#! /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 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,") { 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 " .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