/* Originally written by Bodo Moeller for the OpenSSL project.
* ====================================================================
* Copyright (c) 1998-2005 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 the attached software ("Contribution") are developed by
* SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
*
* The Contribution is licensed pursuant to the OpenSSL open source
* license provided above.
*
* The elliptic curve binary polynomial software is originally written by
* Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems
* Laboratories. */
#include <openssl/ec.h>
#include <string.h>
#include <openssl/bn.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/thread.h>
#include "internal.h"
#include "../internal.h"
/* This file implements the wNAF-based interleaving multi-exponentation method
* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
* */
/* 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 int8_t *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) {
int window_val;
int ok = 0;
int8_t *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) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
r[0] = 0;
*ret_len = 1;
return r;
}
/* 'int8_t' can represent integers with absolute values less than 2^7. */
if (w <= 0 || w > 7) {
OPENSSL_PUT_ERROR(EC, 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;
}
if (scalar->d == NULL || scalar->top == 0) {
OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
goto err;
}
len = BN_num_bits(scalar);
/* The 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). */
r = OPENSSL_malloc(len + 1);
if (r == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
window_val = scalar->d[0] & mask;
j = 0;
/* If j+w+1 >= len, window_val will not increase. */
while (window_val != 0 || j + w + 1 < len) {
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)) {
OPENSSL_PUT_ERROR(EC, 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) {
OPENSSL_PUT_ERROR(EC, 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) {
OPENSSL_PUT_ERROR(EC, ERR_R_INTERNAL_ERROR);
goto err;
}
}
if (j > len + 1) {
OPENSSL_PUT_ERROR(EC, 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)
*/
static size_t window_bits_for_scalar_size(size_t b) {
if (b >= 2000) {
return 6;
}
if (b >= 800) {
return 5;
}
if (b >= 300) {
return 4;
}
if (b >= 70) {
return 3;
}
if (b >= 20) {
return 2;
}
return 1;
}
int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) {
BN_CTX *new_ctx = NULL;
const EC_POINT *generator = NULL;
EC_POINT *tmp = NULL;
size_t total_num = 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 */
int8_t **wNAF = NULL; /* individual wNAFs */
size_t *wNAF_len = NULL;
size_t max_len = 0;
size_t num_val = 0;
EC_POINT **val = NULL; /* precomputation */
EC_POINT **v;
EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
int ret = 0;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
goto err;
}
}
/* TODO: This function used to take |points| and |scalars| as arrays of
* |num| elements. The code below should be simplified to work in terms of |p|
* and |p_scalar|. */
size_t num = p != NULL ? 1 : 0;
const EC_POINT **points = p != NULL ? &p : NULL;
const BIGNUM **scalars = p != NULL ? &p_scalar : NULL;
total_num = num;
if (g_scalar != NULL) {
generator = EC_GROUP_get0_generator(group);
if (generator == NULL) {
OPENSSL_PUT_ERROR(EC, EC_R_UNDEFINED_GENERATOR);
goto err;
}
++total_num; /* treat 'g_scalar' like 'num'-th element of 'scalars' */
}
wsize = OPENSSL_malloc(total_num * sizeof(wsize[0]));
wNAF_len = OPENSSL_malloc(total_num * sizeof(wNAF_len[0]));
wNAF = OPENSSL_malloc(total_num * sizeof(wNAF[0]));
val_sub = OPENSSL_malloc(total_num * sizeof(val_sub[0]));
/* Ensure wNAF is initialised in case we end up going to err. */
if (wNAF != NULL) {
OPENSSL_memset(wNAF, 0, total_num * sizeof(wNAF[0]));
}
if (!wsize || !wNAF_len || !wNAF || !val_sub) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
/* num_val will be the total number of temporarily precomputed points */
num_val = 0;
for (i = 0; i < total_num; i++) {
size_t bits;
bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(g_scalar);
wsize[i] = window_bits_for_scalar_size(bits);
num_val += (size_t)1 << (wsize[i] - 1);
wNAF[i] =
compute_wNAF((i < num ? scalars[i] : g_scalar), wsize[i], &wNAF_len[i]);
if (wNAF[i] == NULL) {
goto err;
}
if (wNAF_len[i] > max_len) {
max_len = wNAF_len[i];
}
}
/* 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. */
val = OPENSSL_malloc(num_val * sizeof(val[0]));
if (val == NULL) {
OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
goto err;
}
OPENSSL_memset(val, 0, num_val * sizeof(val[0]));
/* allocate points for precomputation */
v = val;
for (i = 0; i < total_num; 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)) {
OPENSSL_PUT_ERROR(EC, 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 < total_num; 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 1 /* optional; 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 && !EC_POINT_dbl(group, r, r, ctx)) {
goto err;
}
for (i = 0; i < total_num; 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 && !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 && !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) {
for (i = 0; i < total_num; i++) {
OPENSSL_free(wNAF[i]);
}
OPENSSL_free(wNAF);
}
if (val != NULL) {
for (i = 0; i < num_val; i++) {
EC_POINT_clear_free(val[i]);
}
OPENSSL_free(val);
}
OPENSSL_free(val_sub);
return ret;
}