/*
* 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);
}
