918 lines
28 KiB
C
918 lines
28 KiB
C
/* crypto/ec/ec_mult.c */
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/*
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* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
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*/
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/* ====================================================================
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* Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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/* ====================================================================
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* Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
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* Portions of this software developed by SUN MICROSYSTEMS, INC.,
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* and contributed to the OpenSSL project.
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*/
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#include <string.h>
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#include <openssl/err.h>
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#include "ec_lcl.h"
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/*
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* This file implements the wNAF-based interleaving multi-exponentiation method
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* Formerly at:
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* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp
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* You might now find it here:
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* http://link.springer.com/chapter/10.1007%2F3-540-45537-X_13
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* http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf
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* For multiplication with precomputation, we use wNAF splitting, formerly at:
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* http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp
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*/
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/* structure for precomputed multiples of the generator */
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typedef struct ec_pre_comp_st {
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const EC_GROUP *group; /* parent EC_GROUP object */
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size_t blocksize; /* block size for wNAF splitting */
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size_t numblocks; /* max. number of blocks for which we have
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* precomputation */
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size_t w; /* window size */
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EC_POINT **points; /* array with pre-calculated multiples of
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* generator: 'num' pointers to EC_POINT
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* objects followed by a NULL */
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size_t num; /* numblocks * 2^(w-1) */
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int references;
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} EC_PRE_COMP;
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/* functions to manage EC_PRE_COMP within the EC_GROUP extra_data framework */
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static void *ec_pre_comp_dup(void *);
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static void ec_pre_comp_free(void *);
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static void ec_pre_comp_clear_free(void *);
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static EC_PRE_COMP *ec_pre_comp_new(const EC_GROUP *group)
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{
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EC_PRE_COMP *ret = NULL;
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if (!group)
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return NULL;
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ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
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if (!ret) {
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ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
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return ret;
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}
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ret->group = group;
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ret->blocksize = 8; /* default */
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ret->numblocks = 0;
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ret->w = 4; /* default */
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ret->points = NULL;
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ret->num = 0;
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ret->references = 1;
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return ret;
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}
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static void *ec_pre_comp_dup(void *src_)
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{
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EC_PRE_COMP *src = src_;
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/* no need to actually copy, these objects never change! */
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CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
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return src_;
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}
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static void ec_pre_comp_free(void *pre_)
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{
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int i;
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EC_PRE_COMP *pre = pre_;
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if (!pre)
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return;
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i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
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if (i > 0)
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return;
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if (pre->points) {
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EC_POINT **p;
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for (p = pre->points; *p != NULL; p++)
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EC_POINT_free(*p);
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OPENSSL_free(pre->points);
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}
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OPENSSL_free(pre);
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}
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static void ec_pre_comp_clear_free(void *pre_)
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{
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int i;
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EC_PRE_COMP *pre = pre_;
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if (!pre)
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return;
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i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
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if (i > 0)
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return;
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if (pre->points) {
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EC_POINT **p;
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for (p = pre->points; *p != NULL; p++) {
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EC_POINT_clear_free(*p);
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OPENSSL_cleanse(p, sizeof *p);
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}
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OPENSSL_free(pre->points);
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}
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OPENSSL_cleanse(pre, sizeof *pre);
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OPENSSL_free(pre);
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}
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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
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* absolute value less than 2^w satisfying
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* scalar = \sum_j r[j]*2^j
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* where at most one of any w+1 consecutive digits is non-zero
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* with the exception that the most significant digit may be only
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* 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;
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signed char *r = NULL;
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int sign = 1;
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int bit, next_bit, mask;
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size_t len = 0, j;
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if (BN_is_zero(scalar)) {
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r = OPENSSL_malloc(1);
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if (!r) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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r[0] = 0;
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*ret_len = 1;
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return r;
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}
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if (w <= 0 || w > 7) { /* 'signed char' can represent integers with
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* absolute values less than 2^7 */
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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bit = 1 << w; /* at most 128 */
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next_bit = bit << 1; /* at most 256 */
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mask = next_bit - 1; /* at most 255 */
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if (BN_is_negative(scalar)) {
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sign = -1;
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}
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if (scalar->d == NULL || scalar->top == 0) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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len = BN_num_bits(scalar);
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r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer
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* than binary representation (*ret_len will
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* be set to the actual length, i.e. at most
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* BN_num_bits(scalar) + 1) */
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if (r == NULL) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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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,
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* window_val will not
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* increase */
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int digit = 0;
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/* 0 <= window_val <= 2^(w+1) */
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if (window_val & 1) {
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/* 0 < window_val < 2^(w+1) */
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if (window_val & bit) {
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digit = window_val - next_bit; /* -2^w < digit < 0 */
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#if 1 /* modified wNAF */
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if (j + w + 1 >= len) {
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/*
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* special case for generating modified wNAFs: no new
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* bits will be added into window_val, so using a
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* positive digit here will decrease the total length of
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* the representation
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*/
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digit = window_val & (mask >> 1); /* 0 < digit < 2^w */
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}
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#endif
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} else {
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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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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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window_val -= digit;
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/*
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* now window_val is 0 or 2^(w+1) in standard wNAF generation;
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* for modified window NAFs, it may also be 2^w
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*/
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if (window_val != 0 && window_val != next_bit
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&& window_val != bit) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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}
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r[j++] = sign * digit;
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window_val >>= 1;
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window_val += bit * BN_is_bit_set(scalar, j + w);
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if (window_val > next_bit) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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}
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if (j > len + 1) {
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ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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len = j;
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ok = 1;
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err:
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if (!ok) {
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OPENSSL_free(r);
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r = NULL;
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}
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if (ok)
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*ret_len = len;
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return r;
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}
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/*
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* TODO: table should be optimised for the wNAF-based implementation,
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* sometimes smaller windows will give better performance (thus the
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* boundaries should be increased)
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*/
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#define EC_window_bits_for_scalar_size(b) \
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((size_t) \
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((b) >= 2000 ? 6 : \
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(b) >= 800 ? 5 : \
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(b) >= 300 ? 4 : \
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(b) >= 70 ? 3 : \
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(b) >= 20 ? 2 : \
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1))
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/*-
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* Compute
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* \sum scalars[i]*points[i],
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* also including
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* scalar*generator
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* in the addition if scalar != NULL
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*/
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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[],
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BN_CTX *ctx)
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{
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BN_CTX *new_ctx = NULL;
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const EC_POINT *generator = NULL;
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EC_POINT *tmp = NULL;
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size_t totalnum;
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size_t blocksize = 0, numblocks = 0; /* for wNAF splitting */
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size_t pre_points_per_block = 0;
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size_t i, j;
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int k;
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int r_is_inverted = 0;
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int r_is_at_infinity = 1;
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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;
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size_t max_len = 0;
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size_t num_val;
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EC_POINT **val = NULL; /* precomputation */
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EC_POINT **v;
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EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' or
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* 'pre_comp->points' */
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const EC_PRE_COMP *pre_comp = NULL;
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int num_scalar = 0; /* flag: will be set to 1 if 'scalar' must be
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* treated like other scalars, i.e.
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* precomputation is not available */
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int ret = 0;
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if (group->meth != r->meth) {
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ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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|
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if ((scalar == NULL) && (num == 0)) {
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return EC_POINT_set_to_infinity(group, r);
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}
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|
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for (i = 0; i < num; i++) {
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if (group->meth != points[i]->meth) {
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ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
|
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}
|
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|
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if (ctx == NULL) {
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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goto err;
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}
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|
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if (scalar != NULL) {
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generator = EC_GROUP_get0_generator(group);
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if (generator == NULL) {
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ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR);
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goto err;
|
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}
|
|
|
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/* look if we can use precomputed multiples of generator */
|
|
|
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pre_comp =
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EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup,
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ec_pre_comp_free, ec_pre_comp_clear_free);
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|
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if (pre_comp && pre_comp->numblocks
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&& (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) ==
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0)) {
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blocksize = pre_comp->blocksize;
|
|
|
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/*
|
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* determine maximum number of blocks that wNAF splitting may
|
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* yield (NB: maximum wNAF length is bit length plus one)
|
|
*/
|
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numblocks = (BN_num_bits(scalar) / blocksize) + 1;
|
|
|
|
/*
|
|
* we cannot use more blocks than we have precomputation for
|
|
*/
|
|
if (numblocks > pre_comp->numblocks)
|
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numblocks = pre_comp->numblocks;
|
|
|
|
pre_points_per_block = (size_t)1 << (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]);
|
|
|
|
/* 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) {
|
|
ECerr(EC_F_EC_WNAF_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
/*
|
|
* 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 += (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] : 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 < ((size_t)1 << (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 < ((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) {
|
|
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 = (size_t)1 << (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;
|
|
}
|