openssl/crypto/ec/ec_mult.c

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/* crypto/ec/ec_mult.c */
/*
* Originally written by Bodo Moeller for the OpenSSL project.
*/
/* ====================================================================
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* Copyright (c) 1998-2002 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).
*
*/
/* ====================================================================
* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
* Portions of this software developed by SUN MICROSYSTEMS, INC.,
* and contributed to the OpenSSL project.
*/
#include <openssl/err.h>
#include "ec_lcl.h"
/* TODO: optional precomputation of multiples of the generator */
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/*
* wNAF-based interleaving multi-exponentation method
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* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
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*/
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/* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
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* 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
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* 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.
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*/
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static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
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{
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int window_val;
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int ok = 0;
signed char *r = NULL;
int sign = 1;
int bit, next_bit, mask;
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size_t len = 0, j;
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if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
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{
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_get_sign(scalar))
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{
sign = -1;
}
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len = BN_num_bits(scalar);
r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation */
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if (r == NULL) goto err;
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if (scalar->d == NULL || scalar->top == 0)
{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
window_val = scalar->d[0] & mask;
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j = 0;
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while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */
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{
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int digit = 0;
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/* 0 <= window_val <= 2^(w+1) */
if (window_val & 1)
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{
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/* 0 < window_val < 2^(w+1) */
if (window_val & bit)
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{
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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
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}
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else
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{
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digit = window_val; /* 0 < digit < 2^w */
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}
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if (digit <= -bit || digit >= bit || !(digit & 1))
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{
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
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}
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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)
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{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
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r[j++] = sign * digit;
window_val >>= 1;
window_val += bit * BN_is_bit_set(scalar, j + w);
if (window_val > next_bit)
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{
ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
goto err;
}
}
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if (j > len + 1)
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{
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;
}
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/* TODO: table should be optimised for the wNAF-based implementation,
* sometimes smaller windows will give better performance
* (thus the boundaries should be increased)
*/
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#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_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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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 */
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signed char **wNAF = NULL; /* individual wNAFs */
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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 (scalar != NULL)
{
generator = EC_GROUP_get0_generator(group);
if (generator == NULL)
{
ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
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return 0;
}
}
for (i = 0; i < num; i++)
{
if (group->meth != points[i]->meth)
{
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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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]);
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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_WNAF_MUL, ERR_R_INTERNAL_ERROR);
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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 */
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wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
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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)
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{
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;
}
/* Generic multiplication method.
* If group->meth does not provide a multiplication method, default to ec_wNAF_mul;
* otherwise use the group->meth's multiplication.
*/
int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
{
if (group->meth->mul == 0)
return ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
else
return group->meth->mul(group, r, scalar, num, points, scalars, ctx);
}
int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
{
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_wNAF_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_WNAF_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_WNAF_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;
}
/* Generic multiplicaiton precomputation method.
* If group->meth does not provide a multiplication method, default to ec_wNAF_mul and do its
* precomputation; otherwise use the group->meth's precomputation if it exists.
*/
int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
{
if (group->meth->mul == 0)
return ec_wNAF_precompute_mult(group, ctx);
else if (group->meth->precompute_mult != 0)
return group->meth->precompute_mult(group, ctx);
else
return 1;
}