_GROUP *group) +{ + OPENSSL_assert(group->meth->group_order_bits != NULL); + return group->meth->group_order_bits(group); +} + +int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, + BN_CTX *ctx) +{ + + if (group->cofactor == NULL) + return 0; + if (!BN_copy(cofactor, group->cofactor)) + return 0; + + return !BN_is_zero(group->cofactor); +} + +const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group) +{ + return group->cofactor; +} + +void EC_GROUP_set_curve_name(EC_GROUP *group, int nid) +{ + group->curve_name = nid; +} + +int EC_GROUP_get_curve_name(const EC_GROUP *group) +{ + return group->curve_name; +} + +void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag) +{ + group->asn1_flag = flag; +} + +int EC_GROUP_get_asn1_flag(const EC_GROUP *group) +{ + return group->asn1_flag; +} + +void EC_GROUP_set_point_conversion_form(EC_GROUP *group, + point_conversion_form_t form) +{ + group->asn1_form = form; +} + +point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP + *group) +{ + return group->asn1_form; +} + +size_t EC_GROUP_set_seed(EC_GROUP *group, const unsigned char *p, size_t len) +{ + OPENSSL_free(group->seed); + group->seed = NULL; + group->seed_len = 0; + + if (!len || !p) + return 1; + + if ((group->seed = OPENSSL_malloc(len)) == NULL) + return 0; + memcpy(group->seed, p, len); + group->seed_len = len; + + return len; +} + +unsigned char *EC_GROUP_get0_seed(const EC_GROUP *group) +{ + return group->seed; +} + +size_t EC_GROUP_get_seed_len(const EC_GROUP *group) +{ + return group->seed_len; +} + +int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + if (group->meth->group_set_curve == 0) { + ECerr(EC_F_EC_GROUP_SET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_set_curve(group, p, a, b, ctx); +} + +int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *ctx) +{ + if (group->meth->group_get_curve == 0) { + ECerr(EC_F_EC_GROUP_GET_CURVE_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_get_curve(group, p, a, b, ctx); +} + +#ifndef OPENSSL_NO_EC2M +int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + if (group->meth->group_set_curve == 0) { + ECerr(EC_F_EC_GROUP_SET_CURVE_GF2M, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_set_curve(group, p, a, b, ctx); +} + +int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *ctx) +{ + if (group->meth->group_get_curve == 0) { + ECerr(EC_F_EC_GROUP_GET_CURVE_GF2M, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_get_curve(group, p, a, b, ctx); +} +#endif + +int EC_GROUP_get_degree(const EC_GROUP *group) +{ + if (group->meth->group_get_degree == 0) { + ECerr(EC_F_EC_GROUP_GET_DEGREE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_get_degree(group); +} + +int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) +{ + if (group->meth->group_check_discriminant == 0) { + ECerr(EC_F_EC_GROUP_CHECK_DISCRIMINANT, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + return group->meth->group_check_discriminant(group, ctx); +} + +int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx) +{ + int r = 0; + BIGNUM *a1, *a2, *a3, *b1, *b2, *b3; + BN_CTX *ctx_new = NULL; + + /* compare the field types */ + if (EC_METHOD_get_field_type(EC_GROUP_method_of(a)) != + EC_METHOD_get_field_type(EC_GROUP_method_of(b))) + return 1; + /* compare the curve name (if present in both) */ + if (EC_GROUP_get_curve_name(a) && EC_GROUP_get_curve_name(b) && + EC_GROUP_get_curve_name(a) != EC_GROUP_get_curve_name(b)) + return 1; + if (a->meth->flags & EC_FLAGS_CUSTOM_CURVE) + return 0; + + if (ctx == NULL) + ctx_new = ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + + BN_CTX_start(ctx); + a1 = BN_CTX_get(ctx); + a2 = BN_CTX_get(ctx); + a3 = BN_CTX_get(ctx); + b1 = BN_CTX_get(ctx); + b2 = BN_CTX_get(ctx); + b3 = BN_CTX_get(ctx); + if (b3 == NULL) { + BN_CTX_end(ctx); + BN_CTX_free(ctx_new); + return -1; + } + + /* + * XXX This approach assumes that the external representation of curves + * over the same field type is the same. + */ + if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) || + !b->meth->group_get_curve(b, b1, b2, b3, ctx)) + r = 1; + + if (r || BN_cmp(a1, b1) || BN_cmp(a2, b2) || BN_cmp(a3, b3)) + r = 1; + + /* XXX EC_POINT_cmp() assumes that the methods are equal */ + if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a), + EC_GROUP_get0_generator(b), ctx)) + r = 1; + + if (!r) { + const BIGNUM *ao, *bo, *ac, *bc; + /* compare the order and cofactor */ + ao = EC_GROUP_get0_order(a); + bo = EC_GROUP_get0_order(b); + ac = EC_GROUP_get0_cofactor(a); + bc = EC_GROUP_get0_cofactor(b); + if (ao == NULL || bo == NULL) { + BN_CTX_end(ctx); + BN_CTX_free(ctx_new); + return -1; + } + if (BN_cmp(ao, bo) || BN_cmp(ac, bc)) + r = 1; + } + + BN_CTX_end(ctx); + BN_CTX_free(ctx_new); + + return r; +} + +/* functions for EC_POINT objects */ + +EC_POINT *EC_POINT_new(const EC_GROUP *group) +{ + EC_POINT *ret; + + if (group == NULL) { + ECerr(EC_F_EC_POINT_NEW, ERR_R_PASSED_NULL_PARAMETER); + return NULL; + } + if (group->meth->point_init == 0) { + ECerr(EC_F_EC_POINT_NEW, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return NULL; + } + + ret = OPENSSL_zalloc(sizeof(*ret)); + if (ret == NULL) { + ECerr(EC_F_EC_POINT_NEW, ERR_R_MALLOC_FAILURE); + return NULL; + } + + ret->meth = group->meth; + + if (!ret->meth->point_init(ret)) { + OPENSSL_free(ret); + return NULL; + } + + return ret; +} + +void EC_POINT_free(EC_POINT *point) +{ + if (!point) + return; + + if (point->meth->point_finish != 0) + point->meth->point_finish(point); + OPENSSL_free(point); +} + +void EC_POINT_clear_free(EC_POINT *point) +{ + if (!point) + return; + + if (point->meth->point_clear_finish != 0) + point->meth->point_clear_finish(point); + else if (point->meth->point_finish != 0) + point->meth->point_finish(point); + OPENSSL_clear_free(point, sizeof(*point)); +} + +int EC_POINT_copy(EC_POINT *dest, const EC_POINT *src) +{ + if (dest->meth->point_copy == 0) { + ECerr(EC_F_EC_POINT_COPY, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (dest->meth != src->meth) { + ECerr(EC_F_EC_POINT_COPY, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (dest == src) + return 1; + return dest->meth->point_copy(dest, src); +} + +EC_POINT *EC_POINT_dup(const EC_POINT *a, const EC_GROUP *group) +{ + EC_POINT *t; + int r; + + if (a == NULL) + return NULL; + + t = EC_POINT_new(group); + if (t == NULL) + return (NULL); + r = EC_POINT_copy(t, a); + if (!r) { + EC_POINT_free(t); + return NULL; + } + return t; +} + +const EC_METHOD *EC_POINT_method_of(const EC_POINT *point) +{ + return point->meth; +} + +int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point) +{ + if (group->meth->point_set_to_infinity == 0) { + ECerr(EC_F_EC_POINT_SET_TO_INFINITY, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_TO_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->point_set_to_infinity(group, point); +} + +int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + const BIGNUM *y, const BIGNUM *z, + BN_CTX *ctx) +{ + if (group->meth->point_set_Jprojective_coordinates_GFp == 0) { + ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_JPROJECTIVE_COORDINATES_GFP, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->point_set_Jprojective_coordinates_GFp(group, point, x, + y, z, ctx); +} + +int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, + BIGNUM *y, BIGNUM *z, + BN_CTX *ctx) +{ + if (group->meth->point_get_Jprojective_coordinates_GFp == 0) { + ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_GET_JPROJECTIVE_COORDINATES_GFP, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->point_get_Jprojective_coordinates_GFp(group, point, x, + y, z, ctx); +} + +int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (!group->meth->point_set_affine_coordinates(group, point, x, y, ctx)) + return 0; + + if (EC_POINT_is_on_curve(group, point, ctx) <= 0) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GFP, + EC_R_POINT_IS_NOT_ON_CURVE); + return 0; + } + return 1; +} + +#ifndef OPENSSL_NO_EC2M +int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_set_affine_coordinates == 0) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (!group->meth->point_set_affine_coordinates(group, point, x, y, ctx)) + return 0; + + if (EC_POINT_is_on_curve(group, point, ctx) <= 0) { + ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES_GF2M, + EC_R_POINT_IS_NOT_ON_CURVE); + return 0; + } + return 1; +} +#endif + +int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, + BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { + ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GFP, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} + +#ifndef OPENSSL_NO_EC2M +int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, + BIGNUM *y, BN_CTX *ctx) +{ + if (group->meth->point_get_affine_coordinates == 0) { + ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_GET_AFFINE_COORDINATES_GF2M, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); +} +#endif + +int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + if (group->meth->add == 0) { + ECerr(EC_F_EC_POINT_ADD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if ((group->meth != r->meth) || (r->meth != a->meth) + || (a->meth != b->meth)) { + ECerr(EC_F_EC_POINT_ADD, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->add(group, r, a, b, ctx); +} + +int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ + if (group->meth->dbl == 0) { + ECerr(EC_F_EC_POINT_DBL, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if ((group->meth != r->meth) || (r->meth != a->meth)) { + ECerr(EC_F_EC_POINT_DBL, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->dbl(group, r, a, ctx); +} + +int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx) +{ + if (group->meth->invert == 0) { + ECerr(EC_F_EC_POINT_INVERT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != a->meth) { + ECerr(EC_F_EC_POINT_INVERT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->invert(group, a, ctx); +} + +int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ + if (group->meth->is_at_infinity == 0) { + ECerr(EC_F_EC_POINT_IS_AT_INFINITY, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_IS_AT_INFINITY, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->is_at_infinity(group, point); +} + +/* + * Check whether an EC_POINT is on the curve or not. Note that the return + * value for this function should NOT be treated as a boolean. Return values: + * 1: The point is on the curve + * 0: The point is not on the curve + * -1: An error occurred + */ +int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, + BN_CTX *ctx) +{ + if (group->meth->is_on_curve == 0) { + ECerr(EC_F_EC_POINT_IS_ON_CURVE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_IS_ON_CURVE, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->is_on_curve(group, point, ctx); +} + +int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, + BN_CTX *ctx) +{ + if (group->meth->point_cmp == 0) { + ECerr(EC_F_EC_POINT_CMP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return -1; + } + if ((group->meth != a->meth) || (a->meth != b->meth)) { + ECerr(EC_F_EC_POINT_CMP, EC_R_INCOMPATIBLE_OBJECTS); + return -1; + } + return group->meth->point_cmp(group, a, b, ctx); +} + +int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ + if (group->meth->make_affine == 0) { + ECerr(EC_F_EC_POINT_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + return group->meth->make_affine(group, point, ctx); +} + +int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ + size_t i; + + if (group->meth->points_make_affine == 0) { + ECerr(EC_F_EC_POINTS_MAKE_AFFINE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { + ECerr(EC_F_EC_POINTS_MAKE_AFFINE, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + } + return group->meth->points_make_affine(group, num, points, ctx); +} + +/* + * Functions for point multiplication. If group->meth->mul is 0, we use the + * wNAF-based implementations in ec_mult.c; otherwise we dispatch through + * methods. + */ + +int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + if (group->meth->mul == 0) + /* use default */ + return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); + + return group->meth->mul(group, r, scalar, num, points, scalars, ctx); +} + +int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, + const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) +{ + /* just a convenient interface to EC_POINTs_mul() */ + + const EC_POINT *points[1]; + const BIGNUM *scalars[1]; + + points[0] = point; + scalars[0] = p_scalar; + + return EC_POINTs_mul(group, r, g_scalar, + (point != NULL + && p_scalar != NULL), points, scalars, ctx); +} + +int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + if (group->meth->mul == 0) + /* use default */ + return ec_wNAF_precompute_mult(group, ctx); + + if (group->meth->precompute_mult != 0) + return group->meth->precompute_mult(group, ctx); + else + return 1; /* nothing to do, so report success */ +} + +int EC_GROUP_have_precompute_mult(const EC_GROUP *group) +{ + if (group->meth->mul == 0) + /* use default */ + return ec_wNAF_have_precompute_mult(group); + + if (group->meth->have_precompute_mult != 0) + return group->meth->have_precompute_mult(group); + else + return 0; /* cannot tell whether precomputation has + * been performed */ +} + +/* + * ec_precompute_mont_data sets |group->mont_data| from |group->order| and + * returns one on success. On error it returns zero. + */ +int ec_precompute_mont_data(EC_GROUP *group) +{ + BN_CTX *ctx = BN_CTX_new(); + int ret = 0; + + BN_MONT_CTX_free(group->mont_data); + group->mont_data = NULL; + + if (ctx == NULL) + goto err; + + group->mont_data = BN_MONT_CTX_new(); + if (group->mont_data == NULL) + goto err; + + if (!BN_MONT_CTX_set(group->mont_data, group->order, ctx)) { + BN_MONT_CTX_free(group->mont_data); + group->mont_data = NULL; + goto err; + } + + ret = 1; + + err: + + BN_CTX_free(ctx); + return ret; +} + +int EC_KEY_set_ex_data(EC_KEY *key, int idx, void *arg) +{ + return CRYPTO_set_ex_data(&key->ex_data, idx, arg); +} + +void *EC_KEY_get_ex_data(const EC_KEY *key, int idx) +{ + return CRYPTO_get_ex_data(&key->ex_data, idx); +} + +int ec_group_simple_order_bits(const EC_GROUP *group) +{ + if (group->order == NULL) + return 0; + return BN_num_bits(group->order); +} diff --git a/openssl-1.1.0h/crypto/ec/ec_mult.c b/openssl-1.1.0h/crypto/ec/ec_mult.c new file mode 100644 index 0000000..b39777f --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_mult.c @@ -0,0 +1,684 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <string.h> +#include <openssl/err.h> + +#include "internal/cryptlib.h" +#include "internal/bn_int.h" +#include "ec_lcl.h" + +/* + * This file implements the wNAF-based interleaving multi-exponentiation method + * Formerly at: + * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp + * You might now find it here: + * http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13 + * http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf + * For multiplication with precomputation, we use wNAF splitting, formerly at: + * http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp + */ + +/* structure for precomputed multiples of the generator */ +struct ec_pre_comp_st { + const EC_GROUP *group; /* parent EC_GROUP object */ + size_t blocksize; /* block size for wNAF splitting */ + size_t numblocks; /* max. number of blocks for which we have + * precomputation */ + size_t w; /* window size */ + EC_POINT **points; /* array with pre-calculated multiples of + * generator: 'num' pointers to EC_POINT + * objects followed by a NULL */ + size_t num; /* numblocks * 2^(w-1) */ + int references; + CRYPTO_RWLOCK *lock; +}; + +static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group) +{ + EC_PRE_COMP *ret = NULL; + + if (!group) + return NULL; + + ret = OPENSSL_zalloc(sizeof(*ret)); + if (ret == NULL) { + ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->group = group; + ret->blocksize = 8; /* default */ + ret->w = 4; /* default */ + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre) +{ + int i; + if (pre != NULL) + CRYPTO_atomic_add(&pre->references, 1, &i, pre->lock); + return pre; +} + +void EC_ec_pre_comp_free(EC_PRE_COMP *pre) +{ + int i; + + if (pre == NULL) + return; + + CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock); + REF_PRINT_COUNT("EC_ec", pre); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + if (pre->points != NULL) { + EC_POINT **pts; + + for (pts = pre->points; *pts != NULL; pts++) + EC_POINT_free(*pts); + OPENSSL_free(pre->points); + } + CRYPTO_THREAD_lock_free(pre->lock); + OPENSSL_free(pre); +} + +/* + * TODO: table should be optimised for the wNAF-based implementation, + * sometimes smaller windows will give better performance (thus the + * boundaries should be increased) + */ +#define EC_window_bits_for_scalar_size(b) \ + ((size_t) \ + ((b) >= 2000 ? 6 : \ + (b) >= 800 ? 5 : \ + (b) >= 300 ? 4 : \ + (b) >= 70 ? 3 : \ + (b) >= 20 ? 2 : \ + 1)) + +/*- + * Compute + * \sum scalars[i]*points[i], + * also including + * scalar*generator + * in the addition if scalar != NULL + */ +int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + const EC_POINT *generator = NULL; + EC_POINT *tmp = NULL; + size_t totalnum; + size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */ + size_t pre_points_per_block = 0; + size_t i, j; + int k; + int r_is_inverted = 0; + int r_is_at_infinity = 1; + size_t *wsize = NULL; /* individual window sizes */ + signed char **wNAF = NULL; /* individual wNAFs */ + size_t *wNAF_len = NULL; + size_t max_len = 0; + size_t num_val; + EC_POINT **val = NULL; /* precomputation */ + EC_POINT **v; + EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or + * 'pre_comp->points' */ + const EC_PRE_COMP *pre_comp = NULL; + int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be + * treated like other scalars, i.e. + * precomputation is not available */ + int ret = 0; + + if (group->meth != r->meth) { + ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + + if ((scalar == NULL) && (num == 0)) { + return EC_POINT_set_to_infinity(group, r); + } + + for (i = 0; i < num; i++) { + if (group->meth != points[i]->meth) { + ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + goto err; + } + + if (scalar != NULL) { + generator = EC_GROUP_get0_generator(group); + if (generator == NULL) { + ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); + goto err; + } + + /* look if we can use precomputed multiples of generator */ + + pre_comp = group->pre_comp.ec; + if (pre_comp && pre_comp->numblocks + && (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == + 0)) { + blocksize = pre_comp->blocksize; + + /* + * determine maximum number of blocks that wNAF splitting may + * yield (NB: maximum wNAF length is bit length plus one) + */ + numblocks = (BN_num_bits(scalar) / blocksize) + 1; + + /* + * we cannot use more blocks than we have precomputation for + */ + if (numblocks > pre_comp->numblocks) + numblocks = pre_comp->numblocks; + + pre_points_per_block = (size_t)1 << (pre_comp->w - 1); + + /* check that pre_comp looks sane */ + if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + goto err; + } + } else { + /* can't use precomputation */ + pre_comp = NULL; + numblocks = 1; + num_scalar = 1; /* treat 'scalar' like 'num'-th element of + * 'scalars' */ + } + } + + totalnum = num + numblocks; + + wsize = OPENSSL_malloc(totalnum * sizeof(wsize[0])); + wNAF_len = OPENSSL_malloc(totalnum * sizeof(wNAF_len[0])); + /* include space for pivot */ + wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0])); + val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0])); + + /* Ensure wNAF is initialised in case we end up going to err */ + if (wNAF != NULL) + wNAF[0] = NULL; /* preliminary pivot */ + + if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * num_val will be the total number of temporarily precomputed points + */ + num_val = 0; + + for (i = 0; i < num + num_scalar; i++) { + size_t bits; + + bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); + wsize[i] = EC_window_bits_for_scalar_size(bits); + num_val += (size_t)1 << (wsize[i] - 1); + wNAF[i + 1] = NULL; /* make sure we always have a pivot */ + wNAF[i] = + bn_compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], + &wNAF_len[i]); + if (wNAF[i] == NULL) + goto err; + if (wNAF_len[i] > max_len) + max_len = wNAF_len[i]; + } + + if (numblocks) { + /* we go here iff scalar != NULL */ + + if (pre_comp == NULL) { + if (num_scalar != 1) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + goto err; + } + /* we have already generated a wNAF for 'scalar' */ + } else { + signed char *tmp_wNAF = NULL; + size_t tmp_len = 0; + + if (num_scalar != 0) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + goto err; + } + + /* + * use the window size for which we have precomputation + */ + wsize[num] = pre_comp->w; + tmp_wNAF = bn_compute_wNAF(scalar, wsize[num], &tmp_len); + if (!tmp_wNAF) + goto err; + + if (tmp_len <= max_len) { + /* + * One of the other wNAFs is at least as long as the wNAF + * belonging to the generator, so wNAF splitting will not buy + * us anything. + */ + + numblocks = 1; + totalnum = num + 1; /* don't use wNAF splitting */ + wNAF[num] = tmp_wNAF; + wNAF[num + 1] = NULL; + wNAF_len[num] = tmp_len; + /* + * pre_comp->points starts with the points that we need here: + */ + val_sub[num] = pre_comp->points; + } else { + /* + * don't include tmp_wNAF directly into wNAF array - use wNAF + * splitting and include the blocks + */ + + signed char *pp; + EC_POINT **tmp_points; + + if (tmp_len < numblocks * blocksize) { + /* + * possibly we can do with fewer blocks than estimated + */ + numblocks = (tmp_len + blocksize - 1) / blocksize; + if (numblocks > pre_comp->numblocks) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + OPENSSL_free(tmp_wNAF); + goto err; + } + totalnum = num + numblocks; + } + + /* split wNAF in 'numblocks' parts */ + pp = tmp_wNAF; + tmp_points = pre_comp->points; + + for (i = num; i < totalnum; i++) { + if (i < totalnum - 1) { + wNAF_len[i] = blocksize; + if (tmp_len < blocksize) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + OPENSSL_free(tmp_wNAF); + goto err; + } + tmp_len -= blocksize; + } else + /* + * last block gets whatever is left (this could be + * more or less than 'blocksize'!) + */ + wNAF_len[i] = tmp_len; + + wNAF[i + 1] = NULL; + wNAF[i] = OPENSSL_malloc(wNAF_len[i]); + if (wNAF[i] == NULL) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); + OPENSSL_free(tmp_wNAF); + goto err; + } + memcpy(wNAF[i], pp, wNAF_len[i]); + if (wNAF_len[i] > max_len) + max_len = wNAF_len[i]; + + if (*tmp_points == NULL) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + OPENSSL_free(tmp_wNAF); + goto err; + } + val_sub[i] = tmp_points; + tmp_points += pre_points_per_block; + pp += blocksize; + } + OPENSSL_free(tmp_wNAF); + } + } + } + + /* + * All points we precompute now go into a single array 'val'. + * 'val_sub[i]' is a pointer to the subarray for the i-th point, or to a + * subarray of 'pre_comp->points' if we already have precomputation. + */ + val = OPENSSL_malloc((num_val + 1) * sizeof(val[0])); + if (val == NULL) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + val[num_val] = NULL; /* pivot element */ + + /* allocate points for precomputation */ + v = val; + for (i = 0; i < num + num_scalar; i++) { + val_sub[i] = v; + for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { + *v = EC_POINT_new(group); + if (*v == NULL) + goto err; + v++; + } + } + if (!(v == val + num_val)) { + ECerr(EC_F_EC_WNAF_MUL, ERR_R_INTERNAL_ERROR); + goto err; + } + + if ((tmp = EC_POINT_new(group)) == NULL) + goto err; + + /*- + * prepare precomputed values: + * val_sub[i][0] := points[i] + * val_sub[i][1] := 3 * points[i] + * val_sub[i][2] := 5 * points[i] + * ... + */ + for (i = 0; i < num + num_scalar; i++) { + if (i < num) { + if (!EC_POINT_copy(val_sub[i][0], points[i])) + goto err; + } else { + if (!EC_POINT_copy(val_sub[i][0], generator)) + goto err; + } + + if (wsize[i] > 1) { + if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) + goto err; + for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { + if (!EC_POINT_add + (group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) + goto err; + } + } + } + + if (!EC_POINTs_make_affine(group, num_val, val, ctx)) + goto err; + + r_is_at_infinity = 1; + + for (k = max_len - 1; k >= 0; k--) { + if (!r_is_at_infinity) { + if (!EC_POINT_dbl(group, r, r, ctx)) + goto err; + } + + for (i = 0; i < totalnum; i++) { + if (wNAF_len[i] > (size_t)k) { + int digit = wNAF[i][k]; + int is_neg; + + if (digit) { + is_neg = digit < 0; + + if (is_neg) + digit = -digit; + + if (is_neg != r_is_inverted) { + if (!r_is_at_infinity) { + if (!EC_POINT_invert(group, r, ctx)) + goto err; + } + r_is_inverted = !r_is_inverted; + } + + /* digit > 0 */ + + if (r_is_at_infinity) { + if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) + goto err; + r_is_at_infinity = 0; + } else { + if (!EC_POINT_add + (group, r, r, val_sub[i][digit >> 1], ctx)) + goto err; + } + } + } + } + } + + if (r_is_at_infinity) { + if (!EC_POINT_set_to_infinity(group, r)) + goto err; + } else { + if (r_is_inverted) + if (!EC_POINT_invert(group, r, ctx)) + goto err; + } + + ret = 1; + + err: + BN_CTX_free(new_ctx); + EC_POINT_free(tmp); + OPENSSL_free(wsize); + OPENSSL_free(wNAF_len); + if (wNAF != NULL) { + signed char **w; + + for (w = wNAF; *w != NULL; w++) + OPENSSL_free(*w); + + OPENSSL_free(wNAF); + } + if (val != NULL) { + for (v = val; *v != NULL; v++) + EC_POINT_clear_free(*v); + + OPENSSL_free(val); + } + OPENSSL_free(val_sub); + return ret; +} + +/*- + * ec_wNAF_precompute_mult() + * creates an EC_PRE_COMP object with preprecomputed multiples of the generator + * for use with wNAF splitting as implemented in ec_wNAF_mul(). + * + * 'pre_comp->points' is an array of multiples of the generator + * of the following form: + * points[0] = generator; + * points[1] = 3 * generator; + * ... + * points[2^(w-1)-1] = (2^(w-1)-1) * generator; + * points[2^(w-1)] = 2^blocksize * generator; + * points[2^(w-1)+1] = 3 * 2^blocksize * generator; + * ... + * points[2^(w-1)*(numblocks-1)-1] = (2^(w-1)) * 2^(blocksize*(numblocks-2)) * generator + * points[2^(w-1)*(numblocks-1)] = 2^(blocksize*(numblocks-1)) * generator + * ... + * points[2^(w-1)*numblocks-1] = (2^(w-1)) * 2^(blocksize*(numblocks-1)) * generator + * points[2^(w-1)*numblocks] = NULL + */ +int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + const EC_POINT *generator; + EC_POINT *tmp_point = NULL, *base = NULL, **var; + BN_CTX *new_ctx = NULL; + const BIGNUM *order; + size_t i, bits, w, pre_points_per_block, blocksize, numblocks, num; + EC_POINT **points = NULL; + EC_PRE_COMP *pre_comp; + int ret = 0; + + /* if there is an old EC_PRE_COMP object, throw it away */ + EC_pre_comp_free(group); + if ((pre_comp = ec_pre_comp_new(group)) == NULL) + return 0; + + generator = EC_GROUP_get0_generator(group); + if (generator == NULL) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR); + goto err; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + goto err; + } + + BN_CTX_start(ctx); + + order = EC_GROUP_get0_order(group); + if (order == NULL) + goto err; + if (BN_is_zero(order)) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER); + goto err; + } + + bits = BN_num_bits(order); + /* + * The following parameters mean we precompute (approximately) one point + * per bit. TBD: The combination 8, 4 is perfect for 160 bits; for other + * bit lengths, other parameter combinations might provide better + * efficiency. + */ + blocksize = 8; + w = 4; + if (EC_window_bits_for_scalar_size(bits) > w) { + /* let's not make the window too small ... */ + w = EC_window_bits_for_scalar_size(bits); + } + + numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks + * to use for wNAF + * splitting */ + + pre_points_per_block = (size_t)1 << (w - 1); + num = pre_points_per_block * numblocks; /* number of points to compute + * and store */ + + points = OPENSSL_malloc(sizeof(*points) * (num + 1)); + if (points == NULL) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); + goto err; + } + + var = points; + var[num] = NULL; /* pivot */ + for (i = 0; i < num; i++) { + if ((var[i] = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); + goto err; + } + } + + if ((tmp_point = EC_POINT_new(group)) == NULL + || (base = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_MALLOC_FAILURE); + goto err; + } + + if (!EC_POINT_copy(base, generator)) + goto err; + + /* do the precomputation */ + for (i = 0; i < numblocks; i++) { + size_t j; + + if (!EC_POINT_dbl(group, tmp_point, base, ctx)) + goto err; + + if (!EC_POINT_copy(*var++, base)) + goto err; + + for (j = 1; j < pre_points_per_block; j++, var++) { + /* + * calculate odd multiples of the current base point + */ + if (!EC_POINT_add(group, *var, tmp_point, *(var - 1), ctx)) + goto err; + } + + if (i < numblocks - 1) { + /* + * get the next base (multiply current one by 2^blocksize) + */ + size_t k; + + if (blocksize <= 2) { + ECerr(EC_F_EC_WNAF_PRECOMPUTE_MULT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (!EC_POINT_dbl(group, base, tmp_point, ctx)) + goto err; + for (k = 2; k < blocksize; k++) { + if (!EC_POINT_dbl(group, base, base, ctx)) + goto err; + } + } + } + + if (!EC_POINTs_make_affine(group, num, points, ctx)) + goto err; + + pre_comp->group = group; + pre_comp->blocksize = blocksize; + pre_comp->numblocks = numblocks; + pre_comp->w = w; + pre_comp->points = points; + points = NULL; + pre_comp->num = num; + SETPRECOMP(group, ec, pre_comp); + pre_comp = NULL; + ret = 1; + + err: + if (ctx != NULL) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + EC_ec_pre_comp_free(pre_comp); + if (points) { + EC_POINT **p; + + for (p = points; *p != NULL; p++) + EC_POINT_free(*p); + OPENSSL_free(points); + } + EC_POINT_free(tmp_point); + EC_POINT_free(base); + return ret; +} + +int ec_wNAF_have_precompute_mult(const EC_GROUP *group) +{ + return HAVEPRECOMP(group, ec); +} diff --git a/openssl-1.1.0h/crypto/ec/ec_oct.c b/openssl-1.1.0h/crypto/ec/ec_oct.c new file mode 100644 index 0000000..effc42a --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_oct.c @@ -0,0 +1,165 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Binary polynomial ECC support in OpenSSL originally developed by + * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. + */ + +#include <string.h> + +#include <openssl/err.h> +#include <openssl/opensslv.h> + +#include "ec_lcl.h" + +int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + int y_bit, BN_CTX *ctx) +{ + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates(group, point, x, + y_bit, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, + EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_set_compressed_coordinates(group, point, x, + y_bit, ctx); +#endif + } + return group->meth->point_set_compressed_coordinates(group, point, x, + y_bit, ctx); +} + +#ifndef OPENSSL_NO_EC2M +int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, + EC_POINT *point, const BIGNUM *x, + int y_bit, BN_CTX *ctx) +{ + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, + ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, + EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates(group, point, x, + y_bit, ctx); + else + return ec_GF2m_simple_set_compressed_coordinates(group, point, x, + y_bit, ctx); + } + return group->meth->point_set_compressed_coordinates(group, point, x, + y_bit, ctx); +} +#endif + +size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, unsigned char *buf, + size_t len, BN_CTX *ctx) +{ + if (group->meth->point2oct == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { + ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_point2oct(group, point, form, buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_point2oct(group, point, + form, buf, len, ctx); +#endif + } + + return group->meth->point2oct(group, point, form, buf, len, ctx); +} + +int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ + if (group->meth->oct2point == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) { + ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if (group->meth->flags & EC_FLAGS_DEFAULT_OCT) { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_oct2point(group, point, buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_oct2point(group, point, buf, len, ctx); +#endif + } + return group->meth->oct2point(group, point, buf, len, ctx); +} + +size_t EC_POINT_point2buf(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char **pbuf, BN_CTX *ctx) +{ + size_t len; + unsigned char *buf; + len = EC_POINT_point2oct(group, point, form, NULL, 0, NULL); + if (len == 0) + return 0; + buf = OPENSSL_malloc(len); + if (buf == NULL) + return 0; + len = EC_POINT_point2oct(group, point, form, buf, len, ctx); + if (len == 0) { + OPENSSL_free(buf); + return 0; + } + *pbuf = buf; + return len; +} diff --git a/openssl-1.1.0h/crypto/ec/ec_pmeth.c b/openssl-1.1.0h/crypto/ec/ec_pmeth.c new file mode 100644 index 0000000..68ff2bb --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_pmeth.c @@ -0,0 +1,463 @@ +/* + * Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <stdio.h> +#include "internal/cryptlib.h" +#include <openssl/asn1t.h> +#include <openssl/x509.h> +#include <openssl/ec.h> +#include "ec_lcl.h" +#include <openssl/evp.h> +#include "internal/evp_int.h" + +/* EC pkey context structure */ + +typedef struct { + /* Key and paramgen group */ + EC_GROUP *gen_group; + /* message digest */ + const EVP_MD *md; + /* Duplicate key if custom cofactor needed */ + EC_KEY *co_key; + /* Cofactor mode */ + signed char cofactor_mode; + /* KDF (if any) to use for ECDH */ + char kdf_type; + /* Message digest to use for key derivation */ + const EVP_MD *kdf_md; + /* User key material */ + unsigned char *kdf_ukm; + size_t kdf_ukmlen; + /* KDF output length */ + size_t kdf_outlen; +} EC_PKEY_CTX; + +static int pkey_ec_init(EVP_PKEY_CTX *ctx) +{ + EC_PKEY_CTX *dctx; + + dctx = OPENSSL_zalloc(sizeof(*dctx)); + if (dctx == NULL) + return 0; + + dctx->cofactor_mode = -1; + dctx->kdf_type = EVP_PKEY_ECDH_KDF_NONE; + ctx->data = dctx; + return 1; +} + +static int pkey_ec_copy(EVP_PKEY_CTX *dst, EVP_PKEY_CTX *src) +{ + EC_PKEY_CTX *dctx, *sctx; + if (!pkey_ec_init(dst)) + return 0; + sctx = src->data; + dctx = dst->data; + if (sctx->gen_group) { + dctx->gen_group = EC_GROUP_dup(sctx->gen_group); + if (!dctx->gen_group) + return 0; + } + dctx->md = sctx->md; + + if (sctx->co_key) { + dctx->co_key = EC_KEY_dup(sctx->co_key); + if (!dctx->co_key) + return 0; + } + dctx->kdf_type = sctx->kdf_type; + dctx->kdf_md = sctx->kdf_md; + dctx->kdf_outlen = sctx->kdf_outlen; + if (sctx->kdf_ukm) { + dctx->kdf_ukm = OPENSSL_memdup(sctx->kdf_ukm, sctx->kdf_ukmlen); + if (!dctx->kdf_ukm) + return 0; + } else + dctx->kdf_ukm = NULL; + dctx->kdf_ukmlen = sctx->kdf_ukmlen; + return 1; +} + +static void pkey_ec_cleanup(EVP_PKEY_CTX *ctx) +{ + EC_PKEY_CTX *dctx = ctx->data; + if (dctx) { + EC_GROUP_free(dctx->gen_group); + EC_KEY_free(dctx->co_key); + OPENSSL_free(dctx->kdf_ukm); + OPENSSL_free(dctx); + } +} + +static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, + const unsigned char *tbs, size_t tbslen) +{ + int ret, type; + unsigned int sltmp; + EC_PKEY_CTX *dctx = ctx->data; + EC_KEY *ec = ctx->pkey->pkey.ec; + + if (!sig) { + *siglen = ECDSA_size(ec); + return 1; + } else if (*siglen < (size_t)ECDSA_size(ec)) { + ECerr(EC_F_PKEY_EC_SIGN, EC_R_BUFFER_TOO_SMALL); + return 0; + } + + if (dctx->md) + type = EVP_MD_type(dctx->md); + else + type = NID_sha1; + + ret = ECDSA_sign(type, tbs, tbslen, sig, &sltmp, ec); + + if (ret <= 0) + return ret; + *siglen = (size_t)sltmp; + return 1; +} + +static int pkey_ec_verify(EVP_PKEY_CTX *ctx, + const unsigned char *sig, size_t siglen, + const unsigned char *tbs, size_t tbslen) +{ + int ret, type; + EC_PKEY_CTX *dctx = ctx->data; + EC_KEY *ec = ctx->pkey->pkey.ec; + + if (dctx->md) + type = EVP_MD_type(dctx->md); + else + type = NID_sha1; + + ret = ECDSA_verify(type, tbs, tbslen, sig, siglen, ec); + + return ret; +} + +#ifndef OPENSSL_NO_EC +static int pkey_ec_derive(EVP_PKEY_CTX *ctx, unsigned char *key, + size_t *keylen) +{ + int ret; + size_t outlen; + const EC_POINT *pubkey = NULL; + EC_KEY *eckey; + EC_PKEY_CTX *dctx = ctx->data; + if (!ctx->pkey || !ctx->peerkey) { + ECerr(EC_F_PKEY_EC_DERIVE, EC_R_KEYS_NOT_SET); + return 0; + } + + eckey = dctx->co_key ? dctx->co_key : ctx->pkey->pkey.ec; + + if (!key) { + const EC_GROUP *group; + group = EC_KEY_get0_group(eckey); + *keylen = (EC_GROUP_get_degree(group) + 7) / 8; + return 1; + } + pubkey = EC_KEY_get0_public_key(ctx->peerkey->pkey.ec); + + /* + * NB: unlike PKCS#3 DH, if *outlen is less than maximum size this is not + * an error, the result is truncated. + */ + + outlen = *keylen; + + ret = ECDH_compute_key(key, outlen, pubkey, eckey, 0); + if (ret <= 0) + return 0; + *keylen = ret; + return 1; +} + +static int pkey_ec_kdf_derive(EVP_PKEY_CTX *ctx, + unsigned char *key, size_t *keylen) +{ + EC_PKEY_CTX *dctx = ctx->data; + unsigned char *ktmp = NULL; + size_t ktmplen; + int rv = 0; + if (dctx->kdf_type == EVP_PKEY_ECDH_KDF_NONE) + return pkey_ec_derive(ctx, key, keylen); + if (!key) { + *keylen = dctx->kdf_outlen; + return 1; + } + if (*keylen != dctx->kdf_outlen) + return 0; + if (!pkey_ec_derive(ctx, NULL, &ktmplen)) + return 0; + ktmp = OPENSSL_malloc(ktmplen); + if (ktmp == NULL) + return 0; + if (!pkey_ec_derive(ctx, ktmp, &ktmplen)) + goto err; + /* Do KDF stuff */ + if (!ECDH_KDF_X9_62(key, *keylen, ktmp, ktmplen, + dctx->kdf_ukm, dctx->kdf_ukmlen, dctx->kdf_md)) + goto err; + rv = 1; + + err: + OPENSSL_clear_free(ktmp, ktmplen); + return rv; +} +#endif + +static int pkey_ec_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) +{ + EC_PKEY_CTX *dctx = ctx->data; + EC_GROUP *group; + switch (type) { + case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: + group = EC_GROUP_new_by_curve_name(p1); + if (group == NULL) { + ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_CURVE); + return 0; + } + EC_GROUP_free(dctx->gen_group); + dctx->gen_group = group; + return 1; + + case EVP_PKEY_CTRL_EC_PARAM_ENC: + if (!dctx->gen_group) { + ECerr(EC_F_PKEY_EC_CTRL, EC_R_NO_PARAMETERS_SET); + return 0; + } + EC_GROUP_set_asn1_flag(dctx->gen_group, p1); + return 1; + +#ifndef OPENSSL_NO_EC + case EVP_PKEY_CTRL_EC_ECDH_COFACTOR: + if (p1 == -2) { + if (dctx->cofactor_mode != -1) + return dctx->cofactor_mode; + else { + EC_KEY *ec_key = ctx->pkey->pkey.ec; + return EC_KEY_get_flags(ec_key) & EC_FLAG_COFACTOR_ECDH ? 1 : + 0; + } + } else if (p1 < -1 || p1 > 1) + return -2; + dctx->cofactor_mode = p1; + if (p1 != -1) { + EC_KEY *ec_key = ctx->pkey->pkey.ec; + if (!ec_key->group) + return -2; + /* If cofactor is 1 cofactor mode does nothing */ + if (BN_is_one(ec_key->group->cofactor)) + return 1; + if (!dctx->co_key) { + dctx->co_key = EC_KEY_dup(ec_key); + if (!dctx->co_key) + return 0; + } + if (p1) + EC_KEY_set_flags(dctx->co_key, EC_FLAG_COFACTOR_ECDH); + else + EC_KEY_clear_flags(dctx->co_key, EC_FLAG_COFACTOR_ECDH); + } else { + EC_KEY_free(dctx->co_key); + dctx->co_key = NULL; + } + return 1; +#endif + + case EVP_PKEY_CTRL_EC_KDF_TYPE: + if (p1 == -2) + return dctx->kdf_type; + if (p1 != EVP_PKEY_ECDH_KDF_NONE && p1 != EVP_PKEY_ECDH_KDF_X9_62) + return -2; + dctx->kdf_type = p1; + return 1; + + case EVP_PKEY_CTRL_EC_KDF_MD: + dctx->kdf_md = p2; + return 1; + + case EVP_PKEY_CTRL_GET_EC_KDF_MD: + *(const EVP_MD **)p2 = dctx->kdf_md; + return 1; + + case EVP_PKEY_CTRL_EC_KDF_OUTLEN: + if (p1 <= 0) + return -2; + dctx->kdf_outlen = (size_t)p1; + return 1; + + case EVP_PKEY_CTRL_GET_EC_KDF_OUTLEN: + *(int *)p2 = dctx->kdf_outlen; + return 1; + + case EVP_PKEY_CTRL_EC_KDF_UKM: + OPENSSL_free(dctx->kdf_ukm); + dctx->kdf_ukm = p2; + if (p2) + dctx->kdf_ukmlen = p1; + else + dctx->kdf_ukmlen = 0; + return 1; + + case EVP_PKEY_CTRL_GET_EC_KDF_UKM: + *(unsigned char **)p2 = dctx->kdf_ukm; + return dctx->kdf_ukmlen; + + case EVP_PKEY_CTRL_MD: + if (EVP_MD_type((const EVP_MD *)p2) != NID_sha1 && + EVP_MD_type((const EVP_MD *)p2) != NID_ecdsa_with_SHA1 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha224 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha256 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha384 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha512) { + ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_DIGEST_TYPE); + return 0; + } + dctx->md = p2; + return 1; + + case EVP_PKEY_CTRL_GET_MD: + *(const EVP_MD **)p2 = dctx->md; + return 1; + + case EVP_PKEY_CTRL_PEER_KEY: + /* Default behaviour is OK */ + case EVP_PKEY_CTRL_DIGESTINIT: + case EVP_PKEY_CTRL_PKCS7_SIGN: + case EVP_PKEY_CTRL_CMS_SIGN: + return 1; + + default: + return -2; + + } +} + +static int pkey_ec_ctrl_str(EVP_PKEY_CTX *ctx, + const char *type, const char *value) +{ + if (strcmp(type, "ec_paramgen_curve") == 0) { + int nid; + nid = EC_curve_nist2nid(value); + if (nid == NID_undef) + nid = OBJ_sn2nid(value); + if (nid == NID_undef) + nid = OBJ_ln2nid(value); + if (nid == NID_undef) { + ECerr(EC_F_PKEY_EC_CTRL_STR, EC_R_INVALID_CURVE); + return 0; + } + return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); + } else if (strcmp(type, "ec_param_enc") == 0) { + int param_enc; + if (strcmp(value, "explicit") == 0) + param_enc = 0; + else if (strcmp(value, "named_curve") == 0) + param_enc = OPENSSL_EC_NAMED_CURVE; + else + return -2; + return EVP_PKEY_CTX_set_ec_param_enc(ctx, param_enc); + } else if (strcmp(type, "ecdh_kdf_md") == 0) { + const EVP_MD *md; + if ((md = EVP_get_digestbyname(value)) == NULL) { + ECerr(EC_F_PKEY_EC_CTRL_STR, EC_R_INVALID_DIGEST); + return 0; + } + return EVP_PKEY_CTX_set_ecdh_kdf_md(ctx, md); + } else if (strcmp(type, "ecdh_cofactor_mode") == 0) { + int co_mode; + co_mode = atoi(value); + return EVP_PKEY_CTX_set_ecdh_cofactor_mode(ctx, co_mode); + } + + return -2; +} + +static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) +{ + EC_KEY *ec = NULL; + EC_PKEY_CTX *dctx = ctx->data; + int ret = 0; + if (dctx->gen_group == NULL) { + ECerr(EC_F_PKEY_EC_PARAMGEN, EC_R_NO_PARAMETERS_SET); + return 0; + } + ec = EC_KEY_new(); + if (ec == NULL) + return 0; + ret = EC_KEY_set_group(ec, dctx->gen_group); + if (ret) + EVP_PKEY_assign_EC_KEY(pkey, ec); + else + EC_KEY_free(ec); + return ret; +} + +static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) +{ + EC_KEY *ec = NULL; + EC_PKEY_CTX *dctx = ctx->data; + if (ctx->pkey == NULL && dctx->gen_group == NULL) { + ECerr(EC_F_PKEY_EC_KEYGEN, EC_R_NO_PARAMETERS_SET); + return 0; + } + ec = EC_KEY_new(); + if (!ec) + return 0; + EVP_PKEY_assign_EC_KEY(pkey, ec); + if (ctx->pkey) { + /* Note: if error return, pkey is freed by parent routine */ + if (!EVP_PKEY_copy_parameters(pkey, ctx->pkey)) + return 0; + } else { + if (!EC_KEY_set_group(ec, dctx->gen_group)) + return 0; + } + return EC_KEY_generate_key(pkey->pkey.ec); +} + +const EVP_PKEY_METHOD ec_pkey_meth = { + EVP_PKEY_EC, + 0, + pkey_ec_init, + pkey_ec_copy, + pkey_ec_cleanup, + + 0, + pkey_ec_paramgen, + + 0, + pkey_ec_keygen, + + 0, + pkey_ec_sign, + + 0, + pkey_ec_verify, + + 0, 0, + + 0, 0, 0, 0, + + 0, 0, + + 0, 0, + + 0, +#ifndef OPENSSL_NO_EC + pkey_ec_kdf_derive, +#else + 0, +#endif + pkey_ec_ctrl, + pkey_ec_ctrl_str +}; diff --git a/openssl-1.1.0h/crypto/ec/ec_print.c b/openssl-1.1.0h/crypto/ec/ec_print.c new file mode 100644 index 0000000..1afa2ce --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ec_print.c @@ -0,0 +1,119 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <openssl/crypto.h> +#include "ec_lcl.h" + +BIGNUM *EC_POINT_point2bn(const EC_GROUP *group, + const EC_POINT *point, + point_conversion_form_t form, + BIGNUM *ret, BN_CTX *ctx) +{ + size_t buf_len = 0; + unsigned char *buf; + + buf_len = EC_POINT_point2buf(group, point, form, &buf, ctx); + + if (buf_len == 0) + return NULL; + + ret = BN_bin2bn(buf, buf_len, ret); + + OPENSSL_free(buf); + + return ret; +} + +EC_POINT *EC_POINT_bn2point(const EC_GROUP *group, + const BIGNUM *bn, EC_POINT *point, BN_CTX *ctx) +{ + size_t buf_len = 0; + unsigned char *buf; + EC_POINT *ret; + + if ((buf_len = BN_num_bytes(bn)) == 0) + return NULL; + buf = OPENSSL_malloc(buf_len); + if (buf == NULL) + return NULL; + + if (!BN_bn2bin(bn, buf)) { + OPENSSL_free(buf); + return NULL; + } + + if (point == NULL) { + if ((ret = EC_POINT_new(group)) == NULL) { + OPENSSL_free(buf); + return NULL; + } + } else + ret = point; + + if (!EC_POINT_oct2point(group, ret, buf, buf_len, ctx)) { + if (ret != point) + EC_POINT_clear_free(ret); + OPENSSL_free(buf); + return NULL; + } + + OPENSSL_free(buf); + return ret; +} + +static const char *HEX_DIGITS = "0123456789ABCDEF"; + +/* the return value must be freed (using OPENSSL_free()) */ +char *EC_POINT_point2hex(const EC_GROUP *group, + const EC_POINT *point, + point_conversion_form_t form, BN_CTX *ctx) +{ + char *ret, *p; + size_t buf_len = 0, i; + unsigned char *buf = NULL, *pbuf; + + buf_len = EC_POINT_point2buf(group, point, form, &buf, ctx); + + if (buf_len == 0) + return NULL; + + ret = OPENSSL_malloc(buf_len * 2 + 2); + if (ret == NULL) { + OPENSSL_free(buf); + return NULL; + } + p = ret; + pbuf = buf; + for (i = buf_len; i > 0; i--) { + int v = (int)*(pbuf++); + *(p++) = HEX_DIGITS[v >> 4]; + *(p++) = HEX_DIGITS[v & 0x0F]; + } + *p = '\0'; + + OPENSSL_free(buf); + + return ret; +} + +EC_POINT *EC_POINT_hex2point(const EC_GROUP *group, + const char *buf, EC_POINT *point, BN_CTX *ctx) +{ + EC_POINT *ret = NULL; + BIGNUM *tmp_bn = NULL; + + if (!BN_hex2bn(&tmp_bn, buf)) + return NULL; + + ret = EC_POINT_bn2point(group, tmp_bn, point, ctx); + + BN_clear_free(tmp_bn); + + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecdh_kdf.c b/openssl-1.1.0h/crypto/ec/ecdh_kdf.c new file mode 100644 index 0000000..d47486e --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecdh_kdf.c @@ -0,0 +1,68 @@ +/* + * Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <string.h> +#include <openssl/ec.h> +#include <openssl/evp.h> + +/* Key derivation function from X9.62/SECG */ +/* Way more than we will ever need */ +#define ECDH_KDF_MAX (1 << 30) + +int ECDH_KDF_X9_62(unsigned char *out, size_t outlen, + const unsigned char *Z, size_t Zlen, + const unsigned char *sinfo, size_t sinfolen, + const EVP_MD *md) +{ + EVP_MD_CTX *mctx = NULL; + int rv = 0; + unsigned int i; + size_t mdlen; + unsigned char ctr[4]; + if (sinfolen > ECDH_KDF_MAX || outlen > ECDH_KDF_MAX + || Zlen > ECDH_KDF_MAX) + return 0; + mctx = EVP_MD_CTX_new(); + if (mctx == NULL) + return 0; + mdlen = EVP_MD_size(md); + for (i = 1;; i++) { + unsigned char mtmp[EVP_MAX_MD_SIZE]; + if (!EVP_DigestInit_ex(mctx, md, NULL)) + goto err; + ctr[3] = i & 0xFF; + ctr[2] = (i >> 8) & 0xFF; + ctr[1] = (i >> 16) & 0xFF; + ctr[0] = (i >> 24) & 0xFF; + if (!EVP_DigestUpdate(mctx, Z, Zlen)) + goto err; + if (!EVP_DigestUpdate(mctx, ctr, sizeof(ctr))) + goto err; + if (!EVP_DigestUpdate(mctx, sinfo, sinfolen)) + goto err; + if (outlen >= mdlen) { + if (!EVP_DigestFinal(mctx, out, NULL)) + goto err; + outlen -= mdlen; + if (outlen == 0) + break; + out += mdlen; + } else { + if (!EVP_DigestFinal(mctx, mtmp, NULL)) + goto err; + memcpy(out, mtmp, outlen); + OPENSSL_cleanse(mtmp, mdlen); + break; + } + } + rv = 1; + err: + EVP_MD_CTX_free(mctx); + return rv; +} diff --git a/openssl-1.1.0h/crypto/ec/ecdh_ossl.c b/openssl-1.1.0h/crypto/ec/ecdh_ossl.c new file mode 100644 index 0000000..a865145 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecdh_ossl.c @@ -0,0 +1,147 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The ECDH software is originally written by Douglas Stebila of + * Sun Microsystems Laboratories. + * + */ + +#include <string.h> +#include <limits.h> + +#include "internal/cryptlib.h" + +#include <openssl/err.h> +#include <openssl/bn.h> +#include <openssl/objects.h> +#include <openssl/ec.h> +#include "ec_lcl.h" + +int ossl_ecdh_compute_key(unsigned char **psec, size_t *pseclen, + const EC_POINT *pub_key, const EC_KEY *ecdh) +{ + if (ecdh->group->meth->ecdh_compute_key == NULL) { + ECerr(EC_F_OSSL_ECDH_COMPUTE_KEY, EC_R_CURVE_DOES_NOT_SUPPORT_ECDH); + return 0; + } + + return ecdh->group->meth->ecdh_compute_key(psec, pseclen, pub_key, ecdh); +} + +/*- + * This implementation is based on the following primitives in the IEEE 1363 standard: + * - ECKAS-DH1 + * - ECSVDP-DH + */ +int ecdh_simple_compute_key(unsigned char **pout, size_t *poutlen, + const EC_POINT *pub_key, const EC_KEY *ecdh) +{ + BN_CTX *ctx; + EC_POINT *tmp = NULL; + BIGNUM *x = NULL, *y = NULL; + const BIGNUM *priv_key; + const EC_GROUP *group; + int ret = 0; + size_t buflen, len; + unsigned char *buf = NULL; + + if ((ctx = BN_CTX_new()) == NULL) + goto err; + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_MALLOC_FAILURE); + goto err; + } + + priv_key = EC_KEY_get0_private_key(ecdh); + if (priv_key == NULL) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, EC_R_NO_PRIVATE_VALUE); + goto err; + } + + group = EC_KEY_get0_group(ecdh); + + if (EC_KEY_get_flags(ecdh) & EC_FLAG_COFACTOR_ECDH) { + if (!EC_GROUP_get_cofactor(group, x, NULL) || + !BN_mul(x, x, priv_key, ctx)) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_MALLOC_FAILURE); + goto err; + } + priv_key = x; + } + + if ((tmp = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_MALLOC_FAILURE); + goto err; + } + + if (!EC_POINT_mul(group, tmp, NULL, pub_key, priv_key, ctx)) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, EC_R_POINT_ARITHMETIC_FAILURE); + goto err; + } + + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == + NID_X9_62_prime_field) { + if (!EC_POINT_get_affine_coordinates_GFp(group, tmp, x, y, ctx)) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, EC_R_POINT_ARITHMETIC_FAILURE); + goto err; + } + } +#ifndef OPENSSL_NO_EC2M + else { + if (!EC_POINT_get_affine_coordinates_GF2m(group, tmp, x, y, ctx)) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, EC_R_POINT_ARITHMETIC_FAILURE); + goto err; + } + } +#endif + + buflen = (EC_GROUP_get_degree(group) + 7) / 8; + len = BN_num_bytes(x); + if (len > buflen) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_INTERNAL_ERROR); + goto err; + } + if ((buf = OPENSSL_malloc(buflen)) == NULL) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_MALLOC_FAILURE); + goto err; + } + + memset(buf, 0, buflen - len); + if (len != (size_t)BN_bn2bin(x, buf + buflen - len)) { + ECerr(EC_F_ECDH_SIMPLE_COMPUTE_KEY, ERR_R_BN_LIB); + goto err; + } + + *pout = buf; + *poutlen = buflen; + buf = NULL; + + ret = 1; + + err: + EC_POINT_free(tmp); + if (ctx) + BN_CTX_end(ctx); + BN_CTX_free(ctx); + OPENSSL_free(buf); + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecdsa_ossl.c b/openssl-1.1.0h/crypto/ec/ecdsa_ossl.c new file mode 100644 index 0000000..72e2f0f --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecdsa_ossl.c @@ -0,0 +1,476 @@ +/* + * Copyright 2002-2017 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <string.h> +#include <openssl/err.h> +#include <openssl/obj_mac.h> +#include <openssl/bn.h> +#include <openssl/rand.h> +#include <openssl/ec.h> +#include "ec_lcl.h" + +int ossl_ecdsa_sign(int type, const unsigned char *dgst, int dlen, + unsigned char *sig, unsigned int *siglen, + const BIGNUM *kinv, const BIGNUM *r, EC_KEY *eckey) +{ + ECDSA_SIG *s; + RAND_seed(dgst, dlen); + s = ECDSA_do_sign_ex(dgst, dlen, kinv, r, eckey); + if (s == NULL) { + *siglen = 0; + return 0; + } + *siglen = i2d_ECDSA_SIG(s, &sig); + ECDSA_SIG_free(s); + return 1; +} + +static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, + BIGNUM **kinvp, BIGNUM **rp, + const unsigned char *dgst, int dlen) +{ + BN_CTX *ctx = NULL; + BIGNUM *k = NULL, *r = NULL, *X = NULL; + const BIGNUM *order; + EC_POINT *tmp_point = NULL; + const EC_GROUP *group; + int ret = 0; + int order_bits; + + if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + if (!EC_KEY_can_sign(eckey)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING); + return 0; + } + + if (ctx_in == NULL) { + if ((ctx = BN_CTX_new()) == NULL) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); + return 0; + } + } else + ctx = ctx_in; + + k = BN_new(); /* this value is later returned in *kinvp */ + r = BN_new(); /* this value is later returned in *rp */ + X = BN_new(); + if (k == NULL || r == NULL || X == NULL) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_MALLOC_FAILURE); + goto err; + } + if ((tmp_point = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); + goto err; + } + order = EC_GROUP_get0_order(group); + if (order == NULL) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); + goto err; + } + + /* Preallocate space */ + order_bits = BN_num_bits(order); + if (!BN_set_bit(k, order_bits) + || !BN_set_bit(r, order_bits) + || !BN_set_bit(X, order_bits)) + goto err; + + do { + /* get random k */ + do + if (dgst != NULL) { + if (!BN_generate_dsa_nonce + (k, order, EC_KEY_get0_private_key(eckey), dgst, dlen, + ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, + EC_R_RANDOM_NUMBER_GENERATION_FAILED); + goto err; + } + } else { + if (!BN_rand_range(k, order)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, + EC_R_RANDOM_NUMBER_GENERATION_FAILED); + goto err; + } + } + while (BN_is_zero(k)); + + /* + * We do not want timing information to leak the length of k, so we + * compute G*k using an equivalent scalar of fixed bit-length. + * + * We unconditionally perform both of these additions to prevent a + * small timing information leakage. We then choose the sum that is + * one bit longer than the order. This guarantees the code + * path used in the constant time implementations elsewhere. + * + * TODO: revisit the BN_copy aiming for a memory access agnostic + * conditional copy. + */ + if (!BN_add(r, k, order) + || !BN_add(X, r, order) + || !BN_copy(k, BN_num_bits(r) > order_bits ? r : X)) + goto err; + + /* compute r the x-coordinate of generator * k */ + if (!EC_POINT_mul(group, tmp_point, k, NULL, NULL, ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); + goto err; + } + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == + NID_X9_62_prime_field) { + if (!EC_POINT_get_affine_coordinates_GFp + (group, tmp_point, X, NULL, ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); + goto err; + } + } +#ifndef OPENSSL_NO_EC2M + else { /* NID_X9_62_characteristic_two_field */ + + if (!EC_POINT_get_affine_coordinates_GF2m(group, + tmp_point, X, NULL, + ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_EC_LIB); + goto err; + } + } +#endif + if (!BN_nnmod(r, X, order, ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); + goto err; + } + } + while (BN_is_zero(r)); + + /* compute the inverse of k */ + if (EC_GROUP_get_mont_data(group) != NULL) { + /* + * We want inverse in constant time, therefore we utilize the fact + * order must be prime and use Fermats Little Theorem instead. + */ + if (!BN_set_word(X, 2)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); + goto err; + } + if (!BN_mod_sub(X, order, X, order, ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); + goto err; + } + BN_set_flags(X, BN_FLG_CONSTTIME); + if (!BN_mod_exp_mont_consttime + (k, k, X, order, ctx, EC_GROUP_get_mont_data(group))) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); + goto err; + } + } else { + if (!BN_mod_inverse(k, k, order, ctx)) { + ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB); + goto err; + } + } + + /* clear old values if necessary */ + BN_clear_free(*rp); + BN_clear_free(*kinvp); + /* save the pre-computed values */ + *rp = r; + *kinvp = k; + ret = 1; + err: + if (!ret) { + BN_clear_free(k); + BN_clear_free(r); + } + if (ctx != ctx_in) + BN_CTX_free(ctx); + EC_POINT_free(tmp_point); + BN_clear_free(X); + return (ret); +} + +int ossl_ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, + BIGNUM **rp) +{ + return ecdsa_sign_setup(eckey, ctx_in, kinvp, rp, NULL, 0); +} + +ECDSA_SIG *ossl_ecdsa_sign_sig(const unsigned char *dgst, int dgst_len, + const BIGNUM *in_kinv, const BIGNUM *in_r, + EC_KEY *eckey) +{ + int ok = 0, i; + BIGNUM *kinv = NULL, *s, *m = NULL, *tmp = NULL; + const BIGNUM *order, *ckinv; + BN_CTX *ctx = NULL; + const EC_GROUP *group; + ECDSA_SIG *ret; + const BIGNUM *priv_key; + + group = EC_KEY_get0_group(eckey); + priv_key = EC_KEY_get0_private_key(eckey); + + if (group == NULL || priv_key == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_PASSED_NULL_PARAMETER); + return NULL; + } + + if (!EC_KEY_can_sign(eckey)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING); + return NULL; + } + + ret = ECDSA_SIG_new(); + if (ret == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); + return NULL; + } + ret->r = BN_new(); + ret->s = BN_new(); + if (ret->r == NULL || ret->s == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); + goto err; + } + s = ret->s; + + if ((ctx = BN_CTX_new()) == NULL || + (tmp = BN_new()) == NULL || (m = BN_new()) == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); + goto err; + } + + order = EC_GROUP_get0_order(group); + if (order == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_EC_LIB); + goto err; + } + i = BN_num_bits(order); + /* + * Need to truncate digest if it is too long: first truncate whole bytes. + */ + if (8 * dgst_len > i) + dgst_len = (i + 7) / 8; + if (!BN_bin2bn(dgst, dgst_len, m)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); + goto err; + } + /* If still too long truncate remaining bits with a shift */ + if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7))) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); + goto err; + } + do { + if (in_kinv == NULL || in_r == NULL) { + if (!ecdsa_sign_setup(eckey, ctx, &kinv, &ret->r, dgst, dgst_len)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_ECDSA_LIB); + goto err; + } + ckinv = kinv; + } else { + ckinv = in_kinv; + if (BN_copy(ret->r, in_r) == NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_MALLOC_FAILURE); + goto err; + } + } + + if (!BN_mod_mul(tmp, priv_key, ret->r, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); + goto err; + } + if (!BN_mod_add_quick(s, tmp, m, order)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); + goto err; + } + if (!BN_mod_mul(s, s, ckinv, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, ERR_R_BN_LIB); + goto err; + } + if (BN_is_zero(s)) { + /* + * if kinv and r have been supplied by the caller don't to + * generate new kinv and r values + */ + if (in_kinv != NULL && in_r != NULL) { + ECerr(EC_F_OSSL_ECDSA_SIGN_SIG, EC_R_NEED_NEW_SETUP_VALUES); + goto err; + } + } else + /* s != 0 => we have a valid signature */ + break; + } + while (1); + + ok = 1; + err: + if (!ok) { + ECDSA_SIG_free(ret); + ret = NULL; + } + BN_CTX_free(ctx); + BN_clear_free(m); + BN_clear_free(tmp); + BN_clear_free(kinv); + return ret; +} + +/*- + * returns + * 1: correct signature + * 0: incorrect signature + * -1: error + */ +int ossl_ecdsa_verify(int type, const unsigned char *dgst, int dgst_len, + const unsigned char *sigbuf, int sig_len, EC_KEY *eckey) +{ + ECDSA_SIG *s; + const unsigned char *p = sigbuf; + unsigned char *der = NULL; + int derlen = -1; + int ret = -1; + + s = ECDSA_SIG_new(); + if (s == NULL) + return (ret); + if (d2i_ECDSA_SIG(&s, &p, sig_len) == NULL) + goto err; + /* Ensure signature uses DER and doesn't have trailing garbage */ + derlen = i2d_ECDSA_SIG(s, &der); + if (derlen != sig_len || memcmp(sigbuf, der, derlen) != 0) + goto err; + ret = ECDSA_do_verify(dgst, dgst_len, s, eckey); + err: + OPENSSL_clear_free(der, derlen); + ECDSA_SIG_free(s); + return (ret); +} + +int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len, + const ECDSA_SIG *sig, EC_KEY *eckey) +{ + int ret = -1, i; + BN_CTX *ctx; + const BIGNUM *order; + BIGNUM *u1, *u2, *m, *X; + EC_POINT *point = NULL; + const EC_GROUP *group; + const EC_POINT *pub_key; + + /* check input values */ + if (eckey == NULL || (group = EC_KEY_get0_group(eckey)) == NULL || + (pub_key = EC_KEY_get0_public_key(eckey)) == NULL || sig == NULL) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_MISSING_PARAMETERS); + return -1; + } + + if (!EC_KEY_can_sign(eckey)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_CURVE_DOES_NOT_SUPPORT_SIGNING); + return -1; + } + + ctx = BN_CTX_new(); + if (ctx == NULL) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_MALLOC_FAILURE); + return -1; + } + BN_CTX_start(ctx); + u1 = BN_CTX_get(ctx); + u2 = BN_CTX_get(ctx); + m = BN_CTX_get(ctx); + X = BN_CTX_get(ctx); + if (X == NULL) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + + order = EC_GROUP_get0_order(group); + if (order == NULL) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB); + goto err; + } + + if (BN_is_zero(sig->r) || BN_is_negative(sig->r) || + BN_ucmp(sig->r, order) >= 0 || BN_is_zero(sig->s) || + BN_is_negative(sig->s) || BN_ucmp(sig->s, order) >= 0) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, EC_R_BAD_SIGNATURE); + ret = 0; /* signature is invalid */ + goto err; + } + /* calculate tmp1 = inv(S) mod order */ + if (!BN_mod_inverse(u2, sig->s, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + /* digest -> m */ + i = BN_num_bits(order); + /* + * Need to truncate digest if it is too long: first truncate whole bytes. + */ + if (8 * dgst_len > i) + dgst_len = (i + 7) / 8; + if (!BN_bin2bn(dgst, dgst_len, m)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + /* If still too long truncate remaining bits with a shift */ + if ((8 * dgst_len > i) && !BN_rshift(m, m, 8 - (i & 0x7))) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + /* u1 = m * tmp mod order */ + if (!BN_mod_mul(u1, m, u2, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + /* u2 = r * w mod q */ + if (!BN_mod_mul(u2, sig->r, u2, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + + if ((point = EC_POINT_new(group)) == NULL) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_MALLOC_FAILURE); + goto err; + } + if (!EC_POINT_mul(group, point, u1, pub_key, u2, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB); + goto err; + } + if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == + NID_X9_62_prime_field) { + if (!EC_POINT_get_affine_coordinates_GFp(group, point, X, NULL, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB); + goto err; + } + } +#ifndef OPENSSL_NO_EC2M + else { /* NID_X9_62_characteristic_two_field */ + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, X, NULL, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_EC_LIB); + goto err; + } + } +#endif + if (!BN_nnmod(u1, X, order, ctx)) { + ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB); + goto err; + } + /* if the signature is correct u1 is equal to sig->r */ + ret = (BN_ucmp(u1, sig->r) == 0); + err: + BN_CTX_end(ctx); + BN_CTX_free(ctx); + EC_POINT_free(point); + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecdsa_sign.c b/openssl-1.1.0h/crypto/ec/ecdsa_sign.c new file mode 100644 index 0000000..aee06e9 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecdsa_sign.c @@ -0,0 +1,52 @@ +/* + * Copyright 2015-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <openssl/ec.h> +#include "ec_lcl.h" +#include <openssl/err.h> + +ECDSA_SIG *ECDSA_do_sign(const unsigned char *dgst, int dlen, EC_KEY *eckey) +{ + return ECDSA_do_sign_ex(dgst, dlen, NULL, NULL, eckey); +} + +ECDSA_SIG *ECDSA_do_sign_ex(const unsigned char *dgst, int dlen, + const BIGNUM *kinv, const BIGNUM *rp, + EC_KEY *eckey) +{ + if (eckey->meth->sign_sig != NULL) + return eckey->meth->sign_sig(dgst, dlen, kinv, rp, eckey); + ECerr(EC_F_ECDSA_DO_SIGN_EX, EC_R_OPERATION_NOT_SUPPORTED); + return NULL; +} + +int ECDSA_sign(int type, const unsigned char *dgst, int dlen, unsigned char + *sig, unsigned int *siglen, EC_KEY *eckey) +{ + return ECDSA_sign_ex(type, dgst, dlen, sig, siglen, NULL, NULL, eckey); +} + +int ECDSA_sign_ex(int type, const unsigned char *dgst, int dlen, + unsigned char *sig, unsigned int *siglen, const BIGNUM *kinv, + const BIGNUM *r, EC_KEY *eckey) +{ + if (eckey->meth->sign != NULL) + return eckey->meth->sign(type, dgst, dlen, sig, siglen, kinv, r, eckey); + ECerr(EC_F_ECDSA_SIGN_EX, EC_R_OPERATION_NOT_SUPPORTED); + return 0; +} + +int ECDSA_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in, BIGNUM **kinvp, + BIGNUM **rp) +{ + if (eckey->meth->sign_setup != NULL) + return eckey->meth->sign_setup(eckey, ctx_in, kinvp, rp); + ECerr(EC_F_ECDSA_SIGN_SETUP, EC_R_OPERATION_NOT_SUPPORTED); + return 0; +} diff --git a/openssl-1.1.0h/crypto/ec/ecdsa_vrf.c b/openssl-1.1.0h/crypto/ec/ecdsa_vrf.c new file mode 100644 index 0000000..f61a200 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecdsa_vrf.c @@ -0,0 +1,43 @@ +/* + * Copyright 2002-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <openssl/ec.h> +#include "ec_lcl.h" +#include <openssl/err.h> + +/*- + * returns + * 1: correct signature + * 0: incorrect signature + * -1: error + */ +int ECDSA_do_verify(const unsigned char *dgst, int dgst_len, + const ECDSA_SIG *sig, EC_KEY *eckey) +{ + if (eckey->meth->verify_sig != NULL) + return eckey->meth->verify_sig(dgst, dgst_len, sig, eckey); + ECerr(EC_F_ECDSA_DO_VERIFY, EC_R_OPERATION_NOT_SUPPORTED); + return 0; +} + +/*- + * returns + * 1: correct signature + * 0: incorrect signature + * -1: error + */ +int ECDSA_verify(int type, const unsigned char *dgst, int dgst_len, + const unsigned char *sigbuf, int sig_len, EC_KEY *eckey) +{ + if (eckey->meth->verify != NULL) + return eckey->meth->verify(type, dgst, dgst_len, sigbuf, sig_len, + eckey); + ECerr(EC_F_ECDSA_VERIFY, EC_R_OPERATION_NOT_SUPPORTED); + return 0; +} diff --git a/openssl-1.1.0h/crypto/ec/eck_prn.c b/openssl-1.1.0h/crypto/ec/eck_prn.c new file mode 100644 index 0000000..3e826cb --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/eck_prn.c @@ -0,0 +1,273 @@ +/* + * Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions originally developed by SUN MICROSYSTEMS, INC., and + * contributed to the OpenSSL project. + */ + +#include <stdio.h> +#include "internal/cryptlib.h" +#include <openssl/evp.h> +#include <openssl/ec.h> +#include <openssl/bn.h> + +#ifndef OPENSSL_NO_STDIO +int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off) +{ + BIO *b; + int ret; + + if ((b = BIO_new(BIO_s_file())) == NULL) { + ECerr(EC_F_ECPKPARAMETERS_PRINT_FP, ERR_R_BUF_LIB); + return (0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = ECPKParameters_print(b, x, off); + BIO_free(b); + return (ret); +} + +int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off) +{ + BIO *b; + int ret; + + if ((b = BIO_new(BIO_s_file())) == NULL) { + ECerr(EC_F_EC_KEY_PRINT_FP, ERR_R_BIO_LIB); + return (0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = EC_KEY_print(b, x, off); + BIO_free(b); + return (ret); +} + +int ECParameters_print_fp(FILE *fp, const EC_KEY *x) +{ + BIO *b; + int ret; + + if ((b = BIO_new(BIO_s_file())) == NULL) { + ECerr(EC_F_ECPARAMETERS_PRINT_FP, ERR_R_BIO_LIB); + return (0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = ECParameters_print(b, x); + BIO_free(b); + return (ret); +} +#endif + +static int print_bin(BIO *fp, const char *str, const unsigned char *num, + size_t len, int off); + +int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) +{ + int ret = 0, reason = ERR_R_BIO_LIB; + BN_CTX *ctx = NULL; + const EC_POINT *point = NULL; + BIGNUM *p = NULL, *a = NULL, *b = NULL, *gen = NULL; + const BIGNUM *order = NULL, *cofactor = NULL; + const unsigned char *seed; + size_t seed_len = 0; + + static const char *gen_compressed = "Generator (compressed):"; + static const char *gen_uncompressed = "Generator (uncompressed):"; + static const char *gen_hybrid = "Generator (hybrid):"; + + if (!x) { + reason = ERR_R_PASSED_NULL_PARAMETER; + goto err; + } + + ctx = BN_CTX_new(); + if (ctx == NULL) { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } + + if (EC_GROUP_get_asn1_flag(x)) { + /* the curve parameter are given by an asn1 OID */ + int nid; + const char *nname; + + if (!BIO_indent(bp, off, 128)) + goto err; + + nid = EC_GROUP_get_curve_name(x); + if (nid == 0) + goto err; + if (BIO_printf(bp, "ASN1 OID: %s", OBJ_nid2sn(nid)) <= 0) + goto err; + if (BIO_printf(bp, "\n") <= 0) + goto err; + nname = EC_curve_nid2nist(nid); + if (nname) { + if (!BIO_indent(bp, off, 128)) + goto err; + if (BIO_printf(bp, "NIST CURVE: %s\n", nname) <= 0) + goto err; + } + } else { + /* explicit parameters */ + int is_char_two = 0; + point_conversion_form_t form; + int tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(x)); + + if (tmp_nid == NID_X9_62_characteristic_two_field) + is_char_two = 1; + + if ((p = BN_new()) == NULL || (a = BN_new()) == NULL || + (b = BN_new()) == NULL) { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } +#ifndef OPENSSL_NO_EC2M + if (is_char_two) { + if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) { + reason = ERR_R_EC_LIB; + goto err; + } + } else /* prime field */ +#endif + { + if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) { + reason = ERR_R_EC_LIB; + goto err; + } + } + + if ((point = EC_GROUP_get0_generator(x)) == NULL) { + reason = ERR_R_EC_LIB; + goto err; + } + order = EC_GROUP_get0_order(x); + cofactor = EC_GROUP_get0_cofactor(x); + if (order == NULL) { + reason = ERR_R_EC_LIB; + goto err; + } + + form = EC_GROUP_get_point_conversion_form(x); + + if ((gen = EC_POINT_point2bn(x, point, form, NULL, ctx)) == NULL) { + reason = ERR_R_EC_LIB; + goto err; + } + + if ((seed = EC_GROUP_get0_seed(x)) != NULL) + seed_len = EC_GROUP_get_seed_len(x); + + if (!BIO_indent(bp, off, 128)) + goto err; + + /* print the 'short name' of the field type */ + if (BIO_printf(bp, "Field Type: %s\n", OBJ_nid2sn(tmp_nid)) + <= 0) + goto err; + + if (is_char_two) { + /* print the 'short name' of the base type OID */ + int basis_type = EC_GROUP_get_basis_type(x); + if (basis_type == 0) + goto err; + + if (!BIO_indent(bp, off, 128)) + goto err; + + if (BIO_printf(bp, "Basis Type: %s\n", + OBJ_nid2sn(basis_type)) <= 0) + goto err; + + /* print the polynomial */ + if ((p != NULL) && !ASN1_bn_print(bp, "Polynomial:", p, NULL, + off)) + goto err; + } else { + if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, NULL, off)) + goto err; + } + if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, NULL, off)) + goto err; + if ((b != NULL) && !ASN1_bn_print(bp, "B: ", b, NULL, off)) + goto err; + if (form == POINT_CONVERSION_COMPRESSED) { + if ((gen != NULL) && !ASN1_bn_print(bp, gen_compressed, gen, + NULL, off)) + goto err; + } else if (form == POINT_CONVERSION_UNCOMPRESSED) { + if ((gen != NULL) && !ASN1_bn_print(bp, gen_uncompressed, gen, + NULL, off)) + goto err; + } else { /* form == POINT_CONVERSION_HYBRID */ + + if ((gen != NULL) && !ASN1_bn_print(bp, gen_hybrid, gen, + NULL, off)) + goto err; + } + if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, + NULL, off)) + goto err; + if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, + NULL, off)) + goto err; + if (seed && !print_bin(bp, "Seed:", seed, seed_len, off)) + goto err; + } + ret = 1; + err: + if (!ret) + ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); + BN_free(p); + BN_free(a); + BN_free(b); + BN_free(gen); + BN_CTX_free(ctx); + return (ret); +} + +static int print_bin(BIO *fp, const char *name, const unsigned char *buf, + size_t len, int off) +{ + size_t i; + char str[128 + 1 + 4]; + + if (buf == NULL) + return 1; + if (off > 0) { + if (off > 128) + off = 128; + memset(str, ' ', off); + if (BIO_write(fp, str, off) <= 0) + return 0; + } else { + off = 0; + } + + if (BIO_printf(fp, "%s", name) <= 0) + return 0; + + for (i = 0; i < len; i++) { + if ((i % 15) == 0) { + str[0] = '\n'; + memset(&(str[1]), ' ', off + 4); + if (BIO_write(fp, str, off + 1 + 4) <= 0) + return 0; + } + if (BIO_printf(fp, "%02x%s", buf[i], ((i + 1) == len) ? "" : ":") <= + 0) + return 0; + } + if (BIO_write(fp, "\n", 1) <= 0) + return 0; + + return 1; +} diff --git a/openssl-1.1.0h/crypto/ec/ecp_mont.c b/openssl-1.1.0h/crypto/ec/ecp_mont.c new file mode 100644 index 0000000..994cc1d --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_mont.c @@ -0,0 +1,242 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <openssl/err.h> + +#include "ec_lcl.h" + +const EC_METHOD *EC_GFp_mont_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_mont_group_init, + ec_GFp_mont_group_finish, + ec_GFp_mont_group_clear_finish, + ec_GFp_mont_group_copy, + ec_GFp_mont_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, + 0, 0, 0, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + 0 /* mul */ , + 0 /* precompute_mult */ , + 0 /* have_precompute_mult */ , + ec_GFp_mont_field_mul, + ec_GFp_mont_field_sqr, + 0 /* field_div */ , + ec_GFp_mont_field_encode, + ec_GFp_mont_field_decode, + ec_GFp_mont_field_set_to_one, + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +int ec_GFp_mont_group_init(EC_GROUP *group) +{ + int ok; + + ok = ec_GFp_simple_group_init(group); + group->field_data1 = NULL; + group->field_data2 = NULL; + return ok; +} + +void ec_GFp_mont_group_finish(EC_GROUP *group) +{ + BN_MONT_CTX_free(group->field_data1); + group->field_data1 = NULL; + BN_free(group->field_data2); + group->field_data2 = NULL; + ec_GFp_simple_group_finish(group); +} + +void ec_GFp_mont_group_clear_finish(EC_GROUP *group) +{ + BN_MONT_CTX_free(group->field_data1); + group->field_data1 = NULL; + BN_clear_free(group->field_data2); + group->field_data2 = NULL; + ec_GFp_simple_group_clear_finish(group); +} + +int ec_GFp_mont_group_copy(EC_GROUP *dest, const EC_GROUP *src) +{ + BN_MONT_CTX_free(dest->field_data1); + dest->field_data1 = NULL; + BN_clear_free(dest->field_data2); + dest->field_data2 = NULL; + + if (!ec_GFp_simple_group_copy(dest, src)) + return 0; + + if (src->field_data1 != NULL) { + dest->field_data1 = BN_MONT_CTX_new(); + if (dest->field_data1 == NULL) + return 0; + if (!BN_MONT_CTX_copy(dest->field_data1, src->field_data1)) + goto err; + } + if (src->field_data2 != NULL) { + dest->field_data2 = BN_dup(src->field_data2); + if (dest->field_data2 == NULL) + goto err; + } + + return 1; + + err: + BN_MONT_CTX_free(dest->field_data1); + dest->field_data1 = NULL; + return 0; +} + +int ec_GFp_mont_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BN_MONT_CTX *mont = NULL; + BIGNUM *one = NULL; + int ret = 0; + + BN_MONT_CTX_free(group->field_data1); + group->field_data1 = NULL; + BN_free(group->field_data2); + group->field_data2 = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + mont = BN_MONT_CTX_new(); + if (mont == NULL) + goto err; + if (!BN_MONT_CTX_set(mont, p, ctx)) { + ECerr(EC_F_EC_GFP_MONT_GROUP_SET_CURVE, ERR_R_BN_LIB); + goto err; + } + one = BN_new(); + if (one == NULL) + goto err; + if (!BN_to_montgomery(one, BN_value_one(), mont, ctx)) + goto err; + + group->field_data1 = mont; + mont = NULL; + group->field_data2 = one; + one = NULL; + + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + + if (!ret) { + BN_MONT_CTX_free(group->field_data1); + group->field_data1 = NULL; + BN_free(group->field_data2); + group->field_data2 = NULL; + } + + err: + BN_free(one); + BN_CTX_free(new_ctx); + BN_MONT_CTX_free(mont); + return ret; +} + +int ec_GFp_mont_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { + ECerr(EC_F_EC_GFP_MONT_FIELD_MUL, EC_R_NOT_INITIALIZED); + return 0; + } + + return BN_mod_mul_montgomery(r, a, b, group->field_data1, ctx); +} + +int ec_GFp_mont_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { + ECerr(EC_F_EC_GFP_MONT_FIELD_SQR, EC_R_NOT_INITIALIZED); + return 0; + } + + return BN_mod_mul_montgomery(r, a, a, group->field_data1, ctx); +} + +int ec_GFp_mont_field_encode(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { + ECerr(EC_F_EC_GFP_MONT_FIELD_ENCODE, EC_R_NOT_INITIALIZED); + return 0; + } + + return BN_to_montgomery(r, a, (BN_MONT_CTX *)group->field_data1, ctx); +} + +int ec_GFp_mont_field_decode(const EC_GROUP *group, BIGNUM *r, + const BIGNUM *a, BN_CTX *ctx) +{ + if (group->field_data1 == NULL) { + ECerr(EC_F_EC_GFP_MONT_FIELD_DECODE, EC_R_NOT_INITIALIZED); + return 0; + } + + return BN_from_montgomery(r, a, group->field_data1, ctx); +} + +int ec_GFp_mont_field_set_to_one(const EC_GROUP *group, BIGNUM *r, + BN_CTX *ctx) +{ + if (group->field_data2 == NULL) { + ECerr(EC_F_EC_GFP_MONT_FIELD_SET_TO_ONE, EC_R_NOT_INITIALIZED); + return 0; + } + + if (!BN_copy(r, group->field_data2)) + return 0; + return 1; +} diff --git a/openssl-1.1.0h/crypto/ec/ecp_nist.c b/openssl-1.1.0h/crypto/ec/ecp_nist.c new file mode 100644 index 0000000..615563b --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nist.c @@ -0,0 +1,167 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <limits.h> + +#include <openssl/err.h> +#include <openssl/obj_mac.h> +#include "ec_lcl.h" + +const EC_METHOD *EC_GFp_nist_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_simple_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nist_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, + 0, 0, 0, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + 0 /* mul */ , + 0 /* precompute_mult */ , + 0 /* have_precompute_mult */ , + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src) +{ + dest->field_mod_func = src->field_mod_func; + + return ec_GFp_simple_group_copy(dest, src); +} + +int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + + BN_CTX_start(ctx); + + if (BN_ucmp(BN_get0_nist_prime_192(), p) == 0) + group->field_mod_func = BN_nist_mod_192; + else if (BN_ucmp(BN_get0_nist_prime_224(), p) == 0) + group->field_mod_func = BN_nist_mod_224; + else if (BN_ucmp(BN_get0_nist_prime_256(), p) == 0) + group->field_mod_func = BN_nist_mod_256; + else if (BN_ucmp(BN_get0_nist_prime_384(), p) == 0) + group->field_mod_func = BN_nist_mod_384; + else if (BN_ucmp(BN_get0_nist_prime_521(), p) == 0) + group->field_mod_func = BN_nist_mod_521; + else { + ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_NIST_PRIME); + goto err; + } + + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_nist_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; + + if (!group || !r || !a || !b) { + ECerr(EC_F_EC_GFP_NIST_FIELD_MUL, ERR_R_PASSED_NULL_PARAMETER); + goto err; + } + if (!ctx) + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; + + if (!BN_mul(r, a, b, ctx)) + goto err; + if (!group->field_mod_func(r, r, group->field, ctx)) + goto err; + + ret = 1; + err: + BN_CTX_free(ctx_new); + return ret; +} + +int ec_GFp_nist_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *ctx_new = NULL; + + if (!group || !r || !a) { + ECerr(EC_F_EC_GFP_NIST_FIELD_SQR, EC_R_PASSED_NULL_PARAMETER); + goto err; + } + if (!ctx) + if ((ctx_new = ctx = BN_CTX_new()) == NULL) + goto err; + + if (!BN_sqr(r, a, ctx)) + goto err; + if (!group->field_mod_func(r, r, group->field, ctx)) + goto err; + + ret = 1; + err: + BN_CTX_free(ctx_new); + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistp224.c b/openssl-1.1.0h/crypto/ec/ecp_nistp224.c new file mode 100644 index 0000000..0cd994f --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistp224.c @@ -0,0 +1,1715 @@ +/* + * Copyright 2010-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication + * + * Inspired by Daniel J. Bernstein's public domain nistp224 implementation + * and Adam Langley's public domain 64-bit C implementation of curve25519 + */ + +#include <openssl/opensslconf.h> +#ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 +NON_EMPTY_TRANSLATION_UNIT +#else + +# include <stdint.h> +# include <string.h> +# include <openssl/err.h> +# include "ec_lcl.h" + +# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit + * platforms */ +# else +# error "Need GCC 3.1 or later to define type uint128_t" +# endif + +typedef uint8_t u8; +typedef uint64_t u64; + +/******************************************************************************/ +/*- + * INTERNAL REPRESENTATION OF FIELD ELEMENTS + * + * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 + * using 64-bit coefficients called 'limbs', + * and sometimes (for multiplication results) as + * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 + * using 128-bit coefficients called 'widelimbs'. + * A 4-limb representation is an 'felem'; + * a 7-widelimb representation is a 'widefelem'. + * Even within felems, bits of adjacent limbs overlap, and we don't always + * reduce the representations: we ensure that inputs to each felem + * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, + * and fit into a 128-bit word without overflow. The coefficients are then + * again partially reduced to obtain an felem satisfying a_i < 2^57. + * We only reduce to the unique minimal representation at the end of the + * computation. + */ + +typedef uint64_t limb; +typedef uint128_t widelimb; + +typedef limb felem[4]; +typedef widelimb widefelem[7]; + +/* + * Field element represented as a byte arrary. 28*8 = 224 bits is also the + * group order size for the elliptic curve, and we also use this type for + * scalars for point multiplication. + */ +typedef u8 felem_bytearray[28]; + +static const felem_bytearray nistp224_curve_params[5] = { + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, + {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, + {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, + {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} +}; + +/*- + * Precomputed multiples of the standard generator + * Points are given in coordinates (X, Y, Z) where Z normally is 1 + * (0 for the point at infinity). + * For each field element, slice a_0 is word 0, etc. + * + * The table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^56G + * 3 | 0 0 1 1 | (2^56 + 1)G + * 4 | 0 1 0 0 | 2^112G + * 5 | 0 1 0 1 | (2^112 + 1)G + * 6 | 0 1 1 0 | (2^112 + 2^56)G + * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G + * 8 | 1 0 0 0 | 2^168G + * 9 | 1 0 0 1 | (2^168 + 1)G + * 10 | 1 0 1 0 | (2^168 + 2^56)G + * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G + * 12 | 1 1 0 0 | (2^168 + 2^112)G + * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G + * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G + * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G + * followed by a copy of this with each element multiplied by 2^28. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + */ +static const felem gmul[2][16][3] = { +{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, +{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}} +}; + +/* Precomputation for the group generator. */ +struct nistp224_pre_comp_st { + felem g_pre_comp[2][16][3]; + int references; + CRYPTO_RWLOCK *lock; +}; + +const EC_METHOD *EC_GFp_nistp224_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */ , + 0 /* point2oct */ , + 0 /* oct2point */ , + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/* + * Helper functions to convert field elements to/from internal representation + */ +static void bin28_to_felem(felem out, const u8 in[28]) +{ + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in+20))) >> 8; +} + +static void felem_to_bin28(u8 out[28], const felem in) +{ + unsigned i; + for (i = 0; i < 7; ++i) { + out[i] = in[0] >> (8 * i); + out[i + 7] = in[1] >> (8 * i); + out[i + 14] = in[2] >> (8 * i); + out[i + 21] = in[3] >> (8 * i); + } +} + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) +{ + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len - 1 - i]; +} + +/* From OpenSSL BIGNUM to internal representation */ +static int BN_to_felem(felem out, const BIGNUM *bn) +{ + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof(b_out)); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof(b_out)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; +} + +/* From internal representation to OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) +{ + felem_bytearray b_in, b_out; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, sizeof(b_out)); + return BN_bin2bn(b_out, sizeof(b_out), out); +} + +/******************************************************************************/ +/*- + * FIELD OPERATIONS + * + * Field operations, using the internal representation of field elements. + * NB! These operations are specific to our point multiplication and cannot be + * expected to be correct in general - e.g., multiplication with a large scalar + * will cause an overflow. + * + */ + +static void felem_one(felem out) +{ + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; +} + +static void felem_assign(felem out, const felem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + +/* Sum two field elements: out += in */ +static void felem_sum(felem out, const felem in) +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; +} + +/* Get negative value: out = -in */ +/* Assumes in[i] < 2^57 */ +static void felem_neg(felem out, const felem in) +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; +} + +/* Subtract field elements: out -= in */ +/* Assumes in[i] < 2^57 */ +static void felem_diff(felem out, const felem in) +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/* Subtract in unreduced 128-bit mode: out -= in */ +/* Assumes in[i] < 2^119 */ +static void widefelem_diff(widefelem out, const widefelem in) +{ + static const widelimb two120 = ((widelimb) 1) << 120; + static const widelimb two120m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 64); + static const widelimb two120m104m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; +} + +/* Subtract in mixed mode: out128 -= in64 */ +/* in[i] < 2^63 */ +static void felem_diff_128_64(widefelem out, const felem in) +{ + static const widelimb two64p8 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 8); + static const widelimb two64m48m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/* + * Multiply a field element by a scalar: out = out * scalar The scalars we + * actually use are small, so results fit without overflow + */ +static void felem_scalar(felem out, const limb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; +} + +/* + * Multiply an unreduced field element by a scalar: out = out * scalar The + * scalars we actually use are small, so results fit without overflow + */ +static void widefelem_scalar(widefelem out, const widelimb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; +} + +/* Square a field element: out = in^2 */ +static void felem_square(widefelem out, const felem in) +{ + limb tmp0, tmp1, tmp2; + tmp0 = 2 * in[0]; + tmp1 = 2 * in[1]; + tmp2 = 2 * in[2]; + out[0] = ((widelimb) in[0]) * in[0]; + out[1] = ((widelimb) in[0]) * tmp1; + out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; + out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; + out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; + out[5] = ((widelimb) in[3]) * tmp2; + out[6] = ((widelimb) in[3]) * in[3]; +} + +/* Multiply two field elements: out = in1 * in2 */ +static void felem_mul(widefelem out, const felem in1, const felem in2) +{ + out[0] = ((widelimb) in1[0]) * in2[0]; + out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; + out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + + ((widelimb) in1[2]) * in2[0]; + out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + + ((widelimb) in1[3]) * in2[1]; + out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; + out[6] = ((widelimb) in1[3]) * in2[3]; +} + +/*- + * Reduce seven 128-bit coefficients to four 64-bit coefficients. + * Requires in[i] < 2^126, + * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ +static void felem_reduce(felem out, const widefelem in) +{ + static const widelimb two127p15 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 15); + static const widelimb two127m71 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71); + static const widelimb two127m71m55 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + widelimb output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6] & 0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5] & 0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] = output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + /* output[2] < 2^56 + 2^56 = 2^57 */ + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + /* output[2] < 2^57 + 2^72 */ + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + /* output[3] <= 2^56 + 2^16 */ + out[2] = output[2] & 0x00ffffffffffffff; + + /*- + * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] <= 2^56 + 2^16 (due to final carry), + * so out < 2*p + */ + out[3] = output[3]; +} + +static void felem_square_reduce(felem out, const felem in) +{ + widefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); +} + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) +{ + widefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} + +/* + * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always + * call felem_reduce first) + */ +static void felem_contract(felem out, const felem in) +{ + static const int64_t two56 = ((limb) 1) << 56; + /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ + /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = in[0]; + tmp[1] = in[1]; + tmp[2] = in[2]; + tmp[3] = in[3]; + /* Case 1: a = 1 iff in >= 2^224 */ + a = (in[3] >> 56); + tmp[0] -= a; + tmp[1] += a << 40; + tmp[3] &= 0x00ffffffffffffff; + /* + * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 + * and the lower part is non-zero + */ + a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | + (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + a &= 0x00ffffffffffffff; + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = (a - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one */ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be + * non-zero, so we only need one step + */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= out < p */ + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; +} + +/* + * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field + * elements are reduced to in < 2^225, so we only need to check three cases: + * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 + */ +static limb felem_is_zero(const felem in) +{ + limb zero, two224m96p1, two225m97p2; + + zero = in[0] | in[1] | in[2] | in[3]; + zero = (((int64_t) (zero) - 1) >> 63) & 1; + two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; + two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); +} + +static int felem_is_zero_int(const void *in) +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} + +/* Invert a field element */ +/* Computation chain copied from djb's code */ +static void felem_inv(felem out, const felem in) +{ + felem ftmp, ftmp2, ftmp3, ftmp4; + widefelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); + felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); + felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ +} + +/* + * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy + * out to itself. + */ +static void copy_conditional(felem out, const felem in, limb icopy) +{ + unsigned i; + /* + * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one + */ + const limb copy = -icopy; + for (i = 0; i < 4; ++i) { + const limb tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } +} + +/******************************************************************************/ +/*- + * ELLIPTIC CURVE POINT OPERATIONS + * + * Points are represented in Jacobian projective coordinates: + * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), + * or to the point at infinity if Z == 0. + * + */ + +/*- + * Double an elliptic curve point: + * (X', Y', Z') = 2 * (X, Y, Z), where + * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 + * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 + * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, + * while x_out == y_in is not (maybe this works, but it's not tested). + */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) +{ + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + widefelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + widefelem_diff(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); +} + +/*- + * Add two elliptic curve points: + * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where + * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - + * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 + * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - + * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 + * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) + * + * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. + */ + +/* + * This function is not entirely constant-time: it includes a branch for + * checking whether the two input points are equal, (while not equal to the + * point at infinity). This case never happens during single point + * multiplication, so there is no timing leak for ECDH or ECDSA signing. + */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, + const felem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb z1_is_zero, z2_is_zero, x_equal, y_equal; + + if (!mixed) { + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp2 = z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* ftmp4 = z2^3*y1 */ + felem_assign(ftmp4, y1); + + /* ftmp2 = z2^2*x1 */ + felem_assign(ftmp2, x1); + } + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* tmp = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* tmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* + * the formulae are incorrect if the points are equal so we check for + * this and do doubling if this happens + */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + if (!mixed) { + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + } else { + /* special case z2 = 0 is handled later */ + felem_assign(ftmp5, z1); + } + + /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z_out, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp2); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /*- + * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 + */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x_out, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ + felem_diff(ftmp2, x_out); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* + * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) + */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /*- + * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - + * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 + */ + widefelem_diff(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp2); + + /* + * the result (x_out, y_out, z_out) is incorrect if one of the inputs is + * the point at infinity, so we need to check for this separately + */ + + /* + * if point 1 is at infinity, copy point 2 to output, and vice versa + */ + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + * The pre_comp array argument should be size of |size| argument + */ +static void select_point(const u64 idx, unsigned int size, + const felem pre_comp[][3], felem out[3]) +{ + unsigned i, j; + limb *outlimbs = &out[0][0]; + + memset(out, 0, sizeof(*out) * 3); + for (i = 0; i < size; i++) { + const limb *inlimbs = &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < 4 * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, unsigned i) +{ + if (i >= 224) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], + const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], + const felem g_pre_comp[2][16][3]) +{ + int i, skip; + unsigned num; + unsigned gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, sizeof(nq)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (two in each of the last 28 rounds) and additions of + * other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 27)) { + /* first, look 28 bits upwards */ + bits = get_bit(g_scalar, i + 196) << 3; + bits |= get_bit(g_scalar, i + 140) << 2; + bits |= get_bit(g_scalar, i + 84) << 1; + bits |= get_bit(g_scalar, i + 28); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) { + /* value 1 below is argument for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 168) << 3; + bits |= get_bit(g_scalar, i + 112) << 2; + bits |= get_bit(g_scalar, i + 56) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_conditional(tmp[1], tmp[3], sign); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} + +/******************************************************************************/ +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP224_PRE_COMP *nistp224_pre_comp_new() +{ + NISTP224_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (!ret) { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *p) +{ + int i; + if (p != NULL) + CRYPTO_atomic_add(&p->references, 1, &i, p->lock); + return p; +} + +void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *p) +{ + int i; + + if (p == NULL) + return; + + CRYPTO_atomic_add(&p->references, -1, &i, p->lock); + REF_PRINT_COUNT("EC_nistp224", x); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + CRYPTO_THREAD_lock_free(p->lock); + OPENSSL_free(p); +} + +/******************************************************************************/ +/* + * OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp224_group_init(EC_GROUP *group) +{ + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} + +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; + BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || + (!BN_to_felem(z1, point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +static void make_points_affine(size_t num, felem points[ /* num */ ][3], + felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *))felem_one, + felem_is_zero_int, + (void (*)(void *, const void *)) + felem_assign, + (void (*)(void *, const void *)) + felem_square_reduce, (void (*) + (void *, + const void + *, + const void + *)) + felem_mul_reduce, + (void (*)(void *, const void *)) + felem_inv, + (void (*)(void *, const void *)) + felem_contract); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + unsigned i; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP224_PRE_COMP *pre = NULL; + const felem(*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) { + pre = group->pre_comp.nistp224; + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const felem(*)[16][3])pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[0][1][0]) || + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, + ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points = num_points + 1; + } + + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); + pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); + if (mixed) + tmp_felems = + OPENSSL_malloc(sizeof(felem) * (num_points * 17 + 1)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_felems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + for (i = 0; i < num_points; ++i) { + if (i == num) + /* the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) { + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(p_scalar) > 224) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, p->X)) || + (!BN_to_felem(y_out, p->Y)) || + (!BN_to_felem(z_out, p->Z))) + goto err; + felem_assign(pre_comp[i][1][0], x_out); + felem_assign(pre_comp[i][1][1], y_out); + felem_assign(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][1][0], + pre_comp[i][1][1], pre_comp[i][1][2], 0, + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][j / 2][0], + pre_comp[i][j / 2][1], + pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); + } else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + OPENSSL_free(secrets); + OPENSSL_free(pre_comp); + OPENSSL_free(tmp_felems); + return ret; +} + +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[32]; + + /* throw away old precomputation */ + EC_pre_comp_free(group); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + goto done; + } + if ((!BN_to_felem(pre->g_pre_comp[0][1][0], group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[0][1][1], group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], group->generator->Z))) + goto err; + /* + * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, + * 2^140*G, 2^196*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], + pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2]); + } + } + for (i = 0; i < 2; i++) { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ + point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ + point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ + point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G + */ + point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { + /* odd multiples: add G resp. 2^28*G */ + point_add(pre->g_pre_comp[i][2 * j + 1][0], + pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], + pre->g_pre_comp[i][2 * j][2], 0, + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); + + done: + SETPRECOMP(group, nistp224, pre); + pre = NULL; + ret = 1; + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + EC_nistp224_pre_comp_free(pre); + return ret; +} + +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) +{ + return HAVEPRECOMP(group, nistp224); +} + +#endif diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistp256.c b/openssl-1.1.0h/crypto/ec/ecp_nistp256.c new file mode 100644 index 0000000..ffd2a7d --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistp256.c @@ -0,0 +1,2350 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/opensslconf.h> +#ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 +NON_EMPTY_TRANSLATION_UNIT +#else + +# include <stdint.h> +# include <string.h> +# include <openssl/err.h> +# include "ec_lcl.h" + +# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit + * platforms */ +typedef __int128_t int128_t; +# else +# error "Need GCC 3.1 or later to define type uint128_t" +# endif + +typedef uint8_t u8; +typedef uint32_t u32; +typedef uint64_t u64; + +/* + * The underlying field. P256 operates over GF(2^256-2^224+2^192+2^96-1). We + * can serialise an element of this field into 32 bytes. We call this an + * felem_bytearray. + */ + +typedef u8 felem_bytearray[32]; + +/* + * These are the parameters of P256, taken from FIPS 186-3, page 86. These + * values are big-endian. + */ +static const felem_bytearray nistp256_curve_params[5] = { + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ + {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, + 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, + 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, + 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, + {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ + 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, + 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, + 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, + {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ + 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, + 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, + 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} +}; + +/*- + * The representation of field elements. + * ------------------------------------ + * + * We represent field elements with either four 128-bit values, eight 128-bit + * values, or four 64-bit values. The field element represented is: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p) + * or: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p) + * + * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits + * apart, but are 128-bits wide, the most significant bits of each limb overlap + * with the least significant bits of the next. + * + * A field element with four limbs is an 'felem'. One with eight limbs is a + * 'longfelem' + * + * A field element with four, 64-bit values is called a 'smallfelem'. Small + * values are used as intermediate values before multiplication. + */ + +# define NLIMBS 4 + +typedef uint128_t limb; +typedef limb felem[NLIMBS]; +typedef limb longfelem[NLIMBS * 2]; +typedef u64 smallfelem[NLIMBS]; + +/* This is the value of the prime as four 64-bit words, little-endian. */ +static const u64 kPrime[4] = + { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; +static const u64 bottom63bits = 0x7ffffffffffffffful; + +/* + * bin32_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. + */ +static void bin32_to_felem(felem out, const u8 in[32]) +{ + out[0] = *((u64 *)&in[0]); + out[1] = *((u64 *)&in[8]); + out[2] = *((u64 *)&in[16]); + out[3] = *((u64 *)&in[24]); +} + +/* + * smallfelem_to_bin32 takes a smallfelem and serialises into a little + * endian, 32 byte array. This assumes that the CPU is little-endian. + */ +static void smallfelem_to_bin32(u8 out[32], const smallfelem in) +{ + *((u64 *)&out[0]) = in[0]; + *((u64 *)&out[8]) = in[1]; + *((u64 *)&out[16]) = in[2]; + *((u64 *)&out[24]) = in[3]; +} + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) +{ + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len - 1 - i]; +} + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) +{ + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof(b_out)); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof(b_out)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin32_to_felem(out, b_out); + return 1; +} + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) +{ + felem_bytearray b_in, b_out; + smallfelem_to_bin32(b_in, in); + flip_endian(b_out, b_in, sizeof(b_out)); + return BN_bin2bn(b_out, sizeof(b_out), out); +} + +/*- + * Field operations + * ---------------- + */ + +static void smallfelem_one(smallfelem out) +{ + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; +} + +static void smallfelem_assign(smallfelem out, const smallfelem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + +static void felem_assign(felem out, const felem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + +/* felem_sum sets out = out + in. */ +static void felem_sum(felem out, const felem in) +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; +} + +/* felem_small_sum sets out = out + in. */ +static void felem_small_sum(felem out, const smallfelem in) +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; +} + +/* felem_scalar sets out = out * scalar */ +static void felem_scalar(felem out, const u64 scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; +} + +/* longfelem_scalar sets out = out * scalar */ +static void longfelem_scalar(longfelem out, const u64 scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; +} + +# define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) +# define two105 (((limb)1) << 105) +# define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) + +/* zero105 is 0 mod p */ +static const felem zero105 = + { two105m41m9, two105, two105m41p9, two105m41p9 }; + +/*- + * smallfelem_neg sets |out| to |-small| + * On exit: + * out[i] < out[i] + 2^105 + */ +static void smallfelem_neg(felem out, const smallfelem small) +{ + /* In order to prevent underflow, we subtract from 0 mod p. */ + out[0] = zero105[0] - small[0]; + out[1] = zero105[1] - small[1]; + out[2] = zero105[2] - small[2]; + out[3] = zero105[3] - small[3]; +} + +/*- + * felem_diff subtracts |in| from |out| + * On entry: + * in[i] < 2^104 + * On exit: + * out[i] < out[i] + 2^105 + */ +static void felem_diff(felem out, const felem in) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + out[0] += zero105[0]; + out[1] += zero105[1]; + out[2] += zero105[2]; + out[3] += zero105[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +# define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) +# define two107 (((limb)1) << 107) +# define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) + +/* zero107 is 0 mod p */ +static const felem zero107 = + { two107m43m11, two107, two107m43p11, two107m43p11 }; + +/*- + * An alternative felem_diff for larger inputs |in| + * felem_diff_zero107 subtracts |in| from |out| + * On entry: + * in[i] < 2^106 + * On exit: + * out[i] < out[i] + 2^107 + */ +static void felem_diff_zero107(felem out, const felem in) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + out[0] += zero107[0]; + out[1] += zero107[1]; + out[2] += zero107[2]; + out[3] += zero107[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/*- + * longfelem_diff subtracts |in| from |out| + * On entry: + * in[i] < 7*2^67 + * On exit: + * out[i] < out[i] + 2^70 + 2^40 + */ +static void longfelem_diff(longfelem out, const longfelem in) +{ + static const limb two70m8p6 = + (((limb) 1) << 70) - (((limb) 1) << 8) + (((limb) 1) << 6); + static const limb two70p40 = (((limb) 1) << 70) + (((limb) 1) << 40); + static const limb two70 = (((limb) 1) << 70); + static const limb two70m40m38p6 = + (((limb) 1) << 70) - (((limb) 1) << 40) - (((limb) 1) << 38) + + (((limb) 1) << 6); + static const limb two70m6 = (((limb) 1) << 70) - (((limb) 1) << 6); + + /* add 0 mod p to avoid underflow */ + out[0] += two70m8p6; + out[1] += two70p40; + out[2] += two70; + out[3] += two70m40m38p6; + out[4] += two70m6; + out[5] += two70m6; + out[6] += two70m6; + out[7] += two70m6; + + /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + out[7] -= in[7]; +} + +# define two64m0 (((limb)1) << 64) - 1 +# define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 +# define two64m46 (((limb)1) << 64) - (((limb)1) << 46) +# define two64m32 (((limb)1) << 64) - (((limb)1) << 32) + +/* zero110 is 0 mod p */ +static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; + +/*- + * felem_shrink converts an felem into a smallfelem. The result isn't quite + * minimal as the value may be greater than p. + * + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 2^64 + */ +static void felem_shrink(smallfelem out, const felem in) +{ + felem tmp; + u64 a, b, mask; + u64 high, low; + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + + /* Carry 2->3 */ + tmp[3] = zero110[3] + in[3] + ((u64)(in[2] >> 64)); + /* tmp[3] < 2^110 */ + + tmp[2] = zero110[2] + (u64)in[2]; + tmp[0] = zero110[0] + in[0]; + tmp[1] = zero110[1] + in[1]; + /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ + + /* + * We perform two partial reductions where we eliminate the high-word of + * tmp[3]. We don't update the other words till the end. + */ + a = tmp[3] >> 64; /* a < 2^46 */ + tmp[3] = (u64)tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb) a) << 32; + /* tmp[3] < 2^79 */ + + b = a; + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ + tmp[3] = (u64)tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb) a) << 32; + /* tmp[3] < 2^64 + 2^47 */ + + /* + * This adjusts the other two words to complete the two partial + * reductions. + */ + tmp[0] += b; + tmp[1] -= (((limb) b) << 32); + + /* + * In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. + */ + high = (u64)(tmp[3] >> 64); + /* As tmp[3] < 2^65, high is either 1 or 0 */ + high = 0 - high; + /*- + * high is: + * all ones if the high word of tmp[3] is 1 + * all zeros if the high word of tmp[3] if 0 + */ + low = (u64)tmp[3]; + mask = 0 - (low >> 63); + /*- + * mask is: + * all ones if the MSB of low is 1 + * all zeros if the MSB of low if 0 + */ + low &= bottom63bits; + low -= kPrime3Test; + /* if low was greater than kPrime3Test then the MSB is zero */ + low = ~low; + low = 0 - (low >> 63); + /*- + * low is: + * all ones if low was > kPrime3Test + * all zeros if low was <= kPrime3Test + */ + mask = (mask & low) | high; + tmp[0] -= mask & kPrime[0]; + tmp[1] -= mask & kPrime[1]; + /* kPrime[2] is zero, so omitted */ + tmp[3] -= mask & kPrime[3]; + /* tmp[3] < 2**64 - 2**32 + 1 */ + + tmp[1] += ((u64)(tmp[0] >> 64)); + tmp[0] = (u64)tmp[0]; + tmp[2] += ((u64)(tmp[1] >> 64)); + tmp[1] = (u64)tmp[1]; + tmp[3] += ((u64)(tmp[2] >> 64)); + tmp[2] = (u64)tmp[2]; + /* tmp[i] < 2^64 */ + + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; +} + +/* smallfelem_expand converts a smallfelem to an felem */ +static void smallfelem_expand(felem out, const smallfelem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + +/*- + * smallfelem_square sets |out| = |small|^2 + * On entry: + * small[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_square(longfelem out, const smallfelem small) +{ + limb a; + u64 high, low; + + a = ((uint128_t) small[0]) * small[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small[0]) * small[1]; + low = a; + high = a >> 64; + out[1] += low; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small[0]) * small[2]; + low = a; + high = a >> 64; + out[2] += low; + out[2] *= 2; + out[3] = high; + + a = ((uint128_t) small[0]) * small[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small[1]) * small[2]; + low = a; + high = a >> 64; + out[3] += low; + out[3] *= 2; + out[4] += high; + + a = ((uint128_t) small[1]) * small[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small[1]) * small[3]; + low = a; + high = a >> 64; + out[4] += low; + out[4] *= 2; + out[5] = high; + + a = ((uint128_t) small[2]) * small[3]; + low = a; + high = a >> 64; + out[5] += low; + out[5] *= 2; + out[6] = high; + out[6] += high; + + a = ((uint128_t) small[2]) * small[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small[3]) * small[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; +} + +/*- + * felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_square(longfelem out, const felem in) +{ + u64 small[4]; + felem_shrink(small, in); + smallfelem_square(out, small); +} + +/*- + * smallfelem_mul sets |out| = |small1| * |small2| + * On entry: + * small1[i] < 2^64 + * small2[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_mul(longfelem out, const smallfelem small1, + const smallfelem small2) +{ + limb a; + u64 high, low; + + a = ((uint128_t) small1[0]) * small2[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small1[0]) * small2[1]; + low = a; + high = a >> 64; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small1[1]) * small2[0]; + low = a; + high = a >> 64; + out[1] += low; + out[2] += high; + + a = ((uint128_t) small1[0]) * small2[2]; + low = a; + high = a >> 64; + out[2] += low; + out[3] = high; + + a = ((uint128_t) small1[1]) * small2[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[2]) * small2[0]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[0]) * small2[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small1[1]) * small2[2]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[2]) * small2[1]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[3]) * small2[0]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[1]) * small2[3]; + low = a; + high = a >> 64; + out[4] += low; + out[5] = high; + + a = ((uint128_t) small1[2]) * small2[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[3]) * small2[1]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[2]) * small2[3]; + low = a; + high = a >> 64; + out[5] += low; + out[6] = high; + + a = ((uint128_t) small1[3]) * small2[2]; + low = a; + high = a >> 64; + out[5] += low; + out[6] += high; + + a = ((uint128_t) small1[3]) * small2[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; +} + +/*- + * felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^109 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_mul(longfelem out, const felem in1, const felem in2) +{ + smallfelem small1, small2; + felem_shrink(small1, in1); + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); +} + +/*- + * felem_small_mul sets |out| = |small1| * |in2| + * On entry: + * small1[i] < 2^64 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_small_mul(longfelem out, const smallfelem small1, + const felem in2) +{ + smallfelem small2; + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); +} + +# define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) +# define two100 (((limb)1) << 100) +# define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) +/* zero100 is 0 mod p */ +static const felem zero100 = + { two100m36m4, two100, two100m36p4, two100m36p4 }; + +/*- + * Internal function for the different flavours of felem_reduce. + * felem_reduce_ reduces the higher coefficients in[4]-in[7]. + * On entry: + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[1] >= in[7] + 2^32*in[4] + * out[2] >= in[5] + 2^32*in[5] + * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] + * On exit: + * out[0] <= out[0] + in[4] + 2^32*in[5] + * out[1] <= out[1] + in[5] + 2^33*in[6] + * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] + * out[3] <= out[3] + 2^32*in[4] + 3*in[7] + */ +static void felem_reduce_(felem out, const longfelem in) +{ + int128_t c; + /* combine common terms from below */ + c = in[4] + (in[5] << 32); + out[0] += c; + out[3] -= c; + + c = in[5] - in[7]; + out[1] += c; + out[2] -= c; + + /* the remaining terms */ + /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ + out[1] -= (in[4] << 32); + out[3] += (in[4] << 32); + + /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ + out[2] -= (in[5] << 32); + + /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ + out[0] -= in[6]; + out[0] -= (in[6] << 32); + out[1] += (in[6] << 33); + out[2] += (in[6] * 2); + out[3] -= (in[6] << 32); + + /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ + out[0] -= in[7]; + out[0] -= (in[7] << 32); + out[2] += (in[7] << 33); + out[3] += (in[7] * 3); +} + +/*- + * felem_reduce converts a longfelem into an felem. + * To be called directly after felem_square or felem_mul. + * On entry: + * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 + * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 + * On exit: + * out[i] < 2^101 + */ +static void felem_reduce(felem out, const longfelem in) +{ + out[0] = zero100[0] + in[0]; + out[1] = zero100[1] + in[1]; + out[2] = zero100[2] + in[2]; + out[3] = zero100[3] + in[3]; + + felem_reduce_(out, in); + + /*- + * out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 + * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 + * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 + * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 + * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 + * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + */ +} + +/*- + * felem_reduce_zero105 converts a larger longfelem into an felem. + * On entry: + * in[0] < 2^71 + * On exit: + * out[i] < 2^106 + */ +static void felem_reduce_zero105(felem out, const longfelem in) +{ + out[0] = zero105[0] + in[0]; + out[1] = zero105[1] + in[1]; + out[2] = zero105[2] + in[2]; + out[3] = zero105[3] + in[3]; + + felem_reduce_(out, in); + + /*- + * out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 + * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 + * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 + * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + */ +} + +/* + * subtract_u64 sets *result = *result - v and *carry to one if the + * subtraction underflowed. + */ +static void subtract_u64(u64 *result, u64 *carry, u64 v) +{ + uint128_t r = *result; + r -= v; + *carry = (r >> 64) & 1; + *result = (u64)r; +} + +/* + * felem_contract converts |in| to its unique, minimal representation. On + * entry: in[i] < 2^109 + */ +static void felem_contract(smallfelem out, const felem in) +{ + unsigned i; + u64 all_equal_so_far = 0, result = 0, carry; + + felem_shrink(out, in); + /* small is minimal except that the value might be > p */ + + all_equal_so_far--; + /* + * We are doing a constant time test if out >= kPrime. We need to compare + * each u64, from most-significant to least significant. For each one, if + * all words so far have been equal (m is all ones) then a non-equal + * result is the answer. Otherwise we continue. + */ + for (i = 3; i < 4; i--) { + u64 equal; + uint128_t a = ((uint128_t) kPrime[i]) - out[i]; + /* + * if out[i] > kPrime[i] then a will underflow and the high 64-bits + * will all be set. + */ + result |= all_equal_so_far & ((u64)(a >> 64)); + + /* + * if kPrime[i] == out[i] then |equal| will be all zeros and the + * decrement will make it all ones. + */ + equal = kPrime[i] ^ out[i]; + equal--; + equal &= equal << 32; + equal &= equal << 16; + equal &= equal << 8; + equal &= equal << 4; + equal &= equal << 2; + equal &= equal << 1; + equal = 0 - (equal >> 63); + + all_equal_so_far &= equal; + } + + /* + * if all_equal_so_far is still all ones then the two values are equal + * and so out >= kPrime is true. + */ + result |= all_equal_so_far; + + /* if out >= kPrime then we subtract kPrime. */ + subtract_u64(&out[0], &carry, result & kPrime[0]); + subtract_u64(&out[1], &carry, carry); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[1], &carry, result & kPrime[1]); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[2], &carry, result & kPrime[2]); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[3], &carry, result & kPrime[3]); +} + +static void smallfelem_square_contract(smallfelem out, const smallfelem in) +{ + longfelem longtmp; + felem tmp; + + smallfelem_square(longtmp, in); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); +} + +static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, + const smallfelem in2) +{ + longfelem longtmp; + felem tmp; + + smallfelem_mul(longtmp, in1, in2); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); +} + +/*- + * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * small[i] < 2^64 + */ +static limb smallfelem_is_zero(const smallfelem small) +{ + limb result; + u64 is_p; + + u64 is_zero = small[0] | small[1] | small[2] | small[3]; + is_zero--; + is_zero &= is_zero << 32; + is_zero &= is_zero << 16; + is_zero &= is_zero << 8; + is_zero &= is_zero << 4; + is_zero &= is_zero << 2; + is_zero &= is_zero << 1; + is_zero = 0 - (is_zero >> 63); + + is_p = (small[0] ^ kPrime[0]) | + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | (small[3] ^ kPrime[3]); + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = 0 - (is_p >> 63); + + is_zero |= is_p; + + result = is_zero; + result |= ((limb) is_zero) << 64; + return result; +} + +static int smallfelem_is_zero_int(const void *small) +{ + return (int)(smallfelem_is_zero(small) & ((limb) 1)); +} + +/*- + * felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) +{ + felem ftmp, ftmp2; + /* each e_I will hold |in|^{2^I - 1} */ + felem e2, e4, e8, e16, e32, e64; + longfelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(e2, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); + felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_assign(e4, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); + felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_assign(e8, ftmp); + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); + felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_assign(e16, ftmp); + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); + felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_assign(e32, ftmp); + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ + felem_assign(e64, ftmp); + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + for (i = 0; i < 192; i++) { + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ + + felem_mul(tmp, e64, e32); + felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); + felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); + felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + for (i = 0; i < 4; i++) { + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); + felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); + felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); + felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ +} + +static void smallfelem_inv_contract(smallfelem out, const smallfelem in) +{ + felem tmp; + + smallfelem_expand(tmp, in); + felem_inv(tmp, tmp); + felem_contract(out, tmp); +} + +/*- + * Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates + */ + +/*- + * point_double calculates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). + */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) +{ + longfelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + smallfelem small1, small2; + + felem_assign(ftmp, x_in); + /* ftmp[i] < 2^106 */ + felem_assign(ftmp2, x_in); + /* ftmp2[i] < 2^106 */ + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + /* delta[i] < 2^101 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + /* gamma[i] < 2^101 */ + felem_shrink(small1, gamma); + + /* beta = x*gamma */ + felem_small_mul(tmp, small1, x_in); + felem_reduce(beta, tmp); + /* beta[i] < 2^101 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^105 + 2^106 < 2^107 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^107 < 2^109 */ + felem_mul(tmp, ftmp, ftmp2); + felem_reduce(alpha, tmp); + /* alpha[i] < 2^101 */ + felem_shrink(small2, alpha); + + /* x' = alpha^2 - 8*beta */ + smallfelem_square(tmp, small2); + felem_reduce(x_out, tmp); + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^101 = 2^104 */ + felem_diff(x_out, ftmp); + /* x_out[i] < 2^105 + 2^101 < 2^106 */ + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^101 + 2^101 = 2^102 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^106 + 2^106 = 2^107 */ + felem_square(tmp, ftmp); + felem_reduce(z_out, tmp); + felem_diff(z_out, delta); + /* z_out[i] < 2^105 + 2^101 < 2^106 */ + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^101 = 2^103 */ + felem_diff_zero107(beta, x_out); + /* beta[i] < 2^107 + 2^103 < 2^108 */ + felem_small_mul(tmp, small2, beta); + /* tmp[i] < 7 * 2^64 < 2^67 */ + smallfelem_square(tmp2, small1); + /* tmp2[i] < 7 * 2^64 */ + longfelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ +} + +/* + * point_double_small is the same as point_double, except that it operates on + * smallfelems + */ +static void +point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, + const smallfelem x_in, const smallfelem y_in, + const smallfelem z_in) +{ + felem felem_x_out, felem_y_out, felem_z_out; + felem felem_x_in, felem_y_in, felem_z_in; + + smallfelem_expand(felem_x_in, x_in); + smallfelem_expand(felem_y_in, y_in); + smallfelem_expand(felem_z_in, z_in); + point_double(felem_x_out, felem_y_out, felem_z_out, + felem_x_in, felem_y_in, felem_z_in); + felem_shrink(x_out, felem_x_out); + felem_shrink(y_out, felem_y_out); + felem_shrink(z_out, felem_z_out); +} + +/* copy_conditional copies in to out iff mask is all ones. */ +static void copy_conditional(felem out, const felem in, limb mask) +{ + unsigned i; + for (i = 0; i < NLIMBS; ++i) { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } +} + +/* copy_small_conditional copies in to out iff mask is all ones. */ +static void copy_small_conditional(felem out, const smallfelem in, limb mask) +{ + unsigned i; + const u64 mask64 = mask; + for (i = 0; i < NLIMBS; ++i) { + out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); + } +} + +/*- + * point_add calculates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal, (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. + */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, + const smallfelem y2, const smallfelem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + longfelem tmp, tmp2; + smallfelem small1, small2, small3, small4, small5; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + felem_shrink(small3, z1); + + z1_is_zero = smallfelem_is_zero(small3); + z2_is_zero = smallfelem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + smallfelem_square(tmp, small3); + felem_reduce(ftmp, tmp); + /* ftmp[i] < 2^101 */ + felem_shrink(small1, ftmp); + + if (!mixed) { + /* ftmp2 = z2z2 = z2**2 */ + smallfelem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + /* ftmp2[i] < 2^101 */ + felem_shrink(small2, ftmp2); + + felem_shrink(small5, x1); + + /* u1 = ftmp3 = x1*z2z2 */ + smallfelem_mul(tmp, small5, small2); + felem_reduce(ftmp3, tmp); + /* ftmp3[i] < 2^101 */ + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_small_sum(ftmp5, z2); + /* ftmp5[i] < 2^107 */ + + /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ + felem_square(tmp, ftmp5); + felem_reduce(ftmp5, tmp); + /* ftmp2 = z2z2 + z1z1 */ + felem_sum(ftmp2, ftmp); + /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ + felem_diff(ftmp5, ftmp2); + /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ + + /* ftmp2 = z2 * z2z2 */ + smallfelem_mul(tmp, small2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + /* ftmp6[i] < 2^101 */ + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + /* ftmp3[i] < 2^106 */ + + /* ftmp5 = 2z1z2 */ + felem_assign(ftmp5, z1); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2*2^106 = 2^107 */ + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + /* ftmp6[i] < 2^106 */ + } + + /* u2 = x2*z1z1 */ + smallfelem_mul(tmp, x2, small1); + felem_reduce(ftmp4, tmp); + + /* h = ftmp4 = u2 - u1 */ + felem_diff_zero107(ftmp4, ftmp3); + /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ + felem_shrink(small4, ftmp4); + + x_equal = smallfelem_is_zero(small4); + + /* z_out = ftmp5 * h */ + felem_small_mul(tmp, small4, ftmp5); + felem_reduce(z_out, tmp); + /* z_out[i] < 2^101 */ + + /* ftmp = z1 * z1z1 */ + smallfelem_mul(tmp, small1, small3); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_small_mul(tmp, y2, ftmp); + felem_reduce(ftmp5, tmp); + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_zero107(ftmp5, ftmp6); + /* ftmp5[i] < 2^107 + 2^107 = 2^108 */ + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2^109 */ + felem_shrink(small1, ftmp5); + y_equal = smallfelem_is_zero(small1); + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar(ftmp, 2); + /* ftmp[i] < 2*2^108 = 2^109 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + smallfelem_square(tmp, small1); + felem_reduce(x_out, tmp); + felem_assign(ftmp3, ftmp4); + felem_scalar(ftmp4, 2); + felem_sum(ftmp4, ftmp2); + /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ + felem_diff(x_out, ftmp4); + /* x_out[i] < 2^105 + 2^101 */ + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff_zero107(ftmp3, x_out); + /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ + felem_small_mul(tmp, small1, ftmp3); + felem_mul(tmp2, ftmp6, ftmp2); + longfelem_scalar(tmp2, 2); + /* tmp2[i] < 2*2^67 = 2^68 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + + copy_small_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_small_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_small_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} + +/* + * point_add_small is the same as point_add, except that it operates on + * smallfelems + */ +static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) +{ + felem felem_x3, felem_y3, felem_z3; + felem felem_x1, felem_y1, felem_z1; + smallfelem_expand(felem_x1, x1); + smallfelem_expand(felem_y1, y1); + smallfelem_expand(felem_z1, z1); + point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, + x2, y2, z2); + felem_shrink(x3, felem_x3); + felem_shrink(y3, felem_y3); + felem_shrink(z3, felem_z3); +} + +/*- + * Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^64G + * 3 | 0 0 1 1 | (2^64 + 1)G + * 4 | 0 1 0 0 | 2^128G + * 5 | 0 1 0 1 | (2^128 + 1)G + * 6 | 0 1 1 0 | (2^128 + 2^64)G + * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G + * 8 | 1 0 0 0 | 2^192G + * 9 | 1 0 0 1 | (2^192 + 1)G + * 10 | 1 0 1 0 | (2^192 + 2^64)G + * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G + * 12 | 1 1 0 0 | (2^192 + 2^128)G + * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G + * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G + * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G + * followed by a copy of this with each element multiplied by 2^32. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const smallfelem gmul[2][16][3] = { + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, + 0x6b17d1f2e12c4247}, + {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, + 0x4fe342e2fe1a7f9b}, + {1, 0, 0, 0}}, + {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, + 0x0fa822bc2811aaa5}, + {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, + 0xbff44ae8f5dba80d}, + {1, 0, 0, 0}}, + {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, + 0x300a4bbc89d6726f}, + {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, + 0x72aac7e0d09b4644}, + {1, 0, 0, 0}}, + {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, + 0x447d739beedb5e67}, + {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, + 0x2d4825ab834131ee}, + {1, 0, 0, 0}}, + {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, + 0xef9519328a9c72ff}, + {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, + 0x611e9fc37dbb2c9b}, + {1, 0, 0, 0}}, + {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, + 0x550663797b51f5d8}, + {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, + 0x157164848aecb851}, + {1, 0, 0, 0}}, + {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, + 0xeb5d7745b21141ea}, + {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, + 0xeafd72ebdbecc17b}, + {1, 0, 0, 0}}, + {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, + 0xa6d39677a7849276}, + {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, + 0x674f84749b0b8816}, + {1, 0, 0, 0}}, + {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, + 0x4e769e7672c9ddad}, + {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, + 0x42b99082de830663}, + {1, 0, 0, 0}}, + {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, + 0x78878ef61c6ce04d}, + {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, + 0xb6cb3f5d7b72c321}, + {1, 0, 0, 0}}, + {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, + 0x0c88bc4d716b1287}, + {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, + 0xdd5ddea3f3901dc6}, + {1, 0, 0, 0}}, + {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, + 0x68f344af6b317466}, + {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, + 0x31b9c405f8540a20}, + {1, 0, 0, 0}}, + {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, + 0x4052bf4b6f461db9}, + {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, + 0xfecf4d5190b0fc61}, + {1, 0, 0, 0}}, + {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, + 0x1eddbae2c802e41a}, + {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, + 0x43104d86560ebcfc}, + {1, 0, 0, 0}}, + {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, + 0xb48e26b484f7a21c}, + {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, + 0xfac015404d4d3dab}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, + 0x7fe36b40af22af89}, + {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, + 0xe697d45825b63624}, + {1, 0, 0, 0}}, + {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, + 0x4a5b506612a677a6}, + {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, + 0xeb13461ceac089f1}, + {1, 0, 0, 0}}, + {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, + 0x0781b8291c6a220a}, + {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, + 0x690cde8df0151593}, + {1, 0, 0, 0}}, + {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, + 0x8a535f566ec73617}, + {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, + 0x0455c08468b08bd7}, + {1, 0, 0, 0}}, + {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, + 0x06bada7ab77f8276}, + {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, + 0x5b476dfd0e6cb18a}, + {1, 0, 0, 0}}, + {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, + 0x3e29864e8a2ec908}, + {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, + 0x239b90ea3dc31e7e}, + {1, 0, 0, 0}}, + {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, + 0x820f4dd949f72ff7}, + {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, + 0x140406ec783a05ec}, + {1, 0, 0, 0}}, + {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, + 0x68f6b8542783dfee}, + {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, + 0xcbe1feba92e40ce6}, + {1, 0, 0, 0}}, + {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, + 0xd0b2f94d2f420109}, + {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, + 0x971459828b0719e5}, + {1, 0, 0, 0}}, + {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, + 0x961610004a866aba}, + {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, + 0x7acb9fadcee75e44}, + {1, 0, 0, 0}}, + {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, + 0x24eb9acca333bf5b}, + {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, + 0x69f891c5acd079cc}, + {1, 0, 0, 0}}, + {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, + 0xe51f547c5972a107}, + {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, + 0x1c309a2b25bb1387}, + {1, 0, 0, 0}}, + {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, + 0x20b87b8aa2c4e503}, + {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, + 0xf5c6fa49919776be}, + {1, 0, 0, 0}}, + {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, + 0x1ed7d1b9332010b9}, + {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, + 0x3a2b03f03217257a}, + {1, 0, 0, 0}}, + {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, + 0x15fee545c78dd9f6}, + {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, + 0x4ab5b6b2b8753f81}, + {1, 0, 0, 0}}} +}; + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + */ +static void select_point(const u64 idx, unsigned int size, + const smallfelem pre_comp[16][3], smallfelem out[3]) +{ + unsigned i, j; + u64 *outlimbs = &out[0][0]; + + memset(out, 0, sizeof(*out) * 3); + + for (i = 0; i < size; i++) { + const u64 *inlimbs = (u64 *)&pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) +{ + if ((i < 0) || (i >= 256)) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], + const unsigned num_points, const u8 *g_scalar, + const int mixed, const smallfelem pre_comp[][17][3], + const smallfelem g_pre_comp[2][16][3]) +{ + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], ftmp; + smallfelem tmp[3]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, sizeof(nq)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (two in each of the last 32 rounds) and additions of + * other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 255 : 31); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 31)) { + /* first, look 32 bits upwards */ + bits = get_bit(g_scalar, i + 224) << 3; + bits |= get_bit(g_scalar, i + 160) << 2; + bits |= get_bit(g_scalar, i + 96) << 1; + bits |= get_bit(g_scalar, i + 32); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) { + /* Arg 1 below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 192) << 3; + bits |= get_bit(g_scalar, i + 128) << 2; + bits |= get_bit(g_scalar, i + 64) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + /* Arg 1 below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* + * select the point to add or subtract, in constant time + */ + select_point(digit, 17, pre_comp[num], tmp); + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); + felem_contract(tmp[1], ftmp); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} + +/* Precomputation for the group generator. */ +struct nistp256_pre_comp_st { + smallfelem g_pre_comp[2][16][3]; + int references; + CRYPTO_RWLOCK *lock; +}; + +const EC_METHOD *EC_GFp_nistp256_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp256_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp256_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp256_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */ , + 0 /* point2oct */ , + 0 /* oct2point */ , + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp256_points_mul, + ec_GFp_nistp256_precompute_mult, + ec_GFp_nistp256_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/******************************************************************************/ +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP256_PRE_COMP *nistp256_pre_comp_new() +{ + NISTP256_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (ret == NULL) { + ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *p) +{ + int i; + if (p != NULL) + CRYPTO_atomic_add(&p->references, 1, &i, p->lock); + return p; +} + +void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *pre) +{ + int i; + + if (pre == NULL) + return; + + CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock); + REF_PRINT_COUNT("EC_nistp256", x); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + CRYPTO_THREAD_lock_free(pre->lock); + OPENSSL_free(pre); +} + +/******************************************************************************/ +/* + * OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp256_group_init(EC_GROUP *group) +{ + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} + +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; + BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_256; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in; + smallfelem x_out, y_out; + longfelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || + (!BN_to_felem(z1, point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!smallfelem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!smallfelem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +/* points below is of size |num|, and tmp_smallfelems is of size |num+1| */ +static void make_points_affine(size_t num, smallfelem points[][3], + smallfelem tmp_smallfelems[]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(smallfelem), + tmp_smallfelems, + (void (*)(void *))smallfelem_one, + smallfelem_is_zero_int, + (void (*)(void *, const void *)) + smallfelem_assign, + (void (*)(void *, const void *)) + smallfelem_square_contract, + (void (*) + (void *, const void *, + const void *)) + smallfelem_mul_contract, + (void (*)(void *, const void *)) + smallfelem_inv_contract, + /* nothing to contract */ + (void (*)(void *, const void *)) + smallfelem_assign); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + smallfelem (*pre_comp)[17][3] = NULL; + smallfelem *tmp_smallfelems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + smallfelem x_in, y_in, z_in; + felem x_out, y_out, z_out; + NISTP256_PRE_COMP *pre = NULL; + const smallfelem(*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) { + pre = group->pre_comp.nistp256; + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const smallfelem(*)[16][3])pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, + ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points++; + } + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_malloc(sizeof(*secrets) * num_points); + pre_comp = OPENSSL_malloc(sizeof(*pre_comp) * num_points); + if (mixed) + tmp_smallfelems = + OPENSSL_malloc(sizeof(*tmp_smallfelems) * (num_points * 17 + 1)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_smallfelems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + memset(secrets, 0, sizeof(*secrets) * num_points); + memset(pre_comp, 0, sizeof(*pre_comp) * num_points); + for (i = 0; i < num_points; ++i) { + if (i == num) + /* + * we didn't have a valid precomputation, so we pick the + * generator + */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) { + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(p_scalar) > 256) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, p->X)) || + (!BN_to_felem(y_out, p->Y)) || + (!BN_to_felem(z_out, p->Z))) + goto err; + felem_shrink(pre_comp[i][1][0], x_out); + felem_shrink(pre_comp[i][1][1], y_out); + felem_shrink(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add_small(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][1][0], + pre_comp[i][1][1], pre_comp[i][1][2], + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double_small(pre_comp[i][j][0], + pre_comp[i][j][1], + pre_comp[i][j][2], + pre_comp[i][j / 2][0], + pre_comp[i][j / 2][1], + pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const smallfelem(*)[17][3])pre_comp, g_pre_comp); + } else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const smallfelem(*)[17][3])pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || + (!smallfelem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + OPENSSL_free(secrets); + OPENSSL_free(pre_comp); + OPENSSL_free(tmp_smallfelems); + return ret; +} + +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + NISTP256_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + smallfelem tmp_smallfelems[32]; + felem x_tmp, y_tmp, z_tmp; + + /* throw away old precomputation */ + EC_pre_comp_free(group); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp256_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp256_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + goto done; + } + if ((!BN_to_felem(x_tmp, group->generator->X)) || + (!BN_to_felem(y_tmp, group->generator->Y)) || + (!BN_to_felem(z_tmp, group->generator->Z))) + goto err; + felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); + felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); + felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); + /* + * compute 2^64*G, 2^128*G, 2^192*G for the first table, 2^32*G, 2^96*G, + * 2^160*G, 2^224*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) { + point_double_small(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], + pre->g_pre_comp[0][i][1], + pre->g_pre_comp[0][i][2]); + for (j = 0; j < 31; ++j) { + point_double_small(pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double_small(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2]); + for (j = 0; j < 31; ++j) { + point_double_small(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2]); + } + } + for (i = 0; i < 2; i++) { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ + point_add_small(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ + point_add_small(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ + point_add_small(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G + */ + point_add_small(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { + /* odd multiples: add G resp. 2^32*G */ + point_add_small(pre->g_pre_comp[i][2 * j + 1][0], + pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], + pre->g_pre_comp[i][2 * j][2], + pre->g_pre_comp[i][1][0], + pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); + + done: + SETPRECOMP(group, nistp256, pre); + pre = NULL; + ret = 1; + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + EC_nistp256_pre_comp_free(pre); + return ret; +} + +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) +{ + return HAVEPRECOMP(group, nistp256); +} +#endif diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistp521.c b/openssl-1.1.0h/crypto/ec/ecp_nistp521.c new file mode 100644 index 0000000..133f089 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistp521.c @@ -0,0 +1,2138 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-521 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/e_os2.h> +#ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 +NON_EMPTY_TRANSLATION_UNIT +#else + +# include <string.h> +# include <openssl/err.h> +# include "ec_lcl.h" + +# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit + * platforms */ +# else +# error "Need GCC 3.1 or later to define type uint128_t" +# endif + +typedef uint8_t u8; +typedef uint64_t u64; + +/* + * The underlying field. P521 operates over GF(2^521-1). We can serialise an + * element of this field into 66 bytes where the most significant byte + * contains only a single bit. We call this an felem_bytearray. + */ + +typedef u8 felem_bytearray[66]; + +/* + * These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5. + * These values are big-endian. + */ +static const felem_bytearray nistp521_curve_params[5] = { + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* p */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff}, + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* a = -3 */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xfc}, + {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, /* b */ + 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, + 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, + 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, + 0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, + 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, + 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, + 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, + 0x3f, 0x00}, + {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, /* x */ + 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, + 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, + 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, + 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, + 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, + 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, + 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, + 0xbd, 0x66}, + {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, /* y */ + 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, + 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, + 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, + 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, + 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, + 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, + 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, + 0x66, 0x50} +}; + +/*- + * The representation of field elements. + * ------------------------------------ + * + * We represent field elements with nine values. These values are either 64 or + * 128 bits and the field element represented is: + * v[0]*2^0 + v[1]*2^58 + v[2]*2^116 + ... + v[8]*2^464 (mod p) + * Each of the nine values is called a 'limb'. Since the limbs are spaced only + * 58 bits apart, but are greater than 58 bits in length, the most significant + * bits of each limb overlap with the least significant bits of the next. + * + * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a + * 'largefelem' */ + +# define NLIMBS 9 + +typedef uint64_t limb; +typedef limb felem[NLIMBS]; +typedef uint128_t largefelem[NLIMBS]; + +static const limb bottom57bits = 0x1ffffffffffffff; +static const limb bottom58bits = 0x3ffffffffffffff; + +/* + * bin66_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. + */ +static void bin66_to_felem(felem out, const u8 in[66]) +{ + out[0] = (*((limb *) & in[0])) & bottom58bits; + out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits; + out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits; + out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits; + out[4] = (*((limb *) & in[29])) & bottom58bits; + out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits; + out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits; + out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits; + out[8] = (*((limb *) & in[58])) & bottom57bits; +} + +/* + * felem_to_bin66 takes an felem and serialises into a little endian, 66 byte + * array. This assumes that the CPU is little-endian. + */ +static void felem_to_bin66(u8 out[66], const felem in) +{ + memset(out, 0, 66); + (*((limb *) & out[0])) = in[0]; + (*((limb *) & out[7])) |= in[1] << 2; + (*((limb *) & out[14])) |= in[2] << 4; + (*((limb *) & out[21])) |= in[3] << 6; + (*((limb *) & out[29])) = in[4]; + (*((limb *) & out[36])) |= in[5] << 2; + (*((limb *) & out[43])) |= in[6] << 4; + (*((limb *) & out[50])) |= in[7] << 6; + (*((limb *) & out[58])) = in[8]; +} + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) +{ + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len - 1 - i]; +} + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) +{ + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof(b_out)); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof(b_out)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin66_to_felem(out, b_out); + return 1; +} + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) +{ + felem_bytearray b_in, b_out; + felem_to_bin66(b_in, in); + flip_endian(b_out, b_in, sizeof(b_out)); + return BN_bin2bn(b_out, sizeof(b_out), out); +} + +/*- + * Field operations + * ---------------- + */ + +static void felem_one(felem out) +{ + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 0; +} + +static void felem_assign(felem out, const felem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + out[4] = in[4]; + out[5] = in[5]; + out[6] = in[6]; + out[7] = in[7]; + out[8] = in[8]; +} + +/* felem_sum64 sets out = out + in. */ +static void felem_sum64(felem out, const felem in) +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + out[4] += in[4]; + out[5] += in[5]; + out[6] += in[6]; + out[7] += in[7]; + out[8] += in[8]; +} + +/* felem_scalar sets out = in * scalar */ +static void felem_scalar(felem out, const felem in, limb scalar) +{ + out[0] = in[0] * scalar; + out[1] = in[1] * scalar; + out[2] = in[2] * scalar; + out[3] = in[3] * scalar; + out[4] = in[4] * scalar; + out[5] = in[5] * scalar; + out[6] = in[6] * scalar; + out[7] = in[7] * scalar; + out[8] = in[8] * scalar; +} + +/* felem_scalar64 sets out = out * scalar */ +static void felem_scalar64(felem out, limb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; +} + +/* felem_scalar128 sets out = out * scalar */ +static void felem_scalar128(largefelem out, limb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; +} + +/*- + * felem_neg sets |out| to |-in| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < 2^62 + */ +static void felem_neg(felem out, const felem in) +{ + /* In order to prevent underflow, we subtract from 0 mod p. */ + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); + + out[0] = two62m3 - in[0]; + out[1] = two62m2 - in[1]; + out[2] = two62m2 - in[2]; + out[3] = two62m2 - in[3]; + out[4] = two62m2 - in[4]; + out[5] = two62m2 - in[5]; + out[6] = two62m2 - in[6]; + out[7] = two62m2 - in[7]; + out[8] = two62m2 - in[8]; +} + +/*- + * felem_diff64 subtracts |in| from |out| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < out[i] + 2^62 + */ +static void felem_diff64(felem out, const felem in) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4); + + out[0] += two62m3 - in[0]; + out[1] += two62m2 - in[1]; + out[2] += two62m2 - in[2]; + out[3] += two62m2 - in[3]; + out[4] += two62m2 - in[4]; + out[5] += two62m2 - in[5]; + out[6] += two62m2 - in[6]; + out[7] += two62m2 - in[7]; + out[8] += two62m2 - in[8]; +} + +/*- + * felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^62 + 2^17 + * On exit: + * out[i] < out[i] + 2^63 + */ +static void felem_diff_128_64(largefelem out, const felem in) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5); + static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4); + + out[0] += two63m6 - in[0]; + out[1] += two63m5 - in[1]; + out[2] += two63m5 - in[2]; + out[3] += two63m5 - in[3]; + out[4] += two63m5 - in[4]; + out[5] += two63m5 - in[5]; + out[6] += two63m5 - in[6]; + out[7] += two63m5 - in[7]; + out[8] += two63m5 - in[8]; +} + +/*- + * felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^126 + * On exit: + * out[i] < out[i] + 2^127 - 2^69 + */ +static void felem_diff128(largefelem out, const largefelem in) +{ + /* + * In order to prevent underflow, we add 0 mod p before subtracting. + */ + static const uint128_t two127m70 = + (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70); + static const uint128_t two127m69 = + (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69); + + out[0] += (two127m70 - in[0]); + out[1] += (two127m69 - in[1]); + out[2] += (two127m69 - in[2]); + out[3] += (two127m69 - in[3]); + out[4] += (two127m69 - in[4]); + out[5] += (two127m69 - in[5]); + out[6] += (two127m69 - in[6]); + out[7] += (two127m69 - in[7]); + out[8] += (two127m69 - in[8]); +} + +/*- + * felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^62 + * On exit: + * out[i] < 17 * max(in[i]) * max(in[i]) + */ +static void felem_square(largefelem out, const felem in) +{ + felem inx2, inx4; + felem_scalar(inx2, in, 2); + felem_scalar(inx4, in, 4); + + /*- + * We have many cases were we want to do + * in[x] * in[y] + + * in[y] * in[x] + * This is obviously just + * 2 * in[x] * in[y] + * However, rather than do the doubling on the 128 bit result, we + * double one of the inputs to the multiplication by reading from + * |inx2| + */ + + out[0] = ((uint128_t) in[0]) * in[0]; + out[1] = ((uint128_t) in[0]) * inx2[1]; + out[2] = ((uint128_t) in[0]) * inx2[2] + ((uint128_t) in[1]) * in[1]; + out[3] = ((uint128_t) in[0]) * inx2[3] + ((uint128_t) in[1]) * inx2[2]; + out[4] = ((uint128_t) in[0]) * inx2[4] + + ((uint128_t) in[1]) * inx2[3] + ((uint128_t) in[2]) * in[2]; + out[5] = ((uint128_t) in[0]) * inx2[5] + + ((uint128_t) in[1]) * inx2[4] + ((uint128_t) in[2]) * inx2[3]; + out[6] = ((uint128_t) in[0]) * inx2[6] + + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + ((uint128_t) in[3]) * in[3]; + out[7] = ((uint128_t) in[0]) * inx2[7] + + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + ((uint128_t) in[3]) * inx2[4]; + out[8] = ((uint128_t) in[0]) * inx2[8] + + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + ((uint128_t) in[4]) * in[4]; + + /* + * The remaining limbs fall above 2^521, with the first falling at 2^522. + * They correspond to locations one bit up from the limbs produced above + * so we would have to multiply by two to align them. Again, rather than + * operate on the 128-bit result, we double one of the inputs to the + * multiplication. If we want to double for both this reason, and the + * reason above, then we end up multiplying by four. + */ + + /* 9 */ + out[0] += ((uint128_t) in[1]) * inx4[8] + + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + ((uint128_t) in[4]) * inx4[5]; + + /* 10 */ + out[1] += ((uint128_t) in[2]) * inx4[8] + + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + ((uint128_t) in[5]) * inx2[5]; + + /* 11 */ + out[2] += ((uint128_t) in[3]) * inx4[8] + + ((uint128_t) in[4]) * inx4[7] + ((uint128_t) in[5]) * inx4[6]; + + /* 12 */ + out[3] += ((uint128_t) in[4]) * inx4[8] + + ((uint128_t) in[5]) * inx4[7] + ((uint128_t) in[6]) * inx2[6]; + + /* 13 */ + out[4] += ((uint128_t) in[5]) * inx4[8] + ((uint128_t) in[6]) * inx4[7]; + + /* 14 */ + out[5] += ((uint128_t) in[6]) * inx4[8] + ((uint128_t) in[7]) * inx2[7]; + + /* 15 */ + out[6] += ((uint128_t) in[7]) * inx4[8]; + + /* 16 */ + out[7] += ((uint128_t) in[8]) * inx2[8]; +} + +/*- + * felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^64 + * in2[i] < 2^63 + * On exit: + * out[i] < 17 * max(in1[i]) * max(in2[i]) + */ +static void felem_mul(largefelem out, const felem in1, const felem in2) +{ + felem in2x2; + felem_scalar(in2x2, in2, 2); + + out[0] = ((uint128_t) in1[0]) * in2[0]; + + out[1] = ((uint128_t) in1[0]) * in2[1] + + ((uint128_t) in1[1]) * in2[0]; + + out[2] = ((uint128_t) in1[0]) * in2[2] + + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; + + out[3] = ((uint128_t) in1[0]) * in2[3] + + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; + + out[4] = ((uint128_t) in1[0]) * in2[4] + + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; + + out[5] = ((uint128_t) in1[0]) * in2[5] + + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; + + out[6] = ((uint128_t) in1[0]) * in2[6] + + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; + + out[7] = ((uint128_t) in1[0]) * in2[7] + + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; + + out[8] = ((uint128_t) in1[0]) * in2[8] + + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; + + /* See comment in felem_square about the use of in2x2 here */ + + out[0] += ((uint128_t) in1[1]) * in2x2[8] + + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; + + out[1] += ((uint128_t) in1[2]) * in2x2[8] + + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; + + out[2] += ((uint128_t) in1[3]) * in2x2[8] + + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; + + out[3] += ((uint128_t) in1[4]) * in2x2[8] + + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; + + out[4] += ((uint128_t) in1[5]) * in2x2[8] + + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; + + out[5] += ((uint128_t) in1[6]) * in2x2[8] + + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; + + out[6] += ((uint128_t) in1[7]) * in2x2[8] + + ((uint128_t) in1[8]) * in2x2[7]; + + out[7] += ((uint128_t) in1[8]) * in2x2[8]; +} + +static const limb bottom52bits = 0xfffffffffffff; + +/*- + * felem_reduce converts a largefelem to an felem. + * On entry: + * in[i] < 2^128 + * On exit: + * out[i] < 2^59 + 2^14 + */ +static void felem_reduce(felem out, const largefelem in) +{ + u64 overflow1, overflow2; + + out[0] = ((limb) in[0]) & bottom58bits; + out[1] = ((limb) in[1]) & bottom58bits; + out[2] = ((limb) in[2]) & bottom58bits; + out[3] = ((limb) in[3]) & bottom58bits; + out[4] = ((limb) in[4]) & bottom58bits; + out[5] = ((limb) in[5]) & bottom58bits; + out[6] = ((limb) in[6]) & bottom58bits; + out[7] = ((limb) in[7]) & bottom58bits; + out[8] = ((limb) in[8]) & bottom58bits; + + /* out[i] < 2^58 */ + + out[1] += ((limb) in[0]) >> 58; + out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; + /*- + * out[1] < 2^58 + 2^6 + 2^58 + * = 2^59 + 2^6 + */ + out[2] += ((limb) (in[0] >> 64)) >> 52; + + out[2] += ((limb) in[1]) >> 58; + out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6; + out[3] += ((limb) (in[1] >> 64)) >> 52; + + out[3] += ((limb) in[2]) >> 58; + out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6; + out[4] += ((limb) (in[2] >> 64)) >> 52; + + out[4] += ((limb) in[3]) >> 58; + out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6; + out[5] += ((limb) (in[3] >> 64)) >> 52; + + out[5] += ((limb) in[4]) >> 58; + out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6; + out[6] += ((limb) (in[4] >> 64)) >> 52; + + out[6] += ((limb) in[5]) >> 58; + out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6; + out[7] += ((limb) (in[5] >> 64)) >> 52; + + out[7] += ((limb) in[6]) >> 58; + out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6; + out[8] += ((limb) (in[6] >> 64)) >> 52; + + out[8] += ((limb) in[7]) >> 58; + out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; + /*- + * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 + * < 2^59 + 2^13 + */ + overflow1 = ((limb) (in[7] >> 64)) >> 52; + + overflow1 += ((limb) in[8]) >> 58; + overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; + overflow2 = ((limb) (in[8] >> 64)) >> 52; + + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ + + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + /*- + * out[0] < 2^58 + * out[1] < 2^59 + 2^6 + 2^13 + 2^2 + * < 2^59 + 2^14 + */ +} + +static void felem_square_reduce(felem out, const felem in) +{ + largefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); +} + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) +{ + largefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} + +/*- + * felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) +{ + felem ftmp, ftmp2, ftmp3, ftmp4; + largefelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(ftmp2, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + + felem_assign(ftmp2, ftmp3); + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_assign(ftmp4, ftmp3); + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 64; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 128; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 256; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + + for (i = 0; i < 9; i++) { + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); + felem_reduce(out, tmp); /* 2^512 - 3 */ +} + +/* This is 2^521-1, expressed as an felem */ +static const felem kPrime = { + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff +}; + +/*- + * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static limb felem_is_zero(const felem in) +{ + felem ftmp; + limb is_zero, is_p; + felem_assign(ftmp, in); + + ftmp[0] += ftmp[8] >> 57; + ftmp[8] &= bottom57bits; + /* ftmp[8] < 2^57 */ + ftmp[1] += ftmp[0] >> 58; + ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; + ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; + ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; + ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; + ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; + ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; + ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; + ftmp[7] &= bottom58bits; + /* ftmp[8] < 2^57 + 4 */ + + /* + * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is greater + * than our bound for ftmp[8]. Therefore we only have to check if the + * zero is zero or 2^521-1. + */ + + is_zero = 0; + is_zero |= ftmp[0]; + is_zero |= ftmp[1]; + is_zero |= ftmp[2]; + is_zero |= ftmp[3]; + is_zero |= ftmp[4]; + is_zero |= ftmp[5]; + is_zero |= ftmp[6]; + is_zero |= ftmp[7]; + is_zero |= ftmp[8]; + + is_zero--; + /* + * We know that ftmp[i] < 2^63, therefore the only way that the top bit + * can be set is if is_zero was 0 before the decrement. + */ + is_zero = 0 - (is_zero >> 63); + + is_p = ftmp[0] ^ kPrime[0]; + is_p |= ftmp[1] ^ kPrime[1]; + is_p |= ftmp[2] ^ kPrime[2]; + is_p |= ftmp[3] ^ kPrime[3]; + is_p |= ftmp[4] ^ kPrime[4]; + is_p |= ftmp[5] ^ kPrime[5]; + is_p |= ftmp[6] ^ kPrime[6]; + is_p |= ftmp[7] ^ kPrime[7]; + is_p |= ftmp[8] ^ kPrime[8]; + + is_p--; + is_p = 0 - (is_p >> 63); + + is_zero |= is_p; + return is_zero; +} + +static int felem_is_zero_int(const void *in) +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} + +/*- + * felem_contract converts |in| to its unique, minimal representation. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static void felem_contract(felem out, const felem in) +{ + limb is_p, is_greater, sign; + static const limb two58 = ((limb) 1) << 58; + + felem_assign(out, in); + + out[0] += out[8] >> 57; + out[8] &= bottom57bits; + /* out[8] < 2^57 */ + out[1] += out[0] >> 58; + out[0] &= bottom58bits; + out[2] += out[1] >> 58; + out[1] &= bottom58bits; + out[3] += out[2] >> 58; + out[2] &= bottom58bits; + out[4] += out[3] >> 58; + out[3] &= bottom58bits; + out[5] += out[4] >> 58; + out[4] &= bottom58bits; + out[6] += out[5] >> 58; + out[5] &= bottom58bits; + out[7] += out[6] >> 58; + out[6] &= bottom58bits; + out[8] += out[7] >> 58; + out[7] &= bottom58bits; + /* out[8] < 2^57 + 4 */ + + /* + * If the value is greater than 2^521-1 then we have to subtract 2^521-1 + * out. See the comments in felem_is_zero regarding why we don't test for + * other multiples of the prime. + */ + + /* + * First, if |out| is equal to 2^521-1, we subtract it out to get zero. + */ + + is_p = out[0] ^ kPrime[0]; + is_p |= out[1] ^ kPrime[1]; + is_p |= out[2] ^ kPrime[2]; + is_p |= out[3] ^ kPrime[3]; + is_p |= out[4] ^ kPrime[4]; + is_p |= out[5] ^ kPrime[5]; + is_p |= out[6] ^ kPrime[6]; + is_p |= out[7] ^ kPrime[7]; + is_p |= out[8] ^ kPrime[8]; + + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = 0 - (is_p >> 63); + is_p = ~is_p; + + /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */ + + out[0] &= is_p; + out[1] &= is_p; + out[2] &= is_p; + out[3] &= is_p; + out[4] &= is_p; + out[5] &= is_p; + out[6] &= is_p; + out[7] &= is_p; + out[8] &= is_p; + + /* + * In order to test that |out| >= 2^521-1 we need only test if out[8] >> + * 57 is greater than zero as (2^521-1) + x >= 2^522 + */ + is_greater = out[8] >> 57; + is_greater |= is_greater << 32; + is_greater |= is_greater << 16; + is_greater |= is_greater << 8; + is_greater |= is_greater << 4; + is_greater |= is_greater << 2; + is_greater |= is_greater << 1; + is_greater = 0 - (is_greater >> 63); + + out[0] -= kPrime[0] & is_greater; + out[1] -= kPrime[1] & is_greater; + out[2] -= kPrime[2] & is_greater; + out[3] -= kPrime[3] & is_greater; + out[4] -= kPrime[4] & is_greater; + out[5] -= kPrime[5] & is_greater; + out[6] -= kPrime[6] & is_greater; + out[7] -= kPrime[7] & is_greater; + out[8] -= kPrime[8] & is_greater; + + /* Eliminate negative coefficients */ + sign = -(out[0] >> 63); + out[0] += (two58 & sign); + out[1] -= (1 & sign); + sign = -(out[1] >> 63); + out[1] += (two58 & sign); + out[2] -= (1 & sign); + sign = -(out[2] >> 63); + out[2] += (two58 & sign); + out[3] -= (1 & sign); + sign = -(out[3] >> 63); + out[3] += (two58 & sign); + out[4] -= (1 & sign); + sign = -(out[4] >> 63); + out[4] += (two58 & sign); + out[5] -= (1 & sign); + sign = -(out[0] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); + sign = -(out[5] >> 63); + out[5] += (two58 & sign); + out[6] -= (1 & sign); + sign = -(out[6] >> 63); + out[6] += (two58 & sign); + out[7] -= (1 & sign); + sign = -(out[7] >> 63); + out[7] += (two58 & sign); + out[8] -= (1 & sign); +} + +/*- + * Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates */ + +/*- + * point_double calculates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) +{ + largefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff64(ftmp, delta); + /* ftmp[i] < 2^61 */ + felem_sum64(ftmp2, delta); + /* ftmp2[i] < 2^60 + 2^15 */ + felem_scalar64(ftmp2, 3); + /* ftmp2[i] < 3*2^60 + 3*2^15 */ + felem_mul(tmp, ftmp, ftmp2); + /*- + * tmp[i] < 17(3*2^121 + 3*2^76) + * = 61*2^121 + 61*2^76 + * < 64*2^121 + 64*2^76 + * = 2^127 + 2^82 + * < 2^128 + */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* + * tmp[i] < 17*2^120 < 2^125 + */ + felem_assign(ftmp, beta); + felem_scalar64(ftmp, 8); + /* ftmp[i] < 2^62 + 2^17 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum64(delta, gamma); + /* delta[i] < 2^60 + 2^15 */ + felem_assign(ftmp, y_in); + felem_sum64(ftmp, z_in); + /* ftmp[i] < 2^60 + 2^15 */ + felem_square(tmp, ftmp); + /* + * tmp[i] < 17(2^122) < 2^127 + */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^127 + 2^63 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar64(beta, 4); + /* beta[i] < 2^61 + 2^16 */ + felem_diff64(beta, x_out); + /* beta[i] < 2^61 + 2^60 + 2^16 */ + felem_mul(tmp, alpha, beta); + /*- + * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) + * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) + * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * < 2^128 + */ + felem_square(tmp2, gamma); + /*- + * tmp2[i] < 17*(2^59 + 2^14)^2 + * = 17*(2^118 + 2^74 + 2^28) + */ + felem_scalar128(tmp2, 8); + /*- + * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) + * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 + * < 2^126 + */ + felem_diff128(tmp, tmp2); + /*- + * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + + * 2^74 + 2^69 + 2^34 + 2^30 + * < 2^128 + */ + felem_reduce(y_out, tmp); +} + +/* copy_conditional copies in to out iff mask is all ones. */ +static void copy_conditional(felem out, const felem in, limb mask) +{ + unsigned i; + for (i = 0; i < NLIMBS; ++i) { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } +} + +/*- + * point_add calculates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, + const felem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + largefelem tmp, tmp2; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + if (!mixed) { + /* ftmp2 = z2z2 = z2**2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* u1 = ftmp3 = x1*z2z2 */ + felem_mul(tmp, x1, ftmp2); + felem_reduce(ftmp3, tmp); + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_sum64(ftmp5, z2); + /* ftmp5[i] < 2^61 */ + + /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2 * z2z2 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + + /* ftmp5 = 2*z1z2 */ + felem_scalar(ftmp5, z1, 2); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + } + + /* u2 = x2*z1z1 */ + felem_mul(tmp, x2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* h = ftmp4 = u2 - u1 */ + felem_diff_128_64(tmp, ftmp3); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp4, tmp); + + x_equal = felem_is_zero(ftmp4); + + /* z_out = ftmp5 * h */ + felem_mul(tmp, ftmp5, ftmp4); + felem_reduce(z_out, tmp); + + /* ftmp = z1 * z1z1 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_mul(tmp, y2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_128_64(tmp, ftmp6); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp5, tmp); + y_equal = felem_is_zero(ftmp5); + felem_scalar64(ftmp5, 2); + /* ftmp5[i] < 2^61 */ + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar64(ftmp, 2); + /* ftmp[i] < 2^61 */ + felem_square(tmp, ftmp); + /* tmp[i] < 17*2^122 */ + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_assign(ftmp3, ftmp4); + felem_scalar64(ftmp4, 2); + /* ftmp4[i] < 2^61 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(x_out, tmp); + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff64(ftmp3, x_out); + /* + * ftmp3[i] < 2^60 + 2^60 = 2^61 + */ + felem_mul(tmp, ftmp5, ftmp3); + /* tmp[i] < 17*2^122 */ + felem_mul(tmp2, ftmp6, ftmp2); + /* tmp2[i] < 17*2^120 */ + felem_scalar128(tmp2, 2); + /* tmp2[i] < 17*2^121 */ + felem_diff128(tmp, tmp2); + /*- + * tmp[i] < 2^127 - 2^69 + 17*2^122 + * = 2^126 - 2^122 - 2^6 - 2^2 - 1 + * < 2^127 + */ + felem_reduce(y_out, tmp); + + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} + +/*- + * Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 16 elements: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^130G + * 3 | 0 0 1 1 | (2^130 + 1)G + * 4 | 0 1 0 0 | 2^260G + * 5 | 0 1 0 1 | (2^260 + 1)G + * 6 | 0 1 1 0 | (2^260 + 2^130)G + * 7 | 0 1 1 1 | (2^260 + 2^130 + 1)G + * 8 | 1 0 0 0 | 2^390G + * 9 | 1 0 0 1 | (2^390 + 1)G + * 10 | 1 0 1 0 | (2^390 + 2^130)G + * 11 | 1 0 1 1 | (2^390 + 2^130 + 1)G + * 12 | 1 1 0 0 | (2^390 + 2^260)G + * 13 | 1 1 0 1 | (2^390 + 2^260 + 1)G + * 14 | 1 1 1 0 | (2^390 + 2^260 + 2^130)G + * 15 | 1 1 1 1 | (2^390 + 2^260 + 2^130 + 1)G + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const felem gmul[16][3] = { +{{0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, + 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, + {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, + 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, + 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, + {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, + 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, + 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, + {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, + 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, + 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, + {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, + 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, + 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, + {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, + 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, + 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, + {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, + 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, + 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, + {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, + 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, + 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, + {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, + 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, + 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, + {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, + 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, + 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, + {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, + 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, + 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, + {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, + 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, + 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, + {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, + 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, + 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, + {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, + 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, + 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, + {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, + 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, +{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, + 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, + {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, + 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}} +}; + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + */ + /* pre_comp below is of the size provided in |size| */ +static void select_point(const limb idx, unsigned int size, + const felem pre_comp[][3], felem out[3]) +{ + unsigned i, j; + limb *outlimbs = &out[0][0]; + + memset(out, 0, sizeof(*out) * 3); + + for (i = 0; i < size; i++) { + const limb *inlimbs = &pre_comp[i][0][0]; + limb mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) +{ + if (i < 0) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], + const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], + const felem g_pre_comp[16][3]) +{ + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + limb bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, sizeof(nq)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (last quarter of rounds) and additions of other + * points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 520 : 130); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 130)) { + bits = get_bit(g_scalar, i + 390) << 3; + if (i < 130) { + bits |= get_bit(g_scalar, i + 260) << 2; + bits |= get_bit(g_scalar, i + 130) << 1; + bits |= get_bit(g_scalar, i); + } + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp, tmp); + if (!skip) { + /* The 1 argument below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* + * select the point to add or subtract, in constant time + */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_conditional(tmp[1], tmp[3], (-(limb) sign)); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} + +/* Precomputation for the group generator. */ +struct nistp521_pre_comp_st { + felem g_pre_comp[16][3]; + int references; + CRYPTO_RWLOCK *lock; +}; + +const EC_METHOD *EC_GFp_nistp521_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp521_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp521_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */ , + 0 /* point2oct */ , + 0 /* oct2point */ , + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp521_points_mul, + ec_GFp_nistp521_precompute_mult, + ec_GFp_nistp521_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/******************************************************************************/ +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP521_PRE_COMP *nistp521_pre_comp_new() +{ + NISTP521_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (ret == NULL) { + ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *p) +{ + int i; + if (p != NULL) + CRYPTO_atomic_add(&p->references, 1, &i, p->lock); + return p; +} + +void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *p) +{ + int i; + + if (p == NULL) + return; + + CRYPTO_atomic_add(&p->references, -1, &i, p->lock); + REF_PRINT_COUNT("EC_nistp521", x); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + CRYPTO_THREAD_lock_free(p->lock); + OPENSSL_free(p); +} + +/******************************************************************************/ +/* + * OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp521_group_init(EC_GROUP *group) +{ + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} + +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) + goto err; + BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_521; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in, x_out, y_out; + largefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || + (!BN_to_felem(z1, point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +/* points below is of size |num|, and tmp_felems is of size |num+1/ */ +static void make_points_affine(size_t num, felem points[][3], + felem tmp_felems[]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *))felem_one, + felem_is_zero_int, + (void (*)(void *, const void *)) + felem_assign, + (void (*)(void *, const void *)) + felem_square_reduce, (void (*) + (void *, + const void + *, + const void + *)) + felem_mul_reduce, + (void (*)(void *, const void *)) + felem_inv, + (void (*)(void *, const void *)) + felem_contract); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP521_PRE_COMP *pre = NULL; + felem(*g_pre_comp)[3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) { + pre = group->pre_comp.nistp521; + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = &pre->g_pre_comp[0]; + else + /* try to use the standard precomputation */ + g_pre_comp = (felem(*)[3]) gmul; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[1][0]) || + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, + ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points++; + } + + if (num_points > 0) { + if (num_points >= 2) { + /* + * unless we precompute multiples for just one point, converting + * those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); + pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); + if (mixed) + tmp_felems = + OPENSSL_malloc(sizeof(*tmp_felems) * (num_points * 17 + 1)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_felems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + for (i = 0; i < num_points; ++i) { + if (i == num) + /* + * we didn't have a valid precomputation, so we pick the + * generator + */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) { + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(p_scalar) > 521) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, p->X)) || + (!BN_to_felem(y_out, p->Y)) || + (!BN_to_felem(z_out, p->Z))) + goto err; + memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); + memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); + memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][1][0], + pre_comp[i][1][1], pre_comp[i][1][2], 0, + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][j / 2][0], + pre_comp[i][j / 2][1], + pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3])pre_comp, + (const felem(*)[3])g_pre_comp); + } else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + OPENSSL_free(secrets); + OPENSSL_free(pre_comp); + OPENSSL_free(tmp_felems); + return ret; +} + +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + NISTP521_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[16]; + + /* throw away old precomputation */ + EC_pre_comp_free(group); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp521_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + goto done; + } + if ((!BN_to_felem(pre->g_pre_comp[1][0], group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[1][1], group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], group->generator->Z))) + goto err; + /* compute 2^130*G, 2^260*G, 2^390*G */ + for (i = 1; i <= 4; i <<= 1) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) { + point_double(pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], + pre->g_pre_comp[2 * i][2]); + } + } + /* g_pre_comp[0] is the point at infinity */ + memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); + /* the remaining multiples */ + /* 2^130*G + 2^260*G */ + point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^130*G + 2^390*G */ + point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); + /* 2^130*G + 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) { + /* odd multiples: add G */ + point_add(pre->g_pre_comp[2 * i + 1][0], + pre->g_pre_comp[2 * i + 1][1], + pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0], + pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], 0, + pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } + make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); + + done: + SETPRECOMP(group, nistp521, pre); + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + EC_nistp521_pre_comp_free(pre); + return ret; +} + +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) +{ + return HAVEPRECOMP(group, nistp521); +} + +#endif diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistputil.c b/openssl-1.1.0h/crypto/ec/ecp_nistputil.c new file mode 100644 index 0000000..97fb631 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistputil.c @@ -0,0 +1,223 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include <openssl/opensslconf.h> +#ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 +NON_EMPTY_TRANSLATION_UNIT +#else + +/* + * Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c. + */ + +# include <stddef.h> +# include "ec_lcl.h" + +/* + * Convert an array of points into affine coordinates. (If the point at + * infinity is found (Z = 0), it remains unchanged.) This function is + * essentially an equivalent to EC_POINTs_make_affine(), but works with the + * internal representation of points as used by ecp_nistp###.c rather than + * with (BIGNUM-based) EC_POINT data structures. point_array is the + * input/output buffer ('num' points in projective form, i.e. three + * coordinates each), based on an internal representation of field elements + * of size 'felem_size'. tmp_felems needs to point to a temporary array of + * 'num'+1 field elements for storage of intermediate values. + */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, + void *tmp_felems, + void (*felem_one) (void *out), + int (*felem_is_zero) (const void + *in), + void (*felem_assign) (void *out, + const void + *in), + void (*felem_square) (void *out, + const void + *in), + void (*felem_mul) (void *out, + const void + *in1, + const void + *in2), + void (*felem_inv) (void *out, + const void + *in), + void (*felem_contract) (void + *out, + const + void + *in)) +{ + int i = 0; + +# define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) +# define X(I) (&((char *)point_array)[3*(I) * felem_size]) +# define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size]) +# define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size]) + + if (!felem_is_zero(Z(0))) + felem_assign(tmp_felem(0), Z(0)); + else + felem_one(tmp_felem(0)); + for (i = 1; i < (int)num; i++) { + if (!felem_is_zero(Z(i))) + felem_mul(tmp_felem(i), tmp_felem(i - 1), Z(i)); + else + felem_assign(tmp_felem(i), tmp_felem(i - 1)); + } + /* + * Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any + * zero-valued factors: if Z(i) = 0, we essentially pretend that Z(i) = 1 + */ + + felem_inv(tmp_felem(num - 1), tmp_felem(num - 1)); + for (i = num - 1; i >= 0; i--) { + if (i > 0) + /* + * tmp_felem(i-1) is the product of Z(0) .. Z(i-1), tmp_felem(i) + * is the inverse of the product of Z(0) .. Z(i) + */ + /* 1/Z(i) */ + felem_mul(tmp_felem(num), tmp_felem(i - 1), tmp_felem(i)); + else + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + + if (!felem_is_zero(Z(i))) { + if (i > 0) + /* + * For next iteration, replace tmp_felem(i-1) by its inverse + */ + felem_mul(tmp_felem(i - 1), tmp_felem(i), Z(i)); + + /* + * Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) + */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + felem_contract(X(i), X(i)); + felem_contract(Y(i), Y(i)); + felem_one(Z(i)); + } else { + if (i > 0) + /* + * For next iteration, replace tmp_felem(i-1) by its inverse + */ + felem_assign(tmp_felem(i - 1), tmp_felem(i)); + } + } +} + +/*- + * This function looks at 5+1 scalar bits (5 current, 1 adjacent less + * significant bit), and recodes them into a signed digit for use in fast point + * multiplication: the use of signed rather than unsigned digits means that + * fewer points need to be precomputed, given that point inversion is easy + * (a precomputed point dP makes -dP available as well). + * + * BACKGROUND: + * + * Signed digits for multiplication were introduced by Booth ("A signed binary + * multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, + * pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. + * Booth's original encoding did not generally improve the density of nonzero + * digits over the binary representation, and was merely meant to simplify the + * handling of signed factors given in two's complement; but it has since been + * shown to be the basis of various signed-digit representations that do have + * further advantages, including the wNAF, using the following general approach: + * + * (1) Given a binary representation + * + * b_k ... b_2 b_1 b_0, + * + * of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 + * by using bit-wise subtraction as follows: + * + * b_k b_(k-1) ... b_2 b_1 b_0 + * - b_k ... b_3 b_2 b_1 b_0 + * ------------------------------------- + * s_k b_(k-1) ... s_3 s_2 s_1 s_0 + * + * A left-shift followed by subtraction of the original value yields a new + * representation of the same value, using signed bits s_i = b_(i+1) - b_i. + * This representation from Booth's paper has since appeared in the + * literature under a variety of different names including "reversed binary + * form", "alternating greedy expansion", "mutual opposite form", and + * "sign-alternating {+-1}-representation". + * + * An interesting property is that among the nonzero bits, values 1 and -1 + * strictly alternate. + * + * (2) Various window schemes can be applied to the Booth representation of + * integers: for example, right-to-left sliding windows yield the wNAF + * (a signed-digit encoding independently discovered by various researchers + * in the 1990s), and left-to-right sliding windows yield a left-to-right + * equivalent of the wNAF (independently discovered by various researchers + * around 2004). + * + * To prevent leaking information through side channels in point multiplication, + * we need to recode the given integer into a regular pattern: sliding windows + * as in wNAFs won't do, we need their fixed-window equivalent -- which is a few + * decades older: we'll be using the so-called "modified Booth encoding" due to + * MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 + * (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five + * signed bits into a signed digit: + * + * s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) + * + * The sign-alternating property implies that the resulting digit values are + * integers from -16 to 16. + * + * Of course, we don't actually need to compute the signed digits s_i as an + * intermediate step (that's just a nice way to see how this scheme relates + * to the wNAF): a direct computation obtains the recoded digit from the + * six bits b_(4j + 4) ... b_(4j - 1). + * + * This function takes those five bits as an integer (0 .. 63), writing the + * recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute + * value, in the range 0 .. 8). Note that this integer essentially provides the + * input bits "shifted to the left" by one position: for example, the input to + * compute the least significant recoded digit, given that there's no bit b_-1, + * has to be b_4 b_3 b_2 b_1 b_0 0. + * + */ +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, + unsigned char *digit, unsigned char in) +{ + unsigned char s, d; + + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as + * 6-bit value */ + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; +} +#endif diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistz256.c b/openssl-1.1.0h/crypto/ec/ecp_nistz256.c new file mode 100644 index 0000000..2461898 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistz256.c @@ -0,0 +1,1559 @@ +/* + * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/****************************************************************************** + * * + * Copyright 2014 Intel Corporation * + * * + * Licensed under the Apache License, Version 2.0 (the "License"); * + * you may not use this file except in compliance with the License. * + * You may obtain a copy of the License at * + * * + * http://www.apache.org/licenses/LICENSE-2.0 * + * * + * Unless required by applicable law or agreed to in writing, software * + * distributed under the License is distributed on an "AS IS" BASIS, * + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * + * See the License for the specific language governing permissions and * + * limitations under the License. * + * * + ****************************************************************************** + * * + * Developers and authors: * + * Shay Gueron (1, 2), and Vlad Krasnov (1) * + * (1) Intel Corporation, Israel Development Center * + * (2) University of Haifa * + * Reference: * + * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with * + * 256 Bit Primes" * + * * + ******************************************************************************/ + +#include <string.h> + +#include "internal/cryptlib.h" +#include "internal/bn_int.h" +#include "ec_lcl.h" + +#if BN_BITS2 != 64 +# define TOBN(hi,lo) lo,hi +#else +# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo) +#endif + +#if defined(__GNUC__) +# define ALIGN32 __attribute((aligned(32))) +#elif defined(_MSC_VER) +# define ALIGN32 __declspec(align(32)) +#else +# define ALIGN32 +#endif + +#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N) +#define P256_LIMBS (256/BN_BITS2) + +typedef unsigned short u16; + +typedef struct { + BN_ULONG X[P256_LIMBS]; + BN_ULONG Y[P256_LIMBS]; + BN_ULONG Z[P256_LIMBS]; +} P256_POINT; + +typedef struct { + BN_ULONG X[P256_LIMBS]; + BN_ULONG Y[P256_LIMBS]; +} P256_POINT_AFFINE; + +typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; + +/* structure for precomputed multiples of the generator */ +struct nistz256_pre_comp_st { + const EC_GROUP *group; /* Parent EC_GROUP object */ + size_t w; /* Window size */ + /* + * Constant time access to the X and Y coordinates of the pre-computed, + * generator multiplies, in the Montgomery domain. Pre-calculated + * multiplies are stored in affine form. + */ + PRECOMP256_ROW *precomp; + void *precomp_storage; + int references; + CRYPTO_RWLOCK *lock; +}; + +/* Functions implemented in assembly */ +/* + * Most of below mentioned functions *preserve* the property of inputs + * being fully reduced, i.e. being in [0, modulus) range. Simply put if + * inputs are fully reduced, then output is too. Note that reverse is + * not true, in sense that given partially reduced inputs output can be + * either, not unlikely reduced. And "most" in first sentence refers to + * the fact that given the calculations flow one can tolerate that + * addition, 1st function below, produces partially reduced result *if* + * multiplications by 2 and 3, which customarily use addition, fully + * reduce it. This effectively gives two options: a) addition produces + * fully reduced result [as long as inputs are, just like remaining + * functions]; b) addition is allowed to produce partially reduced + * result, but multiplications by 2 and 3 perform additional reduction + * step. Choice between the two can be platform-specific, but it was a) + * in all cases so far... + */ +/* Modular add: res = a+b mod P */ +void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS], + const BN_ULONG b[P256_LIMBS]); +/* Modular mul by 2: res = 2*a mod P */ +void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS]); +/* Modular mul by 3: res = 3*a mod P */ +void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS]); + +/* Modular div by 2: res = a/2 mod P */ +void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS]); +/* Modular sub: res = a-b mod P */ +void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS], + const BN_ULONG b[P256_LIMBS]); +/* Modular neg: res = -a mod P */ +void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); +/* Montgomery mul: res = a*b*2^-256 mod P */ +void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS], + const BN_ULONG b[P256_LIMBS]); +/* Montgomery sqr: res = a*a*2^-256 mod P */ +void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS], + const BN_ULONG a[P256_LIMBS]); +/* Convert a number from Montgomery domain, by multiplying with 1 */ +void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS], + const BN_ULONG in[P256_LIMBS]); +/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/ +void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS], + const BN_ULONG in[P256_LIMBS]); +/* Functions that perform constant time access to the precomputed tables */ +void ecp_nistz256_scatter_w5(P256_POINT *val, + const P256_POINT *in_t, int idx); +void ecp_nistz256_gather_w5(P256_POINT *val, + const P256_POINT *in_t, int idx); +void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val, + const P256_POINT_AFFINE *in_t, int idx); +void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val, + const P256_POINT_AFFINE *in_t, int idx); + +/* One converted into the Montgomery domain */ +static const BN_ULONG ONE[P256_LIMBS] = { + TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), + TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe) +}; + +static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); + +/* Precomputed tables for the default generator */ +extern const PRECOMP256_ROW ecp_nistz256_precomputed[37]; + +/* Recode window to a signed digit, see ecp_nistputil.c for details */ +static unsigned int _booth_recode_w5(unsigned int in) +{ + unsigned int s, d; + + s = ~((in >> 5) - 1); + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + return (d << 1) + (s & 1); +} + +static unsigned int _booth_recode_w7(unsigned int in) +{ + unsigned int s, d; + + s = ~((in >> 7) - 1); + d = (1 << 8) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + return (d << 1) + (s & 1); +} + +static void copy_conditional(BN_ULONG dst[P256_LIMBS], + const BN_ULONG src[P256_LIMBS], BN_ULONG move) +{ + BN_ULONG mask1 = 0-move; + BN_ULONG mask2 = ~mask1; + + dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); + dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); + dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); + dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); + if (P256_LIMBS == 8) { + dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); + dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); + dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); + dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); + } +} + +static BN_ULONG is_zero(BN_ULONG in) +{ + in |= (0 - in); + in = ~in; + in >>= BN_BITS2 - 1; + return in; +} + +static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], + const BN_ULONG b[P256_LIMBS]) +{ + BN_ULONG res; + + res = a[0] ^ b[0]; + res |= a[1] ^ b[1]; + res |= a[2] ^ b[2]; + res |= a[3] ^ b[3]; + if (P256_LIMBS == 8) { + res |= a[4] ^ b[4]; + res |= a[5] ^ b[5]; + res |= a[6] ^ b[6]; + res |= a[7] ^ b[7]; + } + + return is_zero(res); +} + +static BN_ULONG is_one(const BIGNUM *z) +{ + BN_ULONG res = 0; + BN_ULONG *a = bn_get_words(z); + + if (bn_get_top(z) == (P256_LIMBS - P256_LIMBS / 8)) { + res = a[0] ^ ONE[0]; + res |= a[1] ^ ONE[1]; + res |= a[2] ^ ONE[2]; + res |= a[3] ^ ONE[3]; + if (P256_LIMBS == 8) { + res |= a[4] ^ ONE[4]; + res |= a[5] ^ ONE[5]; + res |= a[6] ^ ONE[6]; + /* + * no check for a[7] (being zero) on 32-bit platforms, + * because value of "one" takes only 7 limbs. + */ + } + res = is_zero(res); + } + + return res; +} + +#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION +void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a); +void ecp_nistz256_point_add(P256_POINT *r, + const P256_POINT *a, const P256_POINT *b); +void ecp_nistz256_point_add_affine(P256_POINT *r, + const P256_POINT *a, + const P256_POINT_AFFINE *b); +#else +/* Point double: r = 2*a */ +static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a) +{ + BN_ULONG S[P256_LIMBS]; + BN_ULONG M[P256_LIMBS]; + BN_ULONG Zsqr[P256_LIMBS]; + BN_ULONG tmp0[P256_LIMBS]; + + const BN_ULONG *in_x = a->X; + const BN_ULONG *in_y = a->Y; + const BN_ULONG *in_z = a->Z; + + BN_ULONG *res_x = r->X; + BN_ULONG *res_y = r->Y; + BN_ULONG *res_z = r->Z; + + ecp_nistz256_mul_by_2(S, in_y); + + ecp_nistz256_sqr_mont(Zsqr, in_z); + + ecp_nistz256_sqr_mont(S, S); + + ecp_nistz256_mul_mont(res_z, in_z, in_y); + ecp_nistz256_mul_by_2(res_z, res_z); + + ecp_nistz256_add(M, in_x, Zsqr); + ecp_nistz256_sub(Zsqr, in_x, Zsqr); + + ecp_nistz256_sqr_mont(res_y, S); + ecp_nistz256_div_by_2(res_y, res_y); + + ecp_nistz256_mul_mont(M, M, Zsqr); + ecp_nistz256_mul_by_3(M, M); + + ecp_nistz256_mul_mont(S, S, in_x); + ecp_nistz256_mul_by_2(tmp0, S); + + ecp_nistz256_sqr_mont(res_x, M); + + ecp_nistz256_sub(res_x, res_x, tmp0); + ecp_nistz256_sub(S, S, res_x); + + ecp_nistz256_mul_mont(S, S, M); + ecp_nistz256_sub(res_y, S, res_y); +} + +/* Point addition: r = a+b */ +static void ecp_nistz256_point_add(P256_POINT *r, + const P256_POINT *a, const P256_POINT *b) +{ + BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; + BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS]; + BN_ULONG Z1sqr[P256_LIMBS]; + BN_ULONG Z2sqr[P256_LIMBS]; + BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; + BN_ULONG Hsqr[P256_LIMBS]; + BN_ULONG Rsqr[P256_LIMBS]; + BN_ULONG Hcub[P256_LIMBS]; + + BN_ULONG res_x[P256_LIMBS]; + BN_ULONG res_y[P256_LIMBS]; + BN_ULONG res_z[P256_LIMBS]; + + BN_ULONG in1infty, in2infty; + + const BN_ULONG *in1_x = a->X; + const BN_ULONG *in1_y = a->Y; + const BN_ULONG *in1_z = a->Z; + + const BN_ULONG *in2_x = b->X; + const BN_ULONG *in2_y = b->Y; + const BN_ULONG *in2_z = b->Z; + + /* + * Infinity in encoded as (,,0) + */ + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); + if (P256_LIMBS == 8) + in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); + + in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]); + if (P256_LIMBS == 8) + in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]); + + in1infty = is_zero(in1infty); + in2infty = is_zero(in2infty); + + ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */ + ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ + + ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ + ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ + + ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ + ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ + ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */ + + ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ + ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ + ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ + + /* + * This should not happen during sign/ecdh, so no constant time violation + */ + if (is_equal(U1, U2) && !in1infty && !in2infty) { + if (is_equal(S1, S2)) { + ecp_nistz256_point_double(r, a); + return; + } else { + memset(r, 0, sizeof(*r)); + return; + } + } + + ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ + ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ + ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ + ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ + ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ + + ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */ + ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ + + ecp_nistz256_sub(res_x, Rsqr, Hsqr); + ecp_nistz256_sub(res_x, res_x, Hcub); + + ecp_nistz256_sub(res_y, U2, res_x); + + ecp_nistz256_mul_mont(S2, S1, Hcub); + ecp_nistz256_mul_mont(res_y, R, res_y); + ecp_nistz256_sub(res_y, res_y, S2); + + copy_conditional(res_x, in2_x, in1infty); + copy_conditional(res_y, in2_y, in1infty); + copy_conditional(res_z, in2_z, in1infty); + + copy_conditional(res_x, in1_x, in2infty); + copy_conditional(res_y, in1_y, in2infty); + copy_conditional(res_z, in1_z, in2infty); + + memcpy(r->X, res_x, sizeof(res_x)); + memcpy(r->Y, res_y, sizeof(res_y)); + memcpy(r->Z, res_z, sizeof(res_z)); +} + +/* Point addition when b is known to be affine: r = a+b */ +static void ecp_nistz256_point_add_affine(P256_POINT *r, + const P256_POINT *a, + const P256_POINT_AFFINE *b) +{ + BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; + BN_ULONG Z1sqr[P256_LIMBS]; + BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; + BN_ULONG Hsqr[P256_LIMBS]; + BN_ULONG Rsqr[P256_LIMBS]; + BN_ULONG Hcub[P256_LIMBS]; + + BN_ULONG res_x[P256_LIMBS]; + BN_ULONG res_y[P256_LIMBS]; + BN_ULONG res_z[P256_LIMBS]; + + BN_ULONG in1infty, in2infty; + + const BN_ULONG *in1_x = a->X; + const BN_ULONG *in1_y = a->Y; + const BN_ULONG *in1_z = a->Z; + + const BN_ULONG *in2_x = b->X; + const BN_ULONG *in2_y = b->Y; + + /* + * Infinity in encoded as (,,0) + */ + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); + if (P256_LIMBS == 8) + in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); + + /* + * In affine representation we encode infinity as (0,0), which is + * not on the curve, so it is OK + */ + in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | + in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); + if (P256_LIMBS == 8) + in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | + in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); + + in1infty = is_zero(in1infty); + in2infty = is_zero(in2infty); + + ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ + + ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ + ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */ + + ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ + + ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ + + ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ + ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */ + + ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ + ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ + ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ + + ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */ + ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ + + ecp_nistz256_sub(res_x, Rsqr, Hsqr); + ecp_nistz256_sub(res_x, res_x, Hcub); + ecp_nistz256_sub(H, U2, res_x); + + ecp_nistz256_mul_mont(S2, in1_y, Hcub); + ecp_nistz256_mul_mont(H, H, R); + ecp_nistz256_sub(res_y, H, S2); + + copy_conditional(res_x, in2_x, in1infty); + copy_conditional(res_x, in1_x, in2infty); + + copy_conditional(res_y, in2_y, in1infty); + copy_conditional(res_y, in1_y, in2infty); + + copy_conditional(res_z, ONE, in1infty); + copy_conditional(res_z, in1_z, in2infty); + + memcpy(r->X, res_x, sizeof(res_x)); + memcpy(r->Y, res_y, sizeof(res_y)); + memcpy(r->Z, res_z, sizeof(res_z)); +} +#endif + +/* r = in^-1 mod p */ +static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS], + const BN_ULONG in[P256_LIMBS]) +{ + /* + * The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff + * ffffffff ffffffff We use FLT and used poly-2 as exponent + */ + BN_ULONG p2[P256_LIMBS]; + BN_ULONG p4[P256_LIMBS]; + BN_ULONG p8[P256_LIMBS]; + BN_ULONG p16[P256_LIMBS]; + BN_ULONG p32[P256_LIMBS]; + BN_ULONG res[P256_LIMBS]; + int i; + + ecp_nistz256_sqr_mont(res, in); + ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ + + ecp_nistz256_sqr_mont(res, p2); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ + + ecp_nistz256_sqr_mont(res, p4); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ + + ecp_nistz256_sqr_mont(res, p8); + for (i = 0; i < 7; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ + + ecp_nistz256_sqr_mont(res, p16); + for (i = 0; i < 15; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ + + ecp_nistz256_sqr_mont(res, p32); + for (i = 0; i < 31; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, in); + + for (i = 0; i < 32 * 4; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p32); + + for (i = 0; i < 32; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p32); + + for (i = 0; i < 16; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p16); + + for (i = 0; i < 8; i++) + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p8); + + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p4); + + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, p2); + + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_sqr_mont(res, res); + ecp_nistz256_mul_mont(res, res, in); + + memcpy(r, res, sizeof(res)); +} + +/* + * ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and + * returns one if it fits. Otherwise it returns zero. + */ +__owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], + const BIGNUM *in) +{ + return bn_copy_words(out, in, P256_LIMBS); +} + +/* r = sum(scalar[i]*point[i]) */ +__owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, + P256_POINT *r, + const BIGNUM **scalar, + const EC_POINT **point, + size_t num, BN_CTX *ctx) +{ + size_t i; + int j, ret = 0; + unsigned int idx; + unsigned char (*p_str)[33] = NULL; + const unsigned int window_size = 5; + const unsigned int mask = (1 << (window_size + 1)) - 1; + unsigned int wvalue; + P256_POINT *temp; /* place for 5 temporary points */ + const BIGNUM **scalars = NULL; + P256_POINT (*table)[16] = NULL; + void *table_storage = NULL; + + if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT) + || (table_storage = + OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL + || (p_str = + OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL + || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { + ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + table = (void *)ALIGNPTR(table_storage, 64); + temp = (P256_POINT *)(table + num); + + for (i = 0; i < num; i++) { + P256_POINT *row = table[i]; + + /* This is an unusual input, we don't guarantee constant-timeness. */ + if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { + BIGNUM *mod; + + if ((mod = BN_CTX_get(ctx)) == NULL) + goto err; + if (!BN_nnmod(mod, scalar[i], group->order, ctx)) { + ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB); + goto err; + } + scalars[i] = mod; + } else + scalars[i] = scalar[i]; + + for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) { + BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES]; + + p_str[i][j + 0] = (unsigned char)d; + p_str[i][j + 1] = (unsigned char)(d >> 8); + p_str[i][j + 2] = (unsigned char)(d >> 16); + p_str[i][j + 3] = (unsigned char)(d >>= 24); + if (BN_BYTES == 8) { + d >>= 8; + p_str[i][j + 4] = (unsigned char)d; + p_str[i][j + 5] = (unsigned char)(d >> 8); + p_str[i][j + 6] = (unsigned char)(d >> 16); + p_str[i][j + 7] = (unsigned char)(d >> 24); + } + } + for (; j < 33; j++) + p_str[i][j] = 0; + + if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X) + || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y) + || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) { + ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, + EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + /* + * row[0] is implicitly (0,0,0) (the point at infinity), therefore it + * is not stored. All other values are actually stored with an offset + * of -1 in table. + */ + + ecp_nistz256_scatter_w5 (row, &temp[0], 1); + ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */ + ecp_nistz256_scatter_w5 (row, &temp[1], 2); + ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */ + ecp_nistz256_scatter_w5 (row, &temp[2], 3); + ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */ + ecp_nistz256_scatter_w5 (row, &temp[1], 4); + ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */ + ecp_nistz256_scatter_w5 (row, &temp[2], 6); + ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */ + ecp_nistz256_scatter_w5 (row, &temp[3], 5); + ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */ + ecp_nistz256_scatter_w5 (row, &temp[4], 7); + ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */ + ecp_nistz256_scatter_w5 (row, &temp[1], 8); + ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */ + ecp_nistz256_scatter_w5 (row, &temp[2], 12); + ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */ + ecp_nistz256_scatter_w5 (row, &temp[3], 10); + ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */ + ecp_nistz256_scatter_w5 (row, &temp[4], 14); + ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/ + ecp_nistz256_scatter_w5 (row, &temp[2], 13); + ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/ + ecp_nistz256_scatter_w5 (row, &temp[3], 11); + ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/ + ecp_nistz256_scatter_w5 (row, &temp[4], 15); + ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */ + ecp_nistz256_scatter_w5 (row, &temp[2], 9); + ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */ + ecp_nistz256_scatter_w5 (row, &temp[1], 16); + } + + idx = 255; + + wvalue = p_str[0][(idx - 1) / 8]; + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + + /* + * We gather to temp[0], because we know it's position relative + * to table + */ + ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1); + memcpy(r, &temp[0], sizeof(temp[0])); + + while (idx >= 5) { + for (i = (idx == 255 ? 1 : 0); i < num; i++) { + unsigned int off = (idx - 1) / 8; + + wvalue = p_str[i][off] | p_str[i][off + 1] << 8; + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + + wvalue = _booth_recode_w5(wvalue); + + ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); + + ecp_nistz256_neg(temp[1].Y, temp[0].Y); + copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1)); + + ecp_nistz256_point_add(r, r, &temp[0]); + } + + idx -= window_size; + + ecp_nistz256_point_double(r, r); + ecp_nistz256_point_double(r, r); + ecp_nistz256_point_double(r, r); + ecp_nistz256_point_double(r, r); + ecp_nistz256_point_double(r, r); + } + + /* Final window */ + for (i = 0; i < num; i++) { + wvalue = p_str[i][0]; + wvalue = (wvalue << 1) & mask; + + wvalue = _booth_recode_w5(wvalue); + + ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); + + ecp_nistz256_neg(temp[1].Y, temp[0].Y); + copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1); + + ecp_nistz256_point_add(r, r, &temp[0]); + } + + ret = 1; + err: + OPENSSL_free(table_storage); + OPENSSL_free(p_str); + OPENSSL_free(scalars); + return ret; +} + +/* Coordinates of G, for which we have precomputed tables */ +static const BN_ULONG def_xG[P256_LIMBS] = { + TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), + TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6) +}; + +static const BN_ULONG def_yG[P256_LIMBS] = { + TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), + TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) +}; + +/* + * ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256 + * generator. + */ +static int ecp_nistz256_is_affine_G(const EC_POINT *generator) +{ + return (bn_get_top(generator->X) == P256_LIMBS) && + (bn_get_top(generator->Y) == P256_LIMBS) && + is_equal(bn_get_words(generator->X), def_xG) && + is_equal(bn_get_words(generator->Y), def_yG) && + is_one(generator->Z); +} + +__owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) +{ + /* + * We precompute a table for a Booth encoded exponent (wNAF) based + * computation. Each table holds 64 values for safe access, with an + * implicit value of infinity at index zero. We use window of size 7, and + * therefore require ceil(256/7) = 37 tables. + */ + const BIGNUM *order; + EC_POINT *P = NULL, *T = NULL; + const EC_POINT *generator; + NISTZ256_PRE_COMP *pre_comp; + BN_CTX *new_ctx = NULL; + int i, j, k, ret = 0; + size_t w; + + PRECOMP256_ROW *preComputedTable = NULL; + unsigned char *precomp_storage = NULL; + + /* if there is an old NISTZ256_PRE_COMP object, throw it away */ + EC_pre_comp_free(group); + generator = EC_GROUP_get0_generator(group); + if (generator == NULL) { + ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR); + return 0; + } + + if (ecp_nistz256_is_affine_G(generator)) { + /* + * No need to calculate tables for the standard generator because we + * have them statically. + */ + return 1; + } + + if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL) + return 0; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + goto err; + } + + BN_CTX_start(ctx); + + order = EC_GROUP_get0_order(group); + if (order == NULL) + goto err; + + if (BN_is_zero(order)) { + ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER); + goto err; + } + + w = 7; + + if ((precomp_storage = + OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) { + ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE); + goto err; + } + + preComputedTable = (void *)ALIGNPTR(precomp_storage, 64); + + P = EC_POINT_new(group); + T = EC_POINT_new(group); + if (P == NULL || T == NULL) + goto err; + + /* + * The zero entry is implicitly infinity, and we skip it, storing other + * values with -1 offset. + */ + if (!EC_POINT_copy(T, generator)) + goto err; + + for (k = 0; k < 64; k++) { + if (!EC_POINT_copy(P, T)) + goto err; + for (j = 0; j < 37; j++) { + P256_POINT_AFFINE temp; + /* + * It would be faster to use EC_POINTs_make_affine and + * make multiple points affine at the same time. + */ + if (!EC_POINT_make_affine(group, P, ctx)) + goto err; + if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) || + !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) { + ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, + EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k); + for (i = 0; i < 7; i++) { + if (!EC_POINT_dbl(group, P, P, ctx)) + goto err; + } + } + if (!EC_POINT_add(group, T, T, generator, ctx)) + goto err; + } + + pre_comp->group = group; + pre_comp->w = w; + pre_comp->precomp = preComputedTable; + pre_comp->precomp_storage = precomp_storage; + precomp_storage = NULL; + SETPRECOMP(group, nistz256, pre_comp); + pre_comp = NULL; + ret = 1; + + err: + if (ctx != NULL) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + + EC_nistz256_pre_comp_free(pre_comp); + OPENSSL_free(precomp_storage); + EC_POINT_free(P); + EC_POINT_free(T); + return ret; +} + +/* + * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great + * code processing 4 points in parallel, corresponding serial operation + * is several times slower, because it uses 29x29=58-bit multiplication + * as opposite to 64x64=128-bit in integer-only scalar case. As result + * it doesn't provide *significant* performance improvement. Note that + * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work, + * you'd need to compile even asm/ecp_nistz256-avx.pl module. + */ +#if defined(ECP_NISTZ256_AVX2) +# if !(defined(__x86_64) || defined(__x86_64__) || \ + defined(_M_AMD64) || defined(_MX64)) || \ + !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */ +# undef ECP_NISTZ256_AVX2 +# else +/* Constant time access, loading four values, from four consecutive tables */ +void ecp_nistz256_avx2_multi_gather_w7(void *result, const void *in, + int index0, int index1, int index2, + int index3); +void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in); +void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4); +void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4, + const void *Bx4); +void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4, + const void *Bx4); +void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4); +void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4); +void ecp_nistz256_avx2_set1(void *RESULTx4); +int ecp_nistz_avx2_eligible(void); + +static void booth_recode_w7(unsigned char *sign, + unsigned char *digit, unsigned char in) +{ + unsigned char s, d; + + s = ~((in >> 7) - 1); + d = (1 << 8) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; +} + +/* + * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the + * precomputed table. It does 4 affine point additions in parallel, + * significantly speeding up point multiplication for a fixed value. + */ +static void ecp_nistz256_avx2_mul_g(P256_POINT *r, + unsigned char p_str[33], + const P256_POINT_AFFINE(*preComputedTable)[64]) +{ + const unsigned int window_size = 7; + const unsigned int mask = (1 << (window_size + 1)) - 1; + unsigned int wvalue; + /* Using 4 windows at a time */ + unsigned char sign0, digit0; + unsigned char sign1, digit1; + unsigned char sign2, digit2; + unsigned char sign3, digit3; + unsigned int idx = 0; + BN_ULONG tmp[P256_LIMBS]; + int i; + + ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 }; + ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 }; + ALIGN32 P256_POINT_AFFINE point_arr[4]; + ALIGN32 P256_POINT res_point_arr[4]; + + /* Initial four windows */ + wvalue = *((u16 *) & p_str[0]); + wvalue = (wvalue << 1) & mask; + idx += window_size; + booth_recode_w7(&sign0, &digit0, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign1, &digit1, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign2, &digit2, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign3, &digit3, wvalue); + + ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[0], + digit0, digit1, digit2, digit3); + + ecp_nistz256_neg(tmp, point_arr[0].Y); + copy_conditional(point_arr[0].Y, tmp, sign0); + ecp_nistz256_neg(tmp, point_arr[1].Y); + copy_conditional(point_arr[1].Y, tmp, sign1); + ecp_nistz256_neg(tmp, point_arr[2].Y); + copy_conditional(point_arr[2].Y, tmp, sign2); + ecp_nistz256_neg(tmp, point_arr[3].Y); + copy_conditional(point_arr[3].Y, tmp, sign3); + + ecp_nistz256_avx2_transpose_convert(aX4, point_arr); + ecp_nistz256_avx2_to_mont(aX4, aX4); + ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]); + ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]); + + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign0, &digit0, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign1, &digit1, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign2, &digit2, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign3, &digit3, wvalue); + + ecp_nistz256_avx2_multi_gather_w7(point_arr, preComputedTable[4 * 1], + digit0, digit1, digit2, digit3); + + ecp_nistz256_neg(tmp, point_arr[0].Y); + copy_conditional(point_arr[0].Y, tmp, sign0); + ecp_nistz256_neg(tmp, point_arr[1].Y); + copy_conditional(point_arr[1].Y, tmp, sign1); + ecp_nistz256_neg(tmp, point_arr[2].Y); + copy_conditional(point_arr[2].Y, tmp, sign2); + ecp_nistz256_neg(tmp, point_arr[3].Y); + copy_conditional(point_arr[3].Y, tmp, sign3); + + ecp_nistz256_avx2_transpose_convert(bX4, point_arr); + ecp_nistz256_avx2_to_mont(bX4, bX4); + ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); + /* Optimized when both inputs are affine */ + ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4); + + for (i = 2; i < 9; i++) { + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign0, &digit0, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign1, &digit1, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign2, &digit2, wvalue); + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + booth_recode_w7(&sign3, &digit3, wvalue); + + ecp_nistz256_avx2_multi_gather_w7(point_arr, + preComputedTable[4 * i], + digit0, digit1, digit2, digit3); + + ecp_nistz256_neg(tmp, point_arr[0].Y); + copy_conditional(point_arr[0].Y, tmp, sign0); + ecp_nistz256_neg(tmp, point_arr[1].Y); + copy_conditional(point_arr[1].Y, tmp, sign1); + ecp_nistz256_neg(tmp, point_arr[2].Y); + copy_conditional(point_arr[2].Y, tmp, sign2); + ecp_nistz256_neg(tmp, point_arr[3].Y); + copy_conditional(point_arr[3].Y, tmp, sign3); + + ecp_nistz256_avx2_transpose_convert(bX4, point_arr); + ecp_nistz256_avx2_to_mont(bX4, bX4); + ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); + + ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4); + } + + ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]); + ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]); + ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]); + + ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4); + /* Last window is performed serially */ + wvalue = *((u16 *) & p_str[(idx - 1) / 8]); + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + booth_recode_w7(&sign0, &digit0, wvalue); + ecp_nistz256_gather_w7((P256_POINT_AFFINE *)r, + preComputedTable[36], digit0); + ecp_nistz256_neg(tmp, r->Y); + copy_conditional(r->Y, tmp, sign0); + memcpy(r->Z, ONE, sizeof(ONE)); + /* Sum the four windows */ + ecp_nistz256_point_add(r, r, &res_point_arr[0]); + ecp_nistz256_point_add(r, r, &res_point_arr[1]); + ecp_nistz256_point_add(r, r, &res_point_arr[2]); + ecp_nistz256_point_add(r, r, &res_point_arr[3]); +} +# endif +#endif + +__owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, + const P256_POINT_AFFINE *in, + BN_CTX *ctx) +{ + BIGNUM *x, *y; + BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS]; + int ret = 0; + + x = BN_new(); + if (x == NULL) + return 0; + y = BN_new(); + if (y == NULL) { + BN_free(x); + return 0; + } + memcpy(d_x, in->X, sizeof(d_x)); + bn_set_static_words(x, d_x, P256_LIMBS); + + memcpy(d_y, in->Y, sizeof(d_y)); + bn_set_static_words(y, d_y, P256_LIMBS); + + ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx); + + BN_free(x); + BN_free(y); + + return ret; +} + +/* r = scalar*G + sum(scalars[i]*points[i]) */ +__owur static int ecp_nistz256_points_mul(const EC_GROUP *group, + EC_POINT *r, + const BIGNUM *scalar, + size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; + size_t j; + unsigned char p_str[33] = { 0 }; + const PRECOMP256_ROW *preComputedTable = NULL; + const NISTZ256_PRE_COMP *pre_comp = NULL; + const EC_POINT *generator = NULL; + BN_CTX *new_ctx = NULL; + const BIGNUM **new_scalars = NULL; + const EC_POINT **new_points = NULL; + unsigned int idx = 0; + const unsigned int window_size = 7; + const unsigned int mask = (1 << (window_size + 1)) - 1; + unsigned int wvalue; + ALIGN32 union { + P256_POINT p; + P256_POINT_AFFINE a; + } t, p; + BIGNUM *tmp_scalar; + + if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + return 0; + } + + if (group->meth != r->meth) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + + if ((scalar == NULL) && (num == 0)) + return EC_POINT_set_to_infinity(group, r); + + for (j = 0; j < num; j++) { + if (group->meth != points[j]->meth) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + goto err; + } + + BN_CTX_start(ctx); + + if (scalar) { + generator = EC_GROUP_get0_generator(group); + if (generator == NULL) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); + goto err; + } + + /* look if we can use precomputed multiples of generator */ + pre_comp = group->pre_comp.nistz256; + + if (pre_comp) { + /* + * If there is a precomputed table for the generator, check that + * it was generated with the same generator. + */ + EC_POINT *pre_comp_generator = EC_POINT_new(group); + if (pre_comp_generator == NULL) + goto err; + + if (!ecp_nistz256_set_from_affine(pre_comp_generator, + group, pre_comp->precomp[0], + ctx)) { + EC_POINT_free(pre_comp_generator); + goto err; + } + + if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx)) + preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp; + + EC_POINT_free(pre_comp_generator); + } + + if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) { + /* + * If there is no precomputed data, but the generator is the + * default, a hardcoded table of precomputed data is used. This + * is because applications, such as Apache, do not use + * EC_KEY_precompute_mult. + */ + preComputedTable = ecp_nistz256_precomputed; + } + + if (preComputedTable) { + if ((BN_num_bits(scalar) > 256) + || BN_is_negative(scalar)) { + if ((tmp_scalar = BN_CTX_get(ctx)) == NULL) + goto err; + + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + scalar = tmp_scalar; + } + + for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) { + BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES]; + + p_str[i + 0] = (unsigned char)d; + p_str[i + 1] = (unsigned char)(d >> 8); + p_str[i + 2] = (unsigned char)(d >> 16); + p_str[i + 3] = (unsigned char)(d >>= 24); + if (BN_BYTES == 8) { + d >>= 8; + p_str[i + 4] = (unsigned char)d; + p_str[i + 5] = (unsigned char)(d >> 8); + p_str[i + 6] = (unsigned char)(d >> 16); + p_str[i + 7] = (unsigned char)(d >> 24); + } + } + + for (; i < 33; i++) + p_str[i] = 0; + +#if defined(ECP_NISTZ256_AVX2) + if (ecp_nistz_avx2_eligible()) { + ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable); + } else +#endif + { + BN_ULONG infty; + + /* First window */ + wvalue = (p_str[0] << 1) & mask; + idx += window_size; + + wvalue = _booth_recode_w7(wvalue); + + ecp_nistz256_gather_w7(&p.a, preComputedTable[0], + wvalue >> 1); + + ecp_nistz256_neg(p.p.Z, p.p.Y); + copy_conditional(p.p.Y, p.p.Z, wvalue & 1); + + /* + * Since affine infinity is encoded as (0,0) and + * Jacobian ias (,,0), we need to harmonize them + * by assigning "one" or zero to Z. + */ + infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] | + p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]); + if (P256_LIMBS == 8) + infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] | + p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]); + + infty = 0 - is_zero(infty); + infty = ~infty; + + p.p.Z[0] = ONE[0] & infty; + p.p.Z[1] = ONE[1] & infty; + p.p.Z[2] = ONE[2] & infty; + p.p.Z[3] = ONE[3] & infty; + if (P256_LIMBS == 8) { + p.p.Z[4] = ONE[4] & infty; + p.p.Z[5] = ONE[5] & infty; + p.p.Z[6] = ONE[6] & infty; + p.p.Z[7] = ONE[7] & infty; + } + + for (i = 1; i < 37; i++) { + unsigned int off = (idx - 1) / 8; + wvalue = p_str[off] | p_str[off + 1] << 8; + wvalue = (wvalue >> ((idx - 1) % 8)) & mask; + idx += window_size; + + wvalue = _booth_recode_w7(wvalue); + + ecp_nistz256_gather_w7(&t.a, + preComputedTable[i], wvalue >> 1); + + ecp_nistz256_neg(t.p.Z, t.a.Y); + copy_conditional(t.a.Y, t.p.Z, wvalue & 1); + + ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); + } + } + } else { + p_is_infinity = 1; + no_precomp_for_generator = 1; + } + } else + p_is_infinity = 1; + + if (no_precomp_for_generator) { + /* + * Without a precomputed table for the generator, it has to be + * handled like a normal point. + */ + new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); + if (new_scalars == NULL) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); + if (new_points == NULL) { + ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + memcpy(new_scalars, scalars, num * sizeof(BIGNUM *)); + new_scalars[num] = scalar; + memcpy(new_points, points, num * sizeof(EC_POINT *)); + new_points[num] = generator; + + scalars = new_scalars; + points = new_points; + num++; + } + + if (num) { + P256_POINT *out = &t.p; + if (p_is_infinity) + out = &p.p; + + if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx)) + goto err; + + if (!p_is_infinity) + ecp_nistz256_point_add(&p.p, &p.p, out); + } + + /* Not constant-time, but we're only operating on the public output. */ + if (!bn_set_words(r->X, p.p.X, P256_LIMBS) || + !bn_set_words(r->Y, p.p.Y, P256_LIMBS) || + !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) { + goto err; + } + r->Z_is_one = is_one(r->Z) & 1; + + ret = 1; + +err: + if (ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + OPENSSL_free(new_points); + OPENSSL_free(new_scalars); + return ret; +} + +__owur static int ecp_nistz256_get_affine(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, BN_CTX *ctx) +{ + BN_ULONG z_inv2[P256_LIMBS]; + BN_ULONG z_inv3[P256_LIMBS]; + BN_ULONG x_aff[P256_LIMBS]; + BN_ULONG y_aff[P256_LIMBS]; + BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; + BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS]; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY); + return 0; + } + + if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) || + !ecp_nistz256_bignum_to_field_elem(point_y, point->Y) || + !ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) { + ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE); + return 0; + } + + ecp_nistz256_mod_inverse(z_inv3, point_z); + ecp_nistz256_sqr_mont(z_inv2, z_inv3); + ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); + + if (x != NULL) { + ecp_nistz256_from_mont(x_ret, x_aff); + if (!bn_set_words(x, x_ret, P256_LIMBS)) + return 0; + } + + if (y != NULL) { + ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); + ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); + ecp_nistz256_from_mont(y_ret, y_aff); + if (!bn_set_words(y, y_ret, P256_LIMBS)) + return 0; + } + + return 1; +} + +static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) +{ + NISTZ256_PRE_COMP *ret = NULL; + + if (!group) + return NULL; + + ret = OPENSSL_zalloc(sizeof(*ret)); + + if (ret == NULL) { + ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->group = group; + ret->w = 6; /* default */ + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p) +{ + int i; + if (p != NULL) + CRYPTO_atomic_add(&p->references, 1, &i, p->lock); + return p; +} + +void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre) +{ + int i; + + if (pre == NULL) + return; + + CRYPTO_atomic_add(&pre->references, -1, &i, pre->lock); + REF_PRINT_COUNT("EC_nistz256", x); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + OPENSSL_free(pre->precomp_storage); + CRYPTO_THREAD_lock_free(pre->lock); + OPENSSL_free(pre); +} + + +static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) +{ + /* There is a hard-coded table for the default generator. */ + const EC_POINT *generator = EC_GROUP_get0_generator(group); + + if (generator != NULL && ecp_nistz256_is_affine_G(generator)) { + /* There is a hard-coded table for the default generator. */ + return 1; + } + + return HAVEPRECOMP(group, nistz256); +} + +const EC_METHOD *EC_GFp_nistz256_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_mont_group_init, + ec_GFp_mont_group_finish, + ec_GFp_mont_group_clear_finish, + ec_GFp_mont_group_copy, + ec_GFp_mont_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ecp_nistz256_get_affine, + 0, 0, 0, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ecp_nistz256_points_mul, /* mul */ + ecp_nistz256_mult_precompute, /* precompute_mult */ + ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */ + ec_GFp_mont_field_mul, + ec_GFp_mont_field_sqr, + 0, /* field_div */ + ec_GFp_mont_field_encode, + ec_GFp_mont_field_decode, + ec_GFp_mont_field_set_to_one, + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecp_nistz256_table.c b/openssl-1.1.0h/crypto/ec/ecp_nistz256_table.c new file mode 100644 index 0000000..3f5625c --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_nistz256_table.c @@ -0,0 +1,9542 @@ +/* + * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* + * This is the precomputed constant time access table for the code in + * ecp_montp256.c, for the default generator. The table consists of 37 + * subtables, each subtable contains 64 affine points. The affine points are + * encoded as eight uint64's, four for the x coordinate and four for the y. + * Both values are in little-endian order. There are 37 tables because a + * signed, 6-bit wNAF form of the scalar is used and ceil(256/(6 + 1)) = 37. + * Within each table there are 64 values because the 6-bit wNAF value can + * take 64 values, ignoring the sign bit, which is implemented by performing + * a negation of the affine point when required. We would like to align it + * to 2MB in order to increase the chances of using a large page but that + * appears to lead to invalid ELF files being produced. + */ + +#if defined(__GNUC__) +__attribute((aligned(4096))) +#elif defined(_MSC_VER) +__declspec(align(4096)) +#elif defined(__SUNPRO_C) +# pragma align 4096(ecp_nistz256_precomputed) +#endif +static const BN_ULONG ecp_nistz256_precomputed[37][64 * + sizeof(P256_POINT_AFFINE) / + sizeof(BN_ULONG)] = { + {TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), + TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6), + TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), + TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85), + TOBN(0x850046d4, 0x10ddd64d), TOBN(0xaa6ae3c1, 0xa433827d), + TOBN(0x73220503, 0x8d1490d9), TOBN(0xf6bb32e4, 0x3dcf3a3b), + TOBN(0x2f3648d3, 0x61bee1a5), TOBN(0x152cd7cb, 0xeb236ff8), + TOBN(0x19a8fb0e, 0x92042dbe), TOBN(0x78c57751, 0x0a5b8a3b), + TOBN(0xffac3f90, 0x4eebc127), TOBN(0xb027f84a, 0x087d81fb), + TOBN(0x66ad77dd, 0x87cbbc98), TOBN(0x26936a3f, 0xb6ff747e), + TOBN(0xb04c5c1f, 0xc983a7eb), TOBN(0x583e47ad, 0x0861fe1a), + TOBN(0x78820831, 0x1a2ee98e), TOBN(0xd5f06a29, 0xe587cc07), + TOBN(0x74b0b50d, 0x46918dcc), TOBN(0x4650a6ed, 0xc623c173), + TOBN(0x0cdaacac, 0xe8100af2), TOBN(0x577362f5, 0x41b0176b), + TOBN(0x2d96f24c, 0xe4cbaba6), TOBN(0x17628471, 0xfad6f447), + TOBN(0x6b6c36de, 0xe5ddd22e), TOBN(0x84b14c39, 0x4c5ab863), + TOBN(0xbe1b8aae, 0xc45c61f5), TOBN(0x90ec649a, 0x94b9537d), + TOBN(0x941cb5aa, 0xd076c20c), TOBN(0xc9079605, 0x890523c8), + TOBN(0xeb309b4a, 0xe7ba4f10), TOBN(0x73c568ef, 0xe5eb882b), + TOBN(0x3540a987, 0x7e7a1f68), TOBN(0x73a076bb, 0x2dd1e916), + TOBN(0x40394737, 0x3e77664a), TOBN(0x55ae744f, 0x346cee3e), + TOBN(0xd50a961a, 0x5b17a3ad), TOBN(0x13074b59, 0x54213673), + TOBN(0x93d36220, 0xd377e44b), TOBN(0x299c2b53, 0xadff14b5), + TOBN(0xf424d44c, 0xef639f11), TOBN(0xa4c9916d, 0x4a07f75f), + TOBN(0x0746354e, 0xa0173b4f), TOBN(0x2bd20213, 0xd23c00f7), + TOBN(0xf43eaab5, 0x0c23bb08), TOBN(0x13ba5119, 0xc3123e03), + TOBN(0x2847d030, 0x3f5b9d4d), TOBN(0x6742f2f2, 0x5da67bdd), + TOBN(0xef933bdc, 0x77c94195), TOBN(0xeaedd915, 0x6e240867), + TOBN(0x27f14cd1, 0x9499a78f), TOBN(0x462ab5c5, 0x6f9b3455), + TOBN(0x8f90f02a, 0xf02cfc6b), TOBN(0xb763891e, 0xb265230d), + TOBN(0xf59da3a9, 0x532d4977), TOBN(0x21e3327d, 0xcf9eba15), + TOBN(0x123c7b84, 0xbe60bbf0), TOBN(0x56ec12f2, 0x7706df76), + TOBN(0x75c96e8f, 0x264e20e8), TOBN(0xabe6bfed, 0x59a7a841), + TOBN(0x2cc09c04, 0x44c8eb00), TOBN(0xe05b3080, 0xf0c4e16b), + TOBN(0x1eb7777a, 0xa45f3314), TOBN(0x56af7bed, 0xce5d45e3), + TOBN(0x2b6e019a, 0x88b12f1a), TOBN(0x086659cd, 0xfd835f9b), + TOBN(0x2c18dbd1, 0x9dc21ec8), TOBN(0x98f9868a, 0x0fcf8139), + TOBN(0x737d2cd6, 0x48250b49), TOBN(0xcc61c947, 0x24b3428f), + TOBN(0x0c2b4078, 0x80dd9e76), TOBN(0xc43a8991, 0x383fbe08), + TOBN(0x5f7d2d65, 0x779be5d2), TOBN(0x78719a54, 0xeb3b4ab5), + TOBN(0xea7d260a, 0x6245e404), 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TOBN(0xa8ce9919, 0x89415078), + TOBN(0x82375b75, 0x41792efe), TOBN(0x4f59bf5c, 0x97d4515b), + TOBN(0xac4f324f, 0x923a277d), TOBN(0xd9bc9b7d, 0x650f3406), + TOBN(0xc6fa87d1, 0x8a39bc51), TOBN(0x82588530, 0x5ccc108f), + TOBN(0x5ced3c9f, 0x82e4c634), TOBN(0x8efb8314, 0x3a4464f8), + TOBN(0xe706381b, 0x7a1dca25), TOBN(0x6cd15a3c, 0x5a2a412b), + TOBN(0x9347a8fd, 0xbfcd8fb5), TOBN(0x31db2eef, 0x6e54cd22), + TOBN(0xc4aeb11e, 0xf8d8932f), TOBN(0x11e7c1ed, 0x344411af), + TOBN(0x2653050c, 0xdc9a151e), TOBN(0x9edbfc08, 0x3bb0a859), + TOBN(0x926c81c7, 0xfd5691e7), TOBN(0x9c1b2342, 0x6f39019a), + TOBN(0x64a81c8b, 0x7f8474b9), TOBN(0x90657c07, 0x01761819), + TOBN(0x390b3331, 0x55e0375a), TOBN(0xc676c626, 0xb6ebc47d), + TOBN(0x51623247, 0xb7d6dee8), TOBN(0x0948d927, 0x79659313), + TOBN(0x99700161, 0xe9ab35ed), TOBN(0x06cc32b4, 0x8ddde408), + TOBN(0x6f2fd664, 0x061ef338), TOBN(0x1606fa02, 0xc202e9ed), + TOBN(0x55388bc1, 0x929ba99b), TOBN(0xc4428c5e, 0x1e81df69), + TOBN(0xce2028ae, 0xf91b0b2a), 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TOBN(0xc7741c97, 0x0101bd45), + TOBN(0x95770c11, 0x07bd9ceb), TOBN(0x1f50250a, 0x8b2e0744), + TOBN(0xf762eec8, 0x1477b654), TOBN(0xc65b900e, 0x15efe59a), + TOBN(0x88c96148, 0x9546a897), TOBN(0x7e8025b3, 0xc30b4d7c), + TOBN(0xae4065ef, 0x12045cf9), TOBN(0x6fcb2caf, 0x9ccce8bd), + TOBN(0x1fa0ba4e, 0xf2cf6525), TOBN(0xf683125d, 0xcb72c312), + TOBN(0xa01da4ea, 0xe312410e), TOBN(0x67e28677, 0x6cd8e830), + TOBN(0xabd95752, 0x98fb3f07), TOBN(0x05f11e11, 0xeef649a5), + TOBN(0xba47faef, 0x9d3472c2), TOBN(0x3adff697, 0xc77d1345), + TOBN(0x4761fa04, 0xdd15afee), TOBN(0x64f1f61a, 0xb9e69462), + TOBN(0xfa691fab, 0x9bfb9093), TOBN(0x3df8ae8f, 0xa1133dfe), + TOBN(0xcd5f8967, 0x58cc710d), TOBN(0xfbb88d50, 0x16c7fe79), + TOBN(0x8e011b4c, 0xe88c50d1), TOBN(0x7532e807, 0xa8771c4f), + TOBN(0x64c78a48, 0xe2278ee4), TOBN(0x0b283e83, 0x3845072a), + TOBN(0x98a6f291, 0x49e69274), TOBN(0xb96e9668, 0x1868b21c), + TOBN(0x38f0adc2, 0xb1a8908e), TOBN(0x90afcff7, 0x1feb829d), + TOBN(0x9915a383, 0x210b0856), TOBN(0xa5a80602, 0xdef04889), + TOBN(0x800e9af9, 0x7c64d509), TOBN(0x81382d0b, 0xb8996f6f), + TOBN(0x490eba53, 0x81927e27), TOBN(0x46c63b32, 0x4af50182), + TOBN(0x784c5fd9, 0xd3ad62ce), TOBN(0xe4fa1870, 0xf8ae8736), + TOBN(0x4ec9d0bc, 0xd7466b25), TOBN(0x84ddbe1a, 0xdb235c65), + TOBN(0x5e2645ee, 0x163c1688), TOBN(0x570bd00e, 0x00eba747), + TOBN(0xfa51b629, 0x128bfa0f), TOBN(0x92fce1bd, 0x6c1d3b68), + TOBN(0x3e7361dc, 0xb66778b1), TOBN(0x9c7d249d, 0x5561d2bb), + TOBN(0xa40b28bf, 0x0bbc6229), TOBN(0x1c83c05e, 0xdfd91497), + TOBN(0x5f9f5154, 0xf083df05), TOBN(0xbac38b3c, 0xeee66c9d), + TOBN(0xf71db7e3, 0xec0dfcfd), TOBN(0xf2ecda8e, 0x8b0a8416), + TOBN(0x52fddd86, 0x7812aa66), TOBN(0x2896ef10, 0x4e6f4272), + TOBN(0xff27186a, 0x0fe9a745), TOBN(0x08249fcd, 0x49ca70db), + TOBN(0x7425a2e6, 0x441cac49), TOBN(0xf4a0885a, 0xece5ff57), + TOBN(0x6e2cb731, 0x7d7ead58), TOBN(0xf96cf7d6, 0x1898d104), + TOBN(0xafe67c9d, 0x4f2c9a89), TOBN(0x89895a50, 0x1c7bf5bc), + TOBN(0xdc7cb8e5, 0x573cecfa), TOBN(0x66497eae, 0xd15f03e6), + TOBN(0x6bc0de69, 0x3f084420), TOBN(0x323b9b36, 0xacd532b0), + TOBN(0xcfed390a, 0x0115a3c1), TOBN(0x9414c40b, 0x2d65ca0e), + TOBN(0x641406bd, 0x2f530c78), TOBN(0x29369a44, 0x833438f2), + TOBN(0x996884f5, 0x903fa271), TOBN(0xe6da0fd2, 0xb9da921e), + TOBN(0xa6f2f269, 0x5db01e54), TOBN(0x1ee3e9bd, 0x6876214e), + TOBN(0xa26e181c, 0xe27a9497), TOBN(0x36d254e4, 0x8e215e04), + TOBN(0x42f32a6c, 0x252cabca), TOBN(0x99481487, 0x80b57614), + TOBN(0x4c4dfe69, 0x40d9cae1), TOBN(0x05869580, 0x11a10f09), + TOBN(0xca287b57, 0x3491b64b), TOBN(0x77862d5d, 0x3fd4a53b), + TOBN(0xbf94856e, 0x50349126), TOBN(0x2be30bd1, 0x71c5268f), + TOBN(0x10393f19, 0xcbb650a6), TOBN(0x639531fe, 0x778cf9fd), + TOBN(0x02556a11, 0xb2935359), TOBN(0xda38aa96, 0xaf8c126e), + TOBN(0x47dbe6c2, 0x0960167f), TOBN(0x37bbabb6, 0x501901cd), + TOBN(0xb6e979e0, 0x2c947778), TOBN(0xd69a5175, 0x7a1a1dc6), + TOBN(0xc3ed5095, 0x9d9faf0c), TOBN(0x4dd9c096, 0x1d5fa5f0), + TOBN(0xa0c4304d, 0x64f16ea8), TOBN(0x8b1cac16, 0x7e718623), + TOBN(0x0b576546, 0x7c67f03e), TOBN(0x559cf5ad, 0xcbd88c01), + TOBN(0x074877bb, 0x0e2af19a), TOBN(0x1f717ec1, 0xa1228c92), + TOBN(0x70bcb800, 0x326e8920), TOBN(0xec6e2c5c, 0x4f312804), + TOBN(0x426aea7d, 0x3fca4752), TOBN(0xf12c0949, 0x2211f62a), + TOBN(0x24beecd8, 0x7be7b6b5), TOBN(0xb77eaf4c, 0x36d7a27d), + TOBN(0x154c2781, 0xfda78fd3), TOBN(0x848a83b0, 0x264eeabe), + TOBN(0x81287ef0, 0x4ffe2bc4), TOBN(0x7b6d88c6, 0xb6b6fc2a), + TOBN(0x805fb947, 0xce417d99), TOBN(0x4b93dcc3, 0x8b916cc4), + TOBN(0x72e65bb3, 0x21273323), TOBN(0xbcc1badd, 0x6ea9886e), + TOBN(0x0e223011, 0x4bc5ee85), TOBN(0xa561be74, 0xc18ee1e4), + TOBN(0x762fd2d4, 0xa6bcf1f1), TOBN(0x50e6a5a4, 0x95231489), + TOBN(0xca96001f, 0xa00b500b), TOBN(0x5c098cfc, 0x5d7dcdf5), + TOBN(0xa64e2d2e, 0x8c446a85), TOBN(0xbae9bcf1, 0x971f3c62), + TOBN(0x4ec22683, 0x8435a2c5), TOBN(0x8ceaed6c, 0x4bad4643), + TOBN(0xe9f8fb47, 0xccccf4e3), TOBN(0xbd4f3fa4, 0x1ce3b21e), + TOBN(0xd79fb110, 0xa3db3292), TOBN(0xe28a37da, 0xb536c66a), + TOBN(0x279ce87b, 0x8e49e6a9), TOBN(0x70ccfe8d, 0xfdcec8e3), + TOBN(0x2193e4e0, 0x3ba464b2), TOBN(0x0f39d60e, 0xaca9a398), + TOBN(0x7d7932af, 0xf82c12ab), TOBN(0xd8ff50ed, 0x91e7e0f7), + TOBN(0xea961058, 0xfa28a7e0), TOBN(0xc726cf25, 0x0bf5ec74), + TOBN(0xe74d55c8, 0xdb229666), TOBN(0x0bd9abbf, 0xa57f5799), + TOBN(0x7479ef07, 0x4dfc47b3), TOBN(0xd9c65fc3, 0x0c52f91d), + TOBN(0x8e0283fe, 0x36a8bde2), TOBN(0xa32a8b5e, 0x7d4b7280), + TOBN(0x6a677c61, 0x12e83233), TOBN(0x0fbb3512, 0xdcc9bf28), + TOBN(0x562e8ea5, 0x0d780f61), TOBN(0x0db8b22b, 0x1dc4e89c), + TOBN(0x0a6fd1fb, 0x89be0144), TOBN(0x8c77d246, 0xca57113b), + TOBN(0x4639075d, 0xff09c91c), TOBN(0x5b47b17f, 0x5060824c), + TOBN(0x58aea2b0, 0x16287b52), TOBN(0xa1343520, 0xd0cd8eb0), + TOBN(0x6148b4d0, 0xc5d58573), TOBN(0xdd2b6170, 0x291c68ae), + TOBN(0xa61b3929, 0x1da3b3b7), TOBN(0x5f946d79, 0x08c4ac10), + TOBN(0x4105d4a5, 0x7217d583), TOBN(0x5061da3d, 0x25e6de5e), + TOBN(0x3113940d, 0xec1b4991), TOBN(0xf12195e1, 0x36f485ae), + TOBN(0xa7507fb2, 0x731a2ee0), TOBN(0x95057a8e, 0x6e9e196e), + TOBN(0xa3c2c911, 0x2e130136), TOBN(0x97dfbb36, 0x33c60d15), + TOBN(0xcaf3c581, 0xb300ee2b), TOBN(0x77f25d90, 0xf4bac8b8), + TOBN(0xdb1c4f98, 0x6d840cd6), TOBN(0x471d62c0, 0xe634288c), + TOBN(0x8ec2f85e, 0xcec8a161), TOBN(0x41f37cbc, 0xfa6f4ae2), + TOBN(0x6793a20f, 0x4b709985), TOBN(0x7a7bd33b, 0xefa8985b), + TOBN(0x2c6a3fbd, 0x938e6446), TOBN(0x19042619, 0x2a8d47c1), + TOBN(0x16848667, 0xcc36975f), TOBN(0x02acf168, 0x9d5f1dfb), + TOBN(0x62d41ad4, 0x613baa94), TOBN(0xb56fbb92, 0x9f684670), + TOBN(0xce610d0d, 0xe9e40569), TOBN(0x7b99c65f, 0x35489fef), + TOBN(0x0c88ad1b, 0x3df18b97), TOBN(0x81b7d9be, 0x5d0e9edb), + TOBN(0xd85218c0, 0xc716cc0a), TOBN(0xf4b5ff90, 0x85691c49), + TOBN(0xa4fd666b, 0xce356ac6), TOBN(0x17c72895, 0x4b327a7a), + TOBN(0xf93d5085, 0xda6be7de), TOBN(0xff71530e, 0x3301d34e), + TOBN(0x4cd96442, 0xd8f448e8), TOBN(0x9283d331, 0x2ed18ffa), + TOBN(0x4d33dd99, 0x2a849870), TOBN(0xa716964b, 0x41576335), + TOBN(0xff5e3a9b, 0x179be0e5), TOBN(0x5b9d6b1b, 0x83b13632), + TOBN(0x3b8bd7d4, 0xa52f313b), TOBN(0xc9dd95a0, 0x637a4660), + TOBN(0x30035962, 0x0b3e218f), TOBN(0xce1481a3, 0xc7b28a3c), + TOBN(0xab41b43a, 0x43228d83), TOBN(0x24ae1c30, 0x4ad63f99), + TOBN(0x8e525f1a, 0x46a51229), TOBN(0x14af860f, 0xcd26d2b4), + TOBN(0xd6baef61, 0x3f714aa1), TOBN(0xf51865ad, 0xeb78795e), + TOBN(0xd3e21fce, 0xe6a9d694), TOBN(0x82ceb1dd, 0x8a37b527)} +}; diff --git a/openssl-1.1.0h/crypto/ec/ecp_oct.c b/openssl-1.1.0h/crypto/ec/ecp_oct.c new file mode 100644 index 0000000..4d142a4 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_oct.c @@ -0,0 +1,372 @@ +/* + * Copyright 2011-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <openssl/err.h> +#include <openssl/symhacks.h> + +#include "ec_lcl.h" + +int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x_, int y_bit, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *tmp1, *tmp2, *x, *y; + int ret = 0; + + /* clear error queue */ + ERR_clear_error(); + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0); + + BN_CTX_start(ctx); + tmp1 = BN_CTX_get(ctx); + tmp2 = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + /*- + * Recover y. We have a Weierstrass equation + * y^2 = x^3 + a*x + b, + * so y is one of the square roots of x^3 + a*x + b. + */ + + /* tmp1 := x^3 */ + if (!BN_nnmod(x, x_, group->field, ctx)) + goto err; + if (group->meth->field_decode == 0) { + /* field_{sqr,mul} work on standard representation */ + if (!group->meth->field_sqr(group, tmp2, x_, ctx)) + goto err; + if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) + goto err; + } else { + if (!BN_mod_sqr(tmp2, x_, group->field, ctx)) + goto err; + if (!BN_mod_mul(tmp1, tmp2, x_, group->field, ctx)) + goto err; + } + + /* tmp1 := tmp1 + a*x */ + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp2, x, group->field)) + goto err; + if (!BN_mod_add_quick(tmp2, tmp2, x, group->field)) + goto err; + if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, group->field)) + goto err; + } else { + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, group->a, ctx)) + goto err; + if (!BN_mod_mul(tmp2, tmp2, x, group->field, ctx)) + goto err; + } else { + /* field_mul works on standard representation */ + if (!group->meth->field_mul(group, tmp2, group->a, x, ctx)) + goto err; + } + + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, group->field)) + goto err; + } + + /* tmp1 := tmp1 + b */ + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, tmp2, group->b, ctx)) + goto err; + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, group->field)) + goto err; + } else { + if (!BN_mod_add_quick(tmp1, tmp1, group->b, group->field)) + goto err; + } + + if (!BN_mod_sqrt(y, tmp1, group->field, ctx)) { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN + && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) { + ERR_clear_error(); + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, + EC_R_INVALID_COMPRESSED_POINT); + } else + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, + ERR_R_BN_LIB); + goto err; + } + + if (y_bit != BN_is_odd(y)) { + if (BN_is_zero(y)) { + int kron; + + kron = BN_kronecker(x, group->field, ctx); + if (kron == -2) + goto err; + + if (kron == 1) + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, + EC_R_INVALID_COMPRESSION_BIT); + else + /* + * BN_mod_sqrt() should have cought this error (not a square) + */ + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, + EC_R_INVALID_COMPRESSED_POINT); + goto err; + } + if (!BN_usub(y, group->field, y)) + goto err; + } + if (y_bit != BN_is_odd(y)) { + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, + ERR_R_INTERNAL_ERROR); + goto err; + } + + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) +{ + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) { + /* encodes to a single 0 octet */ + if (buf != NULL) { + if (len < 1) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + /* ret := required output buffer length */ + field_len = BN_num_bytes(group->field); + ret = + (form == + POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) { + if (len < ret) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + + if ((form == POINT_CONVERSION_COMPRESSED + || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) + buf[0] = form + 1; + else + buf[0] = form; + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED + || form == POINT_CONVERSION_HYBRID) { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return 0; +} + +int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) +{ + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) { + if (len != 1) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = BN_num_bytes(group->field); + enc_len = + (form == + POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len; + + if (len != enc_len) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) + goto err; + if (BN_ucmp(x, group->field) >= 0) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) { + if (!EC_POINT_set_compressed_coordinates_GFp + (group, point, x, y_bit, ctx)) + goto err; + } else { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) + goto err; + if (BN_ucmp(y, group->field) >= 0) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) { + if (y_bit != BN_is_odd(y)) { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + /* + * EC_POINT_set_affine_coordinates_GFp is responsible for checking that + * the point is on the curve. + */ + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} diff --git a/openssl-1.1.0h/crypto/ec/ecp_smpl.c b/openssl-1.1.0h/crypto/ec/ecp_smpl.c new file mode 100644 index 0000000..abd3795 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecp_smpl.c @@ -0,0 +1,1369 @@ +/* + * Copyright 2001-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <openssl/err.h> +#include <openssl/symhacks.h> + +#include "ec_lcl.h" + +const EC_METHOD *EC_GFp_simple_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_simple_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_simple_group_copy, + ec_GFp_simple_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_simple_point_get_affine_coordinates, + 0, 0, 0, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + 0 /* mul */ , + 0 /* precompute_mult */ , + 0 /* have_precompute_mult */ , + ec_GFp_simple_field_mul, + ec_GFp_simple_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/* + * Most method functions in this file are designed to work with + * non-trivial representations of field elements if necessary + * (see ecp_mont.c): while standard modular addition and subtraction + * are used, the field_mul and field_sqr methods will be used for + * multiplication, and field_encode and field_decode (if defined) + * will be used for converting between representations. + * + * Functions ec_GFp_simple_points_make_affine() and + * ec_GFp_simple_point_get_affine_coordinates() specifically assume + * that if a non-trivial representation is used, it is a Montgomery + * representation (i.e. 'encoding' means multiplying by some factor R). + */ + +int ec_GFp_simple_group_init(EC_GROUP *group) +{ + group->field = BN_new(); + group->a = BN_new(); + group->b = BN_new(); + if (group->field == NULL || group->a == NULL || group->b == NULL) { + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); + return 0; + } + group->a_is_minus3 = 0; + return 1; +} + +void ec_GFp_simple_group_finish(EC_GROUP *group) +{ + BN_free(group->field); + BN_free(group->a); + BN_free(group->b); +} + +void ec_GFp_simple_group_clear_finish(EC_GROUP *group) +{ + BN_clear_free(group->field); + BN_clear_free(group->a); + BN_clear_free(group->b); +} + +int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) +{ + if (!BN_copy(dest->field, src->field)) + return 0; + if (!BN_copy(dest->a, src->a)) + return 0; + if (!BN_copy(dest->b, src->b)) + return 0; + + dest->a_is_minus3 = src->a_is_minus3; + + return 1; +} + +int ec_GFp_simple_group_set_curve(EC_GROUP *group, + const BIGNUM *p, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *tmp_a; + + /* p must be a prime > 3 */ + if (BN_num_bits(p) <= 2 || !BN_is_odd(p)) { + ECerr(EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, EC_R_INVALID_FIELD); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + tmp_a = BN_CTX_get(ctx); + if (tmp_a == NULL) + goto err; + + /* group->field */ + if (!BN_copy(group->field, p)) + goto err; + BN_set_negative(group->field, 0); + + /* group->a */ + if (!BN_nnmod(tmp_a, a, p, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, group->a, tmp_a, ctx)) + goto err; + } else if (!BN_copy(group->a, tmp_a)) + goto err; + + /* group->b */ + if (!BN_nnmod(group->b, b, p, ctx)) + goto err; + if (group->meth->field_encode) + if (!group->meth->field_encode(group, group->b, group->b, ctx)) + goto err; + + /* group->a_is_minus3 */ + if (!BN_add_word(tmp_a, 3)) + goto err; + group->a_is_minus3 = (0 == BN_cmp(tmp_a, group->field)); + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_group_get_curve(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, + BIGNUM *b, BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + + if (p != NULL) { + if (!BN_copy(p, group->field)) + return 0; + } + + if (a != NULL || b != NULL) { + if (group->meth->field_decode) { + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + if (a != NULL) { + if (!group->meth->field_decode(group, a, group->a, ctx)) + goto err; + } + if (b != NULL) { + if (!group->meth->field_decode(group, b, group->b, ctx)) + goto err; + } + } else { + if (a != NULL) { + if (!BN_copy(a, group->a)) + goto err; + } + if (b != NULL) { + if (!BN_copy(b, group->b)) + goto err; + } + } + } + + ret = 1; + + err: + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_group_get_degree(const EC_GROUP *group) +{ + return BN_num_bits(group->field); +} + +int ec_GFp_simple_group_check_discriminant(const EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *a, *b, *order, *tmp_1, *tmp_2; + const BIGNUM *p = group->field; + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) { + ECerr(EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, + ERR_R_MALLOC_FAILURE); + goto err; + } + } + BN_CTX_start(ctx); + a = BN_CTX_get(ctx); + b = BN_CTX_get(ctx); + tmp_1 = BN_CTX_get(ctx); + tmp_2 = BN_CTX_get(ctx); + order = BN_CTX_get(ctx); + if (order == NULL) + goto err; + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, a, group->a, ctx)) + goto err; + if (!group->meth->field_decode(group, b, group->b, ctx)) + goto err; + } else { + if (!BN_copy(a, group->a)) + goto err; + if (!BN_copy(b, group->b)) + goto err; + } + + /*- + * check the discriminant: + * y^2 = x^3 + a*x + b is an elliptic curve <=> 4*a^3 + 27*b^2 != 0 (mod p) + * 0 =< a, b < p + */ + if (BN_is_zero(a)) { + if (BN_is_zero(b)) + goto err; + } else if (!BN_is_zero(b)) { + if (!BN_mod_sqr(tmp_1, a, p, ctx)) + goto err; + if (!BN_mod_mul(tmp_2, tmp_1, a, p, ctx)) + goto err; + if (!BN_lshift(tmp_1, tmp_2, 2)) + goto err; + /* tmp_1 = 4*a^3 */ + + if (!BN_mod_sqr(tmp_2, b, p, ctx)) + goto err; + if (!BN_mul_word(tmp_2, 27)) + goto err; + /* tmp_2 = 27*b^2 */ + + if (!BN_mod_add(a, tmp_1, tmp_2, p, ctx)) + goto err; + if (BN_is_zero(a)) + goto err; + } + ret = 1; + + err: + if (ctx != NULL) + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_point_init(EC_POINT *point) +{ + point->X = BN_new(); + point->Y = BN_new(); + point->Z = BN_new(); + point->Z_is_one = 0; + + if (point->X == NULL || point->Y == NULL || point->Z == NULL) { + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); + return 0; + } + return 1; +} + +void ec_GFp_simple_point_finish(EC_POINT *point) +{ + BN_free(point->X); + BN_free(point->Y); + BN_free(point->Z); +} + +void ec_GFp_simple_point_clear_finish(EC_POINT *point) +{ + BN_clear_free(point->X); + BN_clear_free(point->Y); + BN_clear_free(point->Z); + point->Z_is_one = 0; +} + +int ec_GFp_simple_point_copy(EC_POINT *dest, const EC_POINT *src) +{ + if (!BN_copy(dest->X, src->X)) + return 0; + if (!BN_copy(dest->Y, src->Y)) + return 0; + if (!BN_copy(dest->Z, src->Z)) + return 0; + dest->Z_is_one = src->Z_is_one; + + return 1; +} + +int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *group, + EC_POINT *point) +{ + point->Z_is_one = 0; + BN_zero(point->Z); + return 1; +} + +int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x, + const BIGNUM *y, + const BIGNUM *z, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + int ret = 0; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + if (x != NULL) { + if (!BN_nnmod(point->X, x, group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, point->X, point->X, ctx)) + goto err; + } + } + + if (y != NULL) { + if (!BN_nnmod(point->Y, y, group->field, ctx)) + goto err; + if (group->meth->field_encode) { + if (!group->meth->field_encode(group, point->Y, point->Y, ctx)) + goto err; + } + } + + if (z != NULL) { + int Z_is_one; + + if (!BN_nnmod(point->Z, z, group->field, ctx)) + goto err; + Z_is_one = BN_is_one(point->Z); + if (group->meth->field_encode) { + if (Z_is_one && (group->meth->field_set_to_one != 0)) { + if (!group->meth->field_set_to_one(group, point->Z, ctx)) + goto err; + } else { + if (!group-> + meth->field_encode(group, point->Z, point->Z, ctx)) + goto err; + } + } + point->Z_is_one = Z_is_one; + } + + ret = 1; + + err: + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BIGNUM *z, BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + int ret = 0; + + if (group->meth->field_decode != 0) { + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + if (x != NULL) { + if (!group->meth->field_decode(group, x, point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, point->Y, ctx)) + goto err; + } + if (z != NULL) { + if (!group->meth->field_decode(group, z, point->Z, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, point->Y)) + goto err; + } + if (z != NULL) { + if (!BN_copy(z, point->Z)) + goto err; + } + } + + ret = 1; + + err: + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *group, + EC_POINT *point, + const BIGNUM *x, + const BIGNUM *y, BN_CTX *ctx) +{ + if (x == NULL || y == NULL) { + /* + * unlike for projective coordinates, we do not tolerate this + */ + ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + + return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, + BN_value_one(), ctx); +} + +int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *Z, *Z_1, *Z_2, *Z_3; + const BIGNUM *Z_; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + Z = BN_CTX_get(ctx); + Z_1 = BN_CTX_get(ctx); + Z_2 = BN_CTX_get(ctx); + Z_3 = BN_CTX_get(ctx); + if (Z_3 == NULL) + goto err; + + /* transform (X, Y, Z) into (x, y) := (X/Z^2, Y/Z^3) */ + + if (group->meth->field_decode) { + if (!group->meth->field_decode(group, Z, point->Z, ctx)) + goto err; + Z_ = Z; + } else { + Z_ = point->Z; + } + + if (BN_is_one(Z_)) { + if (group->meth->field_decode) { + if (x != NULL) { + if (!group->meth->field_decode(group, x, point->X, ctx)) + goto err; + } + if (y != NULL) { + if (!group->meth->field_decode(group, y, point->Y, ctx)) + goto err; + } + } else { + if (x != NULL) { + if (!BN_copy(x, point->X)) + goto err; + } + if (y != NULL) { + if (!BN_copy(y, point->Y)) + goto err; + } + } + } else { + if (!BN_mod_inverse(Z_1, Z_, group->field, ctx)) { + ECerr(EC_F_EC_GFP_SIMPLE_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + goto err; + } + + if (group->meth->field_encode == 0) { + /* field_sqr works on standard representation */ + if (!group->meth->field_sqr(group, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_sqr(Z_2, Z_1, group->field, ctx)) + goto err; + } + + if (x != NULL) { + /* + * in the Montgomery case, field_mul will cancel out Montgomery + * factor in X: + */ + if (!group->meth->field_mul(group, x, point->X, Z_2, ctx)) + goto err; + } + + if (y != NULL) { + if (group->meth->field_encode == 0) { + /* + * field_mul works on standard representation + */ + if (!group->meth->field_mul(group, Z_3, Z_2, Z_1, ctx)) + goto err; + } else { + if (!BN_mod_mul(Z_3, Z_2, Z_1, group->field, ctx)) + goto err; + } + + /* + * in the Montgomery case, field_mul will cancel out Montgomery + * factor in Y: + */ + if (!group->meth->field_mul(group, y, point->Y, Z_3, ctx)) + goto err; + } + } + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3, *n4, *n5, *n6; + int ret = 0; + + if (a == b) + return EC_POINT_dbl(group, r, a, ctx); + if (EC_POINT_is_at_infinity(group, a)) + return EC_POINT_copy(r, b); + if (EC_POINT_is_at_infinity(group, b)) + return EC_POINT_copy(r, a); + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + n0 = BN_CTX_get(ctx); + n1 = BN_CTX_get(ctx); + n2 = BN_CTX_get(ctx); + n3 = BN_CTX_get(ctx); + n4 = BN_CTX_get(ctx); + n5 = BN_CTX_get(ctx); + n6 = BN_CTX_get(ctx); + if (n6 == NULL) + goto end; + + /* + * Note that in this function we must not read components of 'a' or 'b' + * once we have written the corresponding components of 'r'. ('r' might + * be one of 'a' or 'b'.) + */ + + /* n1, n2 */ + if (b->Z_is_one) { + if (!BN_copy(n1, a->X)) + goto end; + if (!BN_copy(n2, a->Y)) + goto end; + /* n1 = X_a */ + /* n2 = Y_a */ + } else { + if (!field_sqr(group, n0, b->Z, ctx)) + goto end; + if (!field_mul(group, n1, a->X, n0, ctx)) + goto end; + /* n1 = X_a * Z_b^2 */ + + if (!field_mul(group, n0, n0, b->Z, ctx)) + goto end; + if (!field_mul(group, n2, a->Y, n0, ctx)) + goto end; + /* n2 = Y_a * Z_b^3 */ + } + + /* n3, n4 */ + if (a->Z_is_one) { + if (!BN_copy(n3, b->X)) + goto end; + if (!BN_copy(n4, b->Y)) + goto end; + /* n3 = X_b */ + /* n4 = Y_b */ + } else { + if (!field_sqr(group, n0, a->Z, ctx)) + goto end; + if (!field_mul(group, n3, b->X, n0, ctx)) + goto end; + /* n3 = X_b * Z_a^2 */ + + if (!field_mul(group, n0, n0, a->Z, ctx)) + goto end; + if (!field_mul(group, n4, b->Y, n0, ctx)) + goto end; + /* n4 = Y_b * Z_a^3 */ + } + + /* n5, n6 */ + if (!BN_mod_sub_quick(n5, n1, n3, p)) + goto end; + if (!BN_mod_sub_quick(n6, n2, n4, p)) + goto end; + /* n5 = n1 - n3 */ + /* n6 = n2 - n4 */ + + if (BN_is_zero(n5)) { + if (BN_is_zero(n6)) { + /* a is the same point as b */ + BN_CTX_end(ctx); + ret = EC_POINT_dbl(group, r, a, ctx); + ctx = NULL; + goto end; + } else { + /* a is the inverse of b */ + BN_zero(r->Z); + r->Z_is_one = 0; + ret = 1; + goto end; + } + } + + /* 'n7', 'n8' */ + if (!BN_mod_add_quick(n1, n1, n3, p)) + goto end; + if (!BN_mod_add_quick(n2, n2, n4, p)) + goto end; + /* 'n7' = n1 + n3 */ + /* 'n8' = n2 + n4 */ + + /* Z_r */ + if (a->Z_is_one && b->Z_is_one) { + if (!BN_copy(r->Z, n5)) + goto end; + } else { + if (a->Z_is_one) { + if (!BN_copy(n0, b->Z)) + goto end; + } else if (b->Z_is_one) { + if (!BN_copy(n0, a->Z)) + goto end; + } else { + if (!field_mul(group, n0, a->Z, b->Z, ctx)) + goto end; + } + if (!field_mul(group, r->Z, n0, n5, ctx)) + goto end; + } + r->Z_is_one = 0; + /* Z_r = Z_a * Z_b * n5 */ + + /* X_r */ + if (!field_sqr(group, n0, n6, ctx)) + goto end; + if (!field_sqr(group, n4, n5, ctx)) + goto end; + if (!field_mul(group, n3, n1, n4, ctx)) + goto end; + if (!BN_mod_sub_quick(r->X, n0, n3, p)) + goto end; + /* X_r = n6^2 - n5^2 * 'n7' */ + + /* 'n9' */ + if (!BN_mod_lshift1_quick(n0, r->X, p)) + goto end; + if (!BN_mod_sub_quick(n0, n3, n0, p)) + goto end; + /* n9 = n5^2 * 'n7' - 2 * X_r */ + + /* Y_r */ + if (!field_mul(group, n0, n0, n6, ctx)) + goto end; + if (!field_mul(group, n5, n4, n5, ctx)) + goto end; /* now n5 is n5^3 */ + if (!field_mul(group, n1, n2, n5, ctx)) + goto end; + if (!BN_mod_sub_quick(n0, n0, n1, p)) + goto end; + if (BN_is_odd(n0)) + if (!BN_add(n0, n0, p)) + goto end; + /* now 0 <= n0 < 2*p, and n0 is even */ + if (!BN_rshift1(r->Y, n0)) + goto end; + /* Y_r = (n6 * 'n9' - 'n8' * 'n5^3') / 2 */ + + ret = 1; + + end: + if (ctx) /* otherwise we already called BN_CTX_end */ + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, + BN_CTX *ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *n0, *n1, *n2, *n3; + int ret = 0; + + if (EC_POINT_is_at_infinity(group, a)) { + BN_zero(r->Z); + r->Z_is_one = 0; + return 1; + } + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + n0 = BN_CTX_get(ctx); + n1 = BN_CTX_get(ctx); + n2 = BN_CTX_get(ctx); + n3 = BN_CTX_get(ctx); + if (n3 == NULL) + goto err; + + /* + * Note that in this function we must not read components of 'a' once we + * have written the corresponding components of 'r'. ('r' might the same + * as 'a'.) + */ + + /* n1 */ + if (a->Z_is_one) { + if (!field_sqr(group, n0, a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, group->a, p)) + goto err; + /* n1 = 3 * X_a^2 + a_curve */ + } else if (group->a_is_minus3) { + if (!field_sqr(group, n1, a->Z, ctx)) + goto err; + if (!BN_mod_add_quick(n0, a->X, n1, p)) + goto err; + if (!BN_mod_sub_quick(n2, a->X, n1, p)) + goto err; + if (!field_mul(group, n1, n0, n2, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n0, n1, p)) + goto err; + if (!BN_mod_add_quick(n1, n0, n1, p)) + goto err; + /*- + * n1 = 3 * (X_a + Z_a^2) * (X_a - Z_a^2) + * = 3 * X_a^2 - 3 * Z_a^4 + */ + } else { + if (!field_sqr(group, n0, a->X, ctx)) + goto err; + if (!BN_mod_lshift1_quick(n1, n0, p)) + goto err; + if (!BN_mod_add_quick(n0, n0, n1, p)) + goto err; + if (!field_sqr(group, n1, a->Z, ctx)) + goto err; + if (!field_sqr(group, n1, n1, ctx)) + goto err; + if (!field_mul(group, n1, n1, group->a, ctx)) + goto err; + if (!BN_mod_add_quick(n1, n1, n0, p)) + goto err; + /* n1 = 3 * X_a^2 + a_curve * Z_a^4 */ + } + + /* Z_r */ + if (a->Z_is_one) { + if (!BN_copy(n0, a->Y)) + goto err; + } else { + if (!field_mul(group, n0, a->Y, a->Z, ctx)) + goto err; + } + if (!BN_mod_lshift1_quick(r->Z, n0, p)) + goto err; + r->Z_is_one = 0; + /* Z_r = 2 * Y_a * Z_a */ + + /* n2 */ + if (!field_sqr(group, n3, a->Y, ctx)) + goto err; + if (!field_mul(group, n2, a->X, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n2, n2, 2, p)) + goto err; + /* n2 = 4 * X_a * Y_a^2 */ + + /* X_r */ + if (!BN_mod_lshift1_quick(n0, n2, p)) + goto err; + if (!field_sqr(group, r->X, n1, ctx)) + goto err; + if (!BN_mod_sub_quick(r->X, r->X, n0, p)) + goto err; + /* X_r = n1^2 - 2 * n2 */ + + /* n3 */ + if (!field_sqr(group, n0, n3, ctx)) + goto err; + if (!BN_mod_lshift_quick(n3, n0, 3, p)) + goto err; + /* n3 = 8 * Y_a^4 */ + + /* Y_r */ + if (!BN_mod_sub_quick(n0, n2, r->X, p)) + goto err; + if (!field_mul(group, n0, n1, n0, ctx)) + goto err; + if (!BN_mod_sub_quick(r->Y, n0, n3, p)) + goto err; + /* Y_r = n1 * (n2 - X_r) - n3 */ + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx) +{ + if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(point->Y)) + /* point is its own inverse */ + return 1; + + return BN_usub(point->Y, group->field, point->Y); +} + +int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point) +{ + return BN_is_zero(point->Z); +} + +int ec_GFp_simple_is_on_curve(const EC_GROUP *group, const EC_POINT *point, + BN_CTX *ctx) +{ + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + const BIGNUM *p; + BN_CTX *new_ctx = NULL; + BIGNUM *rh, *tmp, *Z4, *Z6; + int ret = -1; + + if (EC_POINT_is_at_infinity(group, point)) + return 1; + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + p = group->field; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + rh = BN_CTX_get(ctx); + tmp = BN_CTX_get(ctx); + Z4 = BN_CTX_get(ctx); + Z6 = BN_CTX_get(ctx); + if (Z6 == NULL) + goto err; + + /*- + * We have a curve defined by a Weierstrass equation + * y^2 = x^3 + a*x + b. + * The point to consider is given in Jacobian projective coordinates + * where (X, Y, Z) represents (x, y) = (X/Z^2, Y/Z^3). + * Substituting this and multiplying by Z^6 transforms the above equation into + * Y^2 = X^3 + a*X*Z^4 + b*Z^6. + * To test this, we add up the right-hand side in 'rh'. + */ + + /* rh := X^2 */ + if (!field_sqr(group, rh, point->X, ctx)) + goto err; + + if (!point->Z_is_one) { + if (!field_sqr(group, tmp, point->Z, ctx)) + goto err; + if (!field_sqr(group, Z4, tmp, ctx)) + goto err; + if (!field_mul(group, Z6, Z4, tmp, ctx)) + goto err; + + /* rh := (rh + a*Z^4)*X */ + if (group->a_is_minus3) { + if (!BN_mod_lshift1_quick(tmp, Z4, p)) + goto err; + if (!BN_mod_add_quick(tmp, tmp, Z4, p)) + goto err; + if (!BN_mod_sub_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, point->X, ctx)) + goto err; + } else { + if (!field_mul(group, tmp, Z4, group->a, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + if (!field_mul(group, rh, rh, point->X, ctx)) + goto err; + } + + /* rh := rh + b*Z^6 */ + if (!field_mul(group, tmp, group->b, Z6, ctx)) + goto err; + if (!BN_mod_add_quick(rh, rh, tmp, p)) + goto err; + } else { + /* point->Z_is_one */ + + /* rh := (rh + a)*X */ + if (!BN_mod_add_quick(rh, rh, group->a, p)) + goto err; + if (!field_mul(group, rh, rh, point->X, ctx)) + goto err; + /* rh := rh + b */ + if (!BN_mod_add_quick(rh, rh, group->b, p)) + goto err; + } + + /* 'lh' := Y^2 */ + if (!field_sqr(group, tmp, point->Y, ctx)) + goto err; + + ret = (0 == BN_ucmp(tmp, rh)); + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, + const EC_POINT *b, BN_CTX *ctx) +{ + /*- + * return values: + * -1 error + * 0 equal (in affine coordinates) + * 1 not equal + */ + + int (*field_mul) (const EC_GROUP *, BIGNUM *, const BIGNUM *, + const BIGNUM *, BN_CTX *); + int (*field_sqr) (const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *); + BN_CTX *new_ctx = NULL; + BIGNUM *tmp1, *tmp2, *Za23, *Zb23; + const BIGNUM *tmp1_, *tmp2_; + int ret = -1; + + if (EC_POINT_is_at_infinity(group, a)) { + return EC_POINT_is_at_infinity(group, b) ? 0 : 1; + } + + if (EC_POINT_is_at_infinity(group, b)) + return 1; + + if (a->Z_is_one && b->Z_is_one) { + return ((BN_cmp(a->X, b->X) == 0) && BN_cmp(a->Y, b->Y) == 0) ? 0 : 1; + } + + field_mul = group->meth->field_mul; + field_sqr = group->meth->field_sqr; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return -1; + } + + BN_CTX_start(ctx); + tmp1 = BN_CTX_get(ctx); + tmp2 = BN_CTX_get(ctx); + Za23 = BN_CTX_get(ctx); + Zb23 = BN_CTX_get(ctx); + if (Zb23 == NULL) + goto end; + + /*- + * We have to decide whether + * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3), + * or equivalently, whether + * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3). + */ + + if (!b->Z_is_one) { + if (!field_sqr(group, Zb23, b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, a->X, Zb23, ctx)) + goto end; + tmp1_ = tmp1; + } else + tmp1_ = a->X; + if (!a->Z_is_one) { + if (!field_sqr(group, Za23, a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, b->X, Za23, ctx)) + goto end; + tmp2_ = tmp2; + } else + tmp2_ = b->X; + + /* compare X_a*Z_b^2 with X_b*Z_a^2 */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ + goto end; + } + + if (!b->Z_is_one) { + if (!field_mul(group, Zb23, Zb23, b->Z, ctx)) + goto end; + if (!field_mul(group, tmp1, a->Y, Zb23, ctx)) + goto end; + /* tmp1_ = tmp1 */ + } else + tmp1_ = a->Y; + if (!a->Z_is_one) { + if (!field_mul(group, Za23, Za23, a->Z, ctx)) + goto end; + if (!field_mul(group, tmp2, b->Y, Za23, ctx)) + goto end; + /* tmp2_ = tmp2 */ + } else + tmp2_ = b->Y; + + /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */ + if (BN_cmp(tmp1_, tmp2_) != 0) { + ret = 1; /* points differ */ + goto end; + } + + /* points are equal */ + ret = 0; + + end: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, + BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + int ret = 0; + + if (point->Z_is_one || EC_POINT_is_at_infinity(group, point)) + return 1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) + goto err; + if (!point->Z_is_one) { + ECerr(EC_F_EC_GFP_SIMPLE_MAKE_AFFINE, ERR_R_INTERNAL_ERROR); + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +int ec_GFp_simple_points_make_affine(const EC_GROUP *group, size_t num, + EC_POINT *points[], BN_CTX *ctx) +{ + BN_CTX *new_ctx = NULL; + BIGNUM *tmp, *tmp_Z; + BIGNUM **prod_Z = NULL; + size_t i; + int ret = 0; + + if (num == 0) + return 1; + + if (ctx == NULL) { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + tmp = BN_CTX_get(ctx); + tmp_Z = BN_CTX_get(ctx); + if (tmp == NULL || tmp_Z == NULL) + goto err; + + prod_Z = OPENSSL_malloc(num * sizeof(prod_Z[0])); + if (prod_Z == NULL) + goto err; + for (i = 0; i < num; i++) { + prod_Z[i] = BN_new(); + if (prod_Z[i] == NULL) + goto err; + } + + /* + * Set each prod_Z[i] to the product of points[0]->Z .. points[i]->Z, + * skipping any zero-valued inputs (pretend that they're 1). + */ + + if (!BN_is_zero(points[0]->Z)) { + if (!BN_copy(prod_Z[0], points[0]->Z)) + goto err; + } else { + if (group->meth->field_set_to_one != 0) { + if (!group->meth->field_set_to_one(group, prod_Z[0], ctx)) + goto err; + } else { + if (!BN_one(prod_Z[0])) + goto err; + } + } + + for (i = 1; i < num; i++) { + if (!BN_is_zero(points[i]->Z)) { + if (!group-> + meth->field_mul(group, prod_Z[i], prod_Z[i - 1], points[i]->Z, + ctx)) + goto err; + } else { + if (!BN_copy(prod_Z[i], prod_Z[i - 1])) + goto err; + } + } + + /* + * Now use a single explicit inversion to replace every non-zero + * points[i]->Z by its inverse. + */ + + if (!BN_mod_inverse(tmp, prod_Z[num - 1], group->field, ctx)) { + ECerr(EC_F_EC_GFP_SIMPLE_POINTS_MAKE_AFFINE, ERR_R_BN_LIB); + goto err; + } + if (group->meth->field_encode != 0) { + /* + * In the Montgomery case, we just turned R*H (representing H) into + * 1/(R*H), but we need R*(1/H) (representing 1/H); i.e. we need to + * multiply by the Montgomery factor twice. + */ + if (!group->meth->field_encode(group, tmp, tmp, ctx)) + goto err; + if (!group->meth->field_encode(group, tmp, tmp, ctx)) + goto err; + } + + for (i = num - 1; i > 0; --i) { + /* + * Loop invariant: tmp is the product of the inverses of points[0]->Z + * .. points[i]->Z (zero-valued inputs skipped). + */ + if (!BN_is_zero(points[i]->Z)) { + /* + * Set tmp_Z to the inverse of points[i]->Z (as product of Z + * inverses 0 .. i, Z values 0 .. i - 1). + */ + if (!group-> + meth->field_mul(group, tmp_Z, prod_Z[i - 1], tmp, ctx)) + goto err; + /* + * Update tmp to satisfy the loop invariant for i - 1. + */ + if (!group->meth->field_mul(group, tmp, tmp, points[i]->Z, ctx)) + goto err; + /* Replace points[i]->Z by its inverse. */ + if (!BN_copy(points[i]->Z, tmp_Z)) + goto err; + } + } + + if (!BN_is_zero(points[0]->Z)) { + /* Replace points[0]->Z by its inverse. */ + if (!BN_copy(points[0]->Z, tmp)) + goto err; + } + + /* Finally, fix up the X and Y coordinates for all points. */ + + for (i = 0; i < num; i++) { + EC_POINT *p = points[i]; + + if (!BN_is_zero(p->Z)) { + /* turn (X, Y, 1/Z) into (X/Z^2, Y/Z^3, 1) */ + + if (!group->meth->field_sqr(group, tmp, p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, p->X, p->X, tmp, ctx)) + goto err; + + if (!group->meth->field_mul(group, tmp, tmp, p->Z, ctx)) + goto err; + if (!group->meth->field_mul(group, p->Y, p->Y, tmp, ctx)) + goto err; + + if (group->meth->field_set_to_one != 0) { + if (!group->meth->field_set_to_one(group, p->Z, ctx)) + goto err; + } else { + if (!BN_one(p->Z)) + goto err; + } + p->Z_is_one = 1; + } + } + + ret = 1; + + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + if (prod_Z != NULL) { + for (i = 0; i < num; i++) { + if (prod_Z[i] == NULL) + break; + BN_clear_free(prod_Z[i]); + } + OPENSSL_free(prod_Z); + } + return ret; +} + +int ec_GFp_simple_field_mul(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + const BIGNUM *b, BN_CTX *ctx) +{ + return BN_mod_mul(r, a, b, group->field, ctx); +} + +int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, + BN_CTX *ctx) +{ + return BN_mod_sqr(r, a, group->field, ctx); +} diff --git a/openssl-1.1.0h/crypto/ec/ecx_meth.c b/openssl-1.1.0h/crypto/ec/ecx_meth.c new file mode 100644 index 0000000..018a941 --- /dev/null +++ b/openssl-1.1.0h/crypto/ec/ecx_meth.c @@ -0,0 +1,373 @@ +/* + * Copyright 2006-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <stdio.h> +#include "internal/cryptlib.h" +#include <openssl/x509.h> +#include <openssl/ec.h> +#include <openssl/rand.h> +#include "internal/asn1_int.h" +#include "internal/evp_int.h" +#include "ec_lcl.h" + +#define X25519_KEYLEN 32 +#define X25519_BITS 253 +#define X25519_SECURITY_BITS 128 + +typedef struct { + unsigned char pubkey[X25519_KEYLEN]; + unsigned char *privkey; +} X25519_KEY; + +typedef enum { + X25519_PUBLIC, + X25519_PRIVATE, + X25519_KEYGEN +} ecx_key_op_t; + +/* Setup EVP_PKEY using public, private or generation */ +static int ecx_key_op(EVP_PKEY *pkey, const X509_ALGOR *palg, + const unsigned char *p, int plen, ecx_key_op_t op) +{ + X25519_KEY *xkey; + + if (op != X25519_KEYGEN) { + if (palg != NULL) { + int ptype; + + /* Algorithm parameters must be absent */ + X509_ALGOR_get0(NULL, &ptype, NULL, palg); + if (ptype != V_ASN1_UNDEF) { + ECerr(EC_F_ECX_KEY_OP, EC_R_INVALID_ENCODING); + return 0; + } + } + + if (p == NULL || plen != X25519_KEYLEN) { + ECerr(EC_F_ECX_KEY_OP, EC_R_INVALID_ENCODING); + return 0; + } + } + + xkey = OPENSSL_zalloc(sizeof(*xkey)); + if (xkey == NULL) { + ECerr(EC_F_ECX_KEY_OP, ERR_R_MALLOC_FAILURE); + return 0; + } + + if (op == X25519_PUBLIC) { + memcpy(xkey->pubkey, p, plen); + } else { + xkey->privkey = OPENSSL_secure_malloc(X25519_KEYLEN); + if (xkey->privkey == NULL) { + ECerr(EC_F_ECX_KEY_OP, ERR_R_MALLOC_FAILURE); + OPENSSL_free(xkey); + return 0; + } + if (op == X25519_KEYGEN) { + if (RAND_bytes(xkey->privkey, X25519_KEYLEN) <= 0) { + OPENSSL_secure_free(xkey->privkey); + OPENSSL_free(xkey); + return 0; + } + xkey->privkey[0] &= 248; + xkey->privkey[31] &= 127; + xkey->privkey[31] |= 64; + } else { + memcpy(xkey->privkey, p, X25519_KEYLEN); + } + X25519_public_from_private(xkey->pubkey, xkey->privkey); + } + + EVP_PKEY_assign(pkey, NID_X25519, xkey); + return 1; +} + +static int ecx_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) +{ + const X25519_KEY *xkey = pkey->pkey.ptr; + unsigned char *penc; + + if (xkey == NULL) { + ECerr(EC_F_ECX_PUB_ENCODE, EC_R_INVALID_KEY); + return 0; + } + + penc = OPENSSL_memdup(xkey->pubkey, X25519_KEYLEN); + if (penc == NULL) { + ECerr(EC_F_ECX_PUB_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + + if (!X509_PUBKEY_set0_param(pk, OBJ_nid2obj(NID_X25519), V_ASN1_UNDEF, + NULL, penc, X25519_KEYLEN)) { + OPENSSL_free(penc); + ECerr(EC_F_ECX_PUB_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + return 1; +} + +static int ecx_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) +{ + const unsigned char *p; + int pklen; + X509_ALGOR *palg; + + if (!X509_PUBKEY_get0_param(NULL, &p, &pklen, &palg, pubkey)) + return 0; + return ecx_key_op(pkey, palg, p, pklen, X25519_PUBLIC); +} + +static int ecx_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b) +{ + const X25519_KEY *akey = a->pkey.ptr; + const X25519_KEY *bkey = b->pkey.ptr; + + if (akey == NULL || bkey == NULL) + return -2; + return !CRYPTO_memcmp(akey->pubkey, bkey->pubkey, X25519_KEYLEN); +} + +static int ecx_priv_decode(EVP_PKEY *pkey, const PKCS8_PRIV_KEY_INFO *p8) +{ + const unsigned char *p; + int plen; + ASN1_OCTET_STRING *oct = NULL; + const X509_ALGOR *palg; + int rv; + + if (!PKCS8_pkey_get0(NULL, &p, &plen, &palg, p8)) + return 0; + + oct = d2i_ASN1_OCTET_STRING(NULL, &p, plen); + if (oct == NULL) { + p = NULL; + plen = 0; + } else { + p = ASN1_STRING_get0_data(oct); + plen = ASN1_STRING_length(oct); + } + + rv = ecx_key_op(pkey, palg, p, plen, X25519_PRIVATE); + ASN1_OCTET_STRING_free(oct); + return rv; +} + +static int ecx_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) +{ + const X25519_KEY *xkey = pkey->pkey.ptr; + ASN1_OCTET_STRING oct; + unsigned char *penc = NULL; + int penclen; + + if (xkey == NULL || xkey->privkey == NULL) { + ECerr(EC_F_ECX_PRIV_ENCODE, EC_R_INVALID_PRIVATE_KEY); + return 0; + } + + oct.data = xkey->privkey; + oct.length = X25519_KEYLEN; + oct.flags = 0; + + penclen = i2d_ASN1_OCTET_STRING(&oct, &penc); + if (penclen < 0) { + ECerr(EC_F_ECX_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + + if (!PKCS8_pkey_set0(p8, OBJ_nid2obj(NID_X25519), 0, + V_ASN1_UNDEF, NULL, penc, penclen)) { + OPENSSL_clear_free(penc, penclen); + ECerr(EC_F_ECX_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + + return 1; +} + +static int ecx_size(const EVP_PKEY *pkey) +{ + return X25519_KEYLEN; +} + +static int ecx_bits(const EVP_PKEY *pkey) +{ + return X25519_BITS; +} + +static int ecx_security_bits(const EVP_PKEY *pkey) +{ + return X25519_SECURITY_BITS; +} + +static void ecx_free(EVP_PKEY *pkey) +{ + X25519_KEY *xkey = pkey->pkey.ptr; + + if (xkey) + OPENSSL_secure_clear_free(xkey->privkey, X25519_KEYLEN); + OPENSSL_free(xkey); +} + +/* "parameters" are always equal */ +static int ecx_cmp_parameters(const EVP_PKEY *a, const EVP_PKEY *b) +{ + return 1; +} + +static int ecx_key_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx, ecx_key_op_t op) +{ + const X25519_KEY *xkey = pkey->pkey.ptr; + + if (op == X25519_PRIVATE) { + if (xkey == NULL || xkey->privkey == NULL) { + if (BIO_printf(bp, "%*s<INVALID PRIVATE KEY>\n", indent, "") <= 0) + return 0; + return 1; + } + if (BIO_printf(bp, "%*sX25519 Private-Key:\n", indent, "") <= 0) + return 0; + if (BIO_printf(bp, "%*spriv:\n", indent, "") <= 0) + return 0; + if (ASN1_buf_print(bp, xkey->privkey, X25519_KEYLEN, indent + 4) == 0) + return 0; + } else { + if (xkey == NULL) { + if (BIO_printf(bp, "%*s<INVALID PUBLIC KEY>\n", indent, "") <= 0) + return 0; + return 1; + } + if (BIO_printf(bp, "%*sX25519 Public-Key:\n", indent, "") <= 0) + return 0; + } + if (BIO_printf(bp, "%*spub:\n", indent, "") <= 0) + return 0; + if (ASN1_buf_print(bp, xkey->pubkey, X25519_KEYLEN, indent + 4) == 0) + return 0; + return 1; +} + +static int ecx_priv_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) +{ + return ecx_key_print(bp, pkey, indent, ctx, X25519_PRIVATE); +} + +static int ecx_pub_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) +{ + return ecx_key_print(bp, pkey, indent, ctx, X25519_PUBLIC); +} + +static int ecx_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) +{ + switch (op) { + + case ASN1_PKEY_CTRL_SET1_TLS_ENCPT: + return ecx_key_op(pkey, NULL, arg2, arg1, X25519_PUBLIC); + + case ASN1_PKEY_CTRL_GET1_TLS_ENCPT: + if (pkey->pkey.ptr != NULL) { + const X25519_KEY *xkey = pkey->pkey.ptr; + unsigned char **ppt = arg2; + *ppt = OPENSSL_memdup(xkey->pubkey, X25519_KEYLEN); + if (*ppt != NULL) + return X25519_KEYLEN; + } + return 0; + + case ASN1_PKEY_CTRL_DEFAULT_MD_NID: + *(int *)arg2 = NID_sha256; + return 2; + + default: + return -2; + + } +} + +const EVP_PKEY_ASN1_METHOD ecx25519_asn1_meth = { + NID_X25519, + NID_X25519, + 0, + "X25519", + "OpenSSL X25519 algorithm", + + ecx_pub_decode, + ecx_pub_encode, + ecx_pub_cmp, + ecx_pub_print, + + ecx_priv_decode, + ecx_priv_encode, + ecx_priv_print, + + ecx_size, + ecx_bits, + ecx_security_bits, + + 0, 0, 0, 0, + ecx_cmp_parameters, + 0, 0, + + ecx_free, + ecx_ctrl, + NULL, + NULL +}; + +static int pkey_ecx_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) +{ + return ecx_key_op(pkey, NULL, NULL, 0, X25519_KEYGEN); +} + +static int pkey_ecx_derive(EVP_PKEY_CTX *ctx, unsigned char *key, + size_t *keylen) +{ + const X25519_KEY *pkey, *peerkey; + + if (ctx->pkey == NULL || ctx->peerkey == NULL) { + ECerr(EC_F_PKEY_ECX_DERIVE, EC_R_KEYS_NOT_SET); + return 0; + } + pkey = ctx->pkey->pkey.ptr; + peerkey = ctx->peerkey->pkey.ptr; + if (pkey == NULL || pkey->privkey == NULL) { + ECerr(EC_F_PKEY_ECX_DERIVE, EC_R_INVALID_PRIVATE_KEY); + return 0; + } + if (peerkey == NULL) { + ECerr(EC_F_PKEY_ECX_DERIVE, EC_R_INVALID_PEER_KEY); + return 0; + } + *keylen = X25519_KEYLEN; + if (key != NULL && X25519(key, pkey->privkey, peerkey->pubkey) == 0) + return 0; + return 1; +} + +static int pkey_ecx_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) +{ + /* Only need to handle peer key for derivation */ + if (type == EVP_PKEY_CTRL_PEER_KEY) + return 1; + return -2; +} + +const EVP_PKEY_METHOD ecx25519_pkey_meth = { + NID_X25519, + 0, 0, 0, 0, 0, 0, 0, + pkey_ecx_keygen, + 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, + pkey_ecx_derive, + pkey_ecx_ctrl, + 0 +}; |