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- /* 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 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) {
- OPENSSL_PUT_ERROR(EC, 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 */
- {
- 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);
- 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) {
- OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
- 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)) {
- 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)
- */
- #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))
-
- 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;
- 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 (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 + 1) *
- sizeof wNAF[0]); /* includes space for pivot */
- val_sub = OPENSSL_malloc(total_num * sizeof val_sub[0]);
-
- /* Ensure wNAF is initialised in case we end up going to err. */
- if (wNAF) {
- wNAF[0] = NULL; /* preliminary pivot */
- }
-
- 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] = 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] =
- 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 + 1) * sizeof val[0]);
- if (val == NULL) {
- OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE);
- goto err;
- }
- val[num_val] = NULL; /* pivot element */
-
- /* 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; 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 && !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) {
- 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;
- }
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