484 lines
11 KiB
C
484 lines
11 KiB
C
/* crypto/ec/ec_mult.c */
|
|
/* ====================================================================
|
|
* Copyright (c) 1998-2001 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
|
|
* openssl-core@openssl.org.
|
|
*
|
|
* 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
|
|
* (eay@cryptsoft.com). This product includes software written by Tim
|
|
* Hudson (tjh@cryptsoft.com).
|
|
*
|
|
*/
|
|
|
|
#include <openssl/err.h>
|
|
|
|
#include "ec_lcl.h"
|
|
|
|
|
|
/* TODO: optional precomputation of multiples of the generator */
|
|
|
|
|
|
|
|
/*
|
|
* wNAF-based interleaving multi-exponentation method
|
|
* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
|
|
*/
|
|
|
|
|
|
/* Determine the 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.
|
|
*/
|
|
static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx)
|
|
{
|
|
BIGNUM *c;
|
|
int ok = 0;
|
|
signed char *r = NULL;
|
|
int sign = 1;
|
|
int bit, next_bit, mask;
|
|
size_t len = 0, j;
|
|
|
|
BN_CTX_start(ctx);
|
|
c = BN_CTX_get(ctx);
|
|
if (c == NULL) goto err;
|
|
|
|
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_copy(c, scalar)) goto err;
|
|
if (c->neg)
|
|
{
|
|
sign = -1;
|
|
c->neg = 0;
|
|
}
|
|
|
|
len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */
|
|
r = OPENSSL_malloc(len);
|
|
if (r == NULL) goto err;
|
|
|
|
j = 0;
|
|
while (!BN_is_zero(c))
|
|
{
|
|
int u = 0;
|
|
|
|
if (BN_is_odd(c))
|
|
{
|
|
if (c->d == NULL || c->top == 0)
|
|
{
|
|
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
u = c->d[0] & mask;
|
|
if (u & bit)
|
|
{
|
|
u -= next_bit;
|
|
/* u < 0 */
|
|
if (!BN_add_word(c, -u)) goto err;
|
|
}
|
|
else
|
|
{
|
|
/* u > 0 */
|
|
if (!BN_sub_word(c, u)) goto err;
|
|
}
|
|
|
|
if (u <= -bit || u >= bit || !(u & 1) || c->neg)
|
|
{
|
|
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
r[j++] = sign * u;
|
|
|
|
if (BN_is_odd(c))
|
|
{
|
|
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
if (!BN_rshift1(c, c)) goto err;
|
|
}
|
|
|
|
if (j > len)
|
|
{
|
|
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
len = j;
|
|
ok = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
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) \
|
|
((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_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)
|
|
{
|
|
BN_CTX *new_ctx = NULL;
|
|
EC_POINT *generator = NULL;
|
|
EC_POINT *tmp = NULL;
|
|
size_t totalnum;
|
|
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' */
|
|
int ret = 0;
|
|
|
|
if (group->meth != r->meth)
|
|
{
|
|
ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
|
|
return 0;
|
|
}
|
|
|
|
if ((scalar == NULL) && (num == 0))
|
|
{
|
|
return EC_POINT_set_to_infinity(group, r);
|
|
}
|
|
|
|
if (scalar != NULL)
|
|
{
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL)
|
|
{
|
|
ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
for (i = 0; i < num; i++)
|
|
{
|
|
if (group->meth != points[i]->meth)
|
|
{
|
|
ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
totalnum = num + (scalar != NULL);
|
|
|
|
wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
|
|
wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
|
|
wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]);
|
|
if (wNAF != NULL)
|
|
{
|
|
wNAF[0] = NULL; /* preliminary pivot */
|
|
}
|
|
if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err;
|
|
|
|
/* num_val := total number of points to precompute */
|
|
num_val = 0;
|
|
for (i = 0; i < totalnum; 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);
|
|
}
|
|
|
|
/* all precomputed points go into a single array 'val',
|
|
* 'val_sub[i]' is a pointer to the subarray for the i-th point */
|
|
val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
|
|
if (val == NULL) goto err;
|
|
val[num_val] = NULL; /* pivot element */
|
|
|
|
val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
|
|
if (val_sub == NULL) goto err;
|
|
|
|
/* allocate points for precomputation */
|
|
v = val;
|
|
for (i = 0; i < totalnum; 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_POINTS_MUL, ERR_R_INTERNAL_ERROR);
|
|
goto err;
|
|
}
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
goto err;
|
|
}
|
|
|
|
tmp = EC_POINT_new(group);
|
|
if (tmp == 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 < totalnum; 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;
|
|
}
|
|
}
|
|
|
|
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], ctx);
|
|
if (wNAF[i] == NULL) goto err;
|
|
if (wNAF_len[i] > max_len)
|
|
max_len = wNAF_len[i];
|
|
}
|
|
|
|
#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;
|
|
}
|
|
|
|
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
const EC_POINT *generator;
|
|
BN_CTX *new_ctx = NULL;
|
|
BIGNUM *order;
|
|
int ret = 0;
|
|
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL)
|
|
{
|
|
ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
|
|
if (ctx == NULL)
|
|
{
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
return 0;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
order = BN_CTX_get(ctx);
|
|
if (order == NULL) goto err;
|
|
|
|
if (!EC_GROUP_get_order(group, order, ctx)) return 0;
|
|
if (BN_is_zero(order))
|
|
{
|
|
ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
|
|
goto err;
|
|
}
|
|
|
|
/* TODO */
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
if (new_ctx != NULL)
|
|
BN_CTX_free(new_ctx);
|
|
return ret;
|
|
}
|