/* crypto/ec/ec_mult.c */
/*
* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
*/
/* ====================================================================
* Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
*
* 3. All advertising materials mentioning features or use of this
* software must display the following acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
*
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
* endorse or promote products derived from this software without
* prior written permission. For written permission, please contact
* [email protected].
*
* 5. Products derived from this software may not be called "OpenSSL"
* nor may "OpenSSL" appear in their names without prior written
* permission of the OpenSSL Project.
*
* 6. Redistributions of any form whatsoever must retain the following
* acknowledgment:
* "This product includes software developed by the OpenSSL Project
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
*
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
* ====================================================================
*
* This product includes cryptographic software written by Eric Young
* ([email protected]). This product includes software written by Tim
* Hudson ([email protected]).
*
*/
/* ====================================================================
* 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 "ec_lcl.h"
/*
* This file implements the wNAF-based interleaving multi-exponentation method
* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
* for multiplication with precomputation, we use wNAF splitting
* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
*/
/* structure for precomputed multiples of the generator */
typedef 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;
} EC_PRE_COMP;
/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
static void *ec_pre_comp_dup(void *);
static void ec_pre_comp_free(void *);
static void ec_pre_comp_clear_free(void *);
static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
{
EC_PRE_COMP *ret = NULL;
if (!group)
return NULL;
ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
if (!ret)
{
ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
return ret;
}
ret->group = group;
ret->blocksize = 8; /* default */
ret->numblocks = 0;
ret->w = 4; /* default */
ret->points = NULL;
ret->num = 0;
ret->references = 1;
return ret;
}
static void *ec_pre_comp_dup(void *src_)
{
EC_PRE_COMP *src = src_;
/* no need to actually copy, these objects never change! */
CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
return src_;
}
static void ec_pre_comp_free(void *pre_)
{
int i;
EC_PRE_COMP *pre = pre_;
if (!pre)
return;
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
if (i > 0)
return;
if (pre->points)
{
EC_POINT **p;
for (p = pre->points; *p != NULL; p++)
EC_POINT_free(*p);
OPENSSL_free(pre->points);
}
OPENSSL_free(pre);
}
static void ec_pre_comp_clear_free(void *pre_)
{
int i;
EC_PRE_COMP *pre = pre_;
if (!pre)
return;
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
if (i > 0)
return;
if (pre->points)
{
EC_POINT **p;
for (p = pre->points; *p != NULL; p++)
EC_POINT_clear_free(*p);
OPENSSL_cleanse(pre->points, sizeof pre->points);
OPENSSL_free(pre->points);
}
OPENSSL_cleanse(pre, sizeof pre);
OPENSSL_free(pre);
}
/* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
* This is an array r[] of values that are either zero or odd with an
* absolute value less than 2^w satisfying
* scalar = \sum_j r[j]*2^j
* where at most one of any w+1 consecutive digits is non-zero
* with the exception that the most significant digit may be only
* w-1 zeros away from that next non-zero digit.
*/
static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
{
int window_val;
int ok = 0;
signed char *r = NULL;
int sign = 1;
int bit, next_bit, mask;
size_t len = 0, j;
if (BN_is_zero(scalar))
{
r = OPENSSL_malloc(1);
if (!r)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
goto err;
}
r[0] = 0;
*ret_len = 1;
return r;
}
if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
bit = 1 << w; /* at most 128 */
next_bit = bit << 1; /* at most 256 */
mask = next_bit - 1; /* at most 255 */
if (BN_is_negative(scalar))
{
sign = -1;
}
len = BN_num_bits(scalar);
r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation
* (*ret_len will be set to the actual length, i.e. at most
* BN_num_bits(scalar) + 1) */
if (r == NULL)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
goto err;
}
if (scalar->d == NULL || scalar->top == 0)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
window_val = scalar->d[0] & mask;
j = 0;
while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
{
int digit = 0;
/* 0 <= window_val <= 2^(w+1) */
if (window_val & 1)
{
/* 0 < window_val < 2^(w+1) */
if (window_val & bit)
{
digit = window_val - next_bit; /* -2^w < digit < 0 */
#if 1 /* modified wNAF */
if (j + w + 1 >= len)
{
/* special case for generating modified wNAFs:
* no new bits will be added into window_val,
* so using a positive digit here will decrease
* the total length of the representation */
digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
}
#endif
}
else
{
digit = window_val; /* 0 < digit < 2^w */
}
if (digit <= -bit || digit >= bit || !(digit & 1))
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
window_val -= digit;
/* now window_val is 0 or 2^(w+1) in standard wNAF generation;
* for modified window NAFs, it may also be 2^w
*/
if (window_val != 0 && window_val != next_bit && window_val != bit)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
r[j++] = sign * digit;
window_val >>= 1;
window_val += bit * BN_is_bit_set(scalar, j + w);
if (window_val > next_bit)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
if (j > len + 1)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
len = j;
ok = 1;
err:
if (!ok)
{
OPENSSL_free(r);
r = NULL;
}
if (ok)
*ret_len = len;
return r;
}
/* 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 = EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
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 = 1u << (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]);
wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]); /* includes space for pivot */
val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
if (!wsize || !wNAF_len || !wNAF || !val_sub)
{
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
goto err;
}
wNAF[0] = NULL; /* preliminary pivot */
/* 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 += 1u << (wsize[i] - 1);
wNAF[i + 1] = NULL; /* make sure we always have a pivot */
wNAF[i] = 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 = 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;
if (tmp_len > max_len)
max_len = 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);
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);
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 < (1u << (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)))
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 < (1u << (wsize[i] - 1)); j++)
{
if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
}
}
}
#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
if (!EC_POINTs_make_affine(group, num_val, val, ctx))
goto err;
#endif
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:
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
if (tmp != NULL)
EC_POINT_free(tmp);
if (wsize != NULL)
OPENSSL_free(wsize);
if (wNAF_len != NULL)
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);
}
if (val_sub != NULL)
{
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;
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_EX_DATA_free_data(&group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free);
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 = BN_CTX_get(ctx);
if (order == NULL) goto err;
if (!EC_GROUP_get_order(group, order, ctx)) 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 = 1u << (w - 1);
num = pre_points_per_block * numblocks; /* number of points to compute and store */
points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1));
if (!points)
{
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)) || !(base = EC_POINT_new(group)))
{
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;
if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free))
goto err;
pre_comp = NULL;
ret = 1;
err:
if (ctx != NULL)
BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
if (pre_comp)
ec_pre_comp_free(pre_comp);
if (points)
{
EC_POINT **p;
for (p = points; *p != NULL; p++)
EC_POINT_free(*p);
OPENSSL_free(points);
}
if (tmp_point)
EC_POINT_free(tmp_point);
if (base)
EC_POINT_free(base);
return ret;
}
int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
{
if (EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, ec_pre_comp_free, ec_pre_comp_clear_free) != NULL)
return 1;
else
return 0;
}
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