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913 lines
28 KiB
913 lines
28 KiB
/* 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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|
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#include <string.h> |
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|
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#include <openssl/err.h> |
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|
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#include "ec_lcl.h" |
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|
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/* |
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* This file implements the 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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* for multiplication with precomputation, we use wNAF splitting |
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* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>). |
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*/ |
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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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|
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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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|
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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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|
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if (!group) |
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return NULL; |
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|
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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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|
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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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|
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/* no need to actually copy, these objects never change! */ |
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|
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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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|
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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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|
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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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|
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if (pre->points) { |
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EC_POINT **p; |
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|
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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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|
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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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|
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if (!pre) |
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return; |
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|
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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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|
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if (pre->points) { |
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EC_POINT **p; |
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|
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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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/*- |
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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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|
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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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|
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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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|
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if (BN_is_negative(scalar)) { |
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sign = -1; |
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} |
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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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|
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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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|
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/* 0 <= window_val <= 2^(w+1) */ |
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|
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if (window_val & 1) { |
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/* 0 < window_val < 2^(w+1) */ |
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|
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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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|
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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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/* |
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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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|
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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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|
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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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|
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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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/* |
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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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/*- |
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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. |
|
* precomputation is not available */ |
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int ret = 0; |
|
|
|
if (group->meth != r->meth) { |
|
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
|
return 0; |
|
} |
|
|
|
if ((scalar == NULL) && (num == 0)) { |
|
return EC_POINT_set_to_infinity(group, r); |
|
} |
|
|
|
for (i = 0; i < num; i++) { |
|
if (group->meth != points[i]->meth) { |
|
ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS); |
|
return 0; |
|
} |
|
} |
|
|
|
if (ctx == NULL) { |
|
ctx = new_ctx = BN_CTX_new(); |
|
if (ctx == NULL) |
|
goto err; |
|
} |
|
|
|
if (scalar != NULL) { |
|
generator = EC_GROUP_get0_generator(group); |
|
if (generator == NULL) { |
|
ECerr(EC_F_EC_WNAF_MUL, EC_R_UNDEFINED_GENERATOR); |
|
goto err; |
|
} |
|
|
|
/* look if we can use precomputed multiples of generator */ |
|
|
|
pre_comp = |
|
EC_EX_DATA_get_data(group->extra_data, ec_pre_comp_dup, |
|
ec_pre_comp_free, ec_pre_comp_clear_free); |
|
|
|
if (pre_comp && pre_comp->numblocks |
|
&& (EC_POINT_cmp(group, generator, pre_comp->points[0], ctx) == |
|
0)) { |
|
blocksize = pre_comp->blocksize; |
|
|
|
/* |
|
* determine maximum number of blocks that wNAF splitting may |
|
* yield (NB: maximum wNAF length is bit length plus one) |
|
*/ |
|
numblocks = (BN_num_bits(scalar) / blocksize) + 1; |
|
|
|
/* |
|
* we cannot use more blocks than we have precomputation for |
|
*/ |
|
if (numblocks > pre_comp->numblocks) |
|
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; |
|
}
|
|
|