486 lines
11 KiB
C
486 lines
11 KiB
C
/* crypto/ec/ec_mult.c */
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/* ====================================================================
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* Copyright (c) 1998-2001 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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#include <openssl/err.h>
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#include "ec_lcl.h"
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/* TODO: optional precomputation of multiples of the generator */
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/*
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* wNAF-based interleaving multi-exponentation method
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* (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>)
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*/
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/* Determine the 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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*/
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static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx)
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{
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BIGNUM *c;
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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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BN_CTX_start(ctx);
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c = BN_CTX_get(ctx);
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if (c == NULL) goto err;
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if (w <= 0 || w > 7) /* 'signed char' can represent integers with absolute values less than 2^7 */
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{
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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_copy(c, scalar)) goto err;
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if (c->neg)
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{
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sign = -1;
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c->neg = 0;
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}
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len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */
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r = OPENSSL_malloc(len);
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if (r == NULL) goto err;
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j = 0;
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while (!BN_is_zero(c))
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{
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int u = 0;
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if (BN_is_odd(c))
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{
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if (c->d == NULL || c->top == 0)
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{
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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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u = c->d[0] & mask;
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if (u & bit)
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{
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u -= next_bit;
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/* u < 0 */
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if (!BN_add_word(c, -u)) goto err;
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}
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else
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{
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/* u > 0 */
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if (!BN_sub_word(c, u)) goto err;
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}
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if (u <= -bit || u >= bit || !(u & 1) || c->neg)
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{
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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 * u;
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if (BN_is_odd(c))
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{
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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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if (!BN_rshift1(c, c)) goto err;
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}
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if (j > len)
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{
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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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BN_CTX_end(ctx);
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if (!ok)
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{
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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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/* TODO: table should be optimised for the wNAF-based implementation,
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* sometimes smaller windows will give better performance
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* (thus the 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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/* 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_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
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{
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BN_CTX *new_ctx = NULL;
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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 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' */
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int ret = 0;
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if (group->meth != r->meth)
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{
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ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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if ((scalar == NULL) && (num == 0))
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{
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return EC_POINT_set_to_infinity(group, r);
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}
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if (scalar != NULL)
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{
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generator = EC_GROUP_get0_generator(group);
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if (generator == NULL)
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{
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ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
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return 0;
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}
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}
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for (i = 0; i < num; i++)
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{
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if (group->meth != points[i]->meth)
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{
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ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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return 0;
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}
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}
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totalnum = num + (scalar != NULL);
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wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
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wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]);
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wNAF = OPENSSL_malloc((totalnum + 1) * sizeof wNAF[0]);
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if (wNAF != NULL)
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{
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wNAF[0] = NULL; /* preliminary pivot */
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}
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if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err;
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/* num_val := total number of points to precompute */
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num_val = 0;
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for (i = 0; i < totalnum; i++)
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{
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size_t bits;
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bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
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wsize[i] = EC_window_bits_for_scalar_size(bits);
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num_val += 1u << (wsize[i] - 1);
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}
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/* all precomputed points go into a single array 'val',
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* 'val_sub[i]' is a pointer to the subarray for the i-th point */
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val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
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if (val == NULL) goto err;
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val[num_val] = NULL; /* pivot element */
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val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
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if (val_sub == NULL) goto err;
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/* allocate points for precomputation */
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v = val;
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for (i = 0; i < totalnum; i++)
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{
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val_sub[i] = v;
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for (j = 0; j < (1u << (wsize[i] - 1)); j++)
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{
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*v = EC_POINT_new(group);
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if (*v == NULL) goto err;
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v++;
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}
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}
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if (!(v == val + num_val))
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{
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ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
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goto err;
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}
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if (ctx == NULL)
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{
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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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tmp = EC_POINT_new(group);
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if (tmp == NULL) goto err;
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/* prepare precomputed values:
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* val_sub[i][0] := points[i]
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* val_sub[i][1] := 3 * points[i]
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* val_sub[i][2] := 5 * points[i]
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* ...
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*/
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for (i = 0; i < totalnum; i++)
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{
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if (i < num)
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{
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if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
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}
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else
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{
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if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
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}
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if (wsize[i] > 1)
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{
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if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
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for (j = 1; j < (1u << (wsize[i] - 1)); j++)
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{
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if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
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}
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}
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wNAF[i + 1] = NULL; /* make sure we always have a pivot */
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wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i], ctx);
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if (wNAF[i] == NULL) goto err;
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if (wNAF_len[i] > max_len)
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max_len = wNAF_len[i];
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}
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#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
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if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;
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#endif
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r_is_at_infinity = 1;
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for (k = max_len - 1; k >= 0; k--)
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{
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if (!r_is_at_infinity)
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{
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if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
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}
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for (i = 0; i < totalnum; i++)
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{
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if (wNAF_len[i] > (size_t)k)
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{
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int digit = wNAF[i][k];
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int is_neg;
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if (digit)
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{
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is_neg = digit < 0;
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if (is_neg)
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digit = -digit;
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if (is_neg != r_is_inverted)
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{
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if (!r_is_at_infinity)
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{
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if (!EC_POINT_invert(group, r, ctx)) goto err;
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}
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r_is_inverted = !r_is_inverted;
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}
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/* digit > 0 */
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if (r_is_at_infinity)
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{
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if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err;
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r_is_at_infinity = 0;
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}
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else
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{
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if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err;
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}
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}
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}
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}
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}
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if (r_is_at_infinity)
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{
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if (!EC_POINT_set_to_infinity(group, r)) goto err;
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}
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else
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{
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if (r_is_inverted)
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if (!EC_POINT_invert(group, r, ctx)) goto err;
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}
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ret = 1;
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err:
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if (new_ctx != NULL)
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BN_CTX_free(new_ctx);
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if (tmp != NULL)
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EC_POINT_free(tmp);
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if (wsize != NULL)
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OPENSSL_free(wsize);
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if (wNAF_len != NULL)
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OPENSSL_free(wNAF_len);
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if (wNAF != NULL)
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{
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signed char **w;
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for (w = wNAF; *w != NULL; w++)
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OPENSSL_free(*w);
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OPENSSL_free(wNAF);
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}
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if (val != NULL)
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{
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for (v = val; *v != NULL; v++)
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EC_POINT_clear_free(*v);
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OPENSSL_free(val);
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}
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if (val_sub != NULL)
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{
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OPENSSL_free(val_sub);
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}
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return ret;
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}
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int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
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{
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const EC_POINT *points[1];
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const BIGNUM *scalars[1];
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points[0] = point;
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scalars[0] = p_scalar;
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return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx);
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}
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int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
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{
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const EC_POINT *generator;
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BN_CTX *new_ctx = NULL;
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BIGNUM *order;
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int ret = 0;
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generator = EC_GROUP_get0_generator(group);
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if (generator == NULL)
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{
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ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
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return 0;
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}
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if (ctx == NULL)
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{
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ctx = new_ctx = BN_CTX_new();
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if (ctx == NULL)
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return 0;
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}
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BN_CTX_start(ctx);
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order = BN_CTX_get(ctx);
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if (order == NULL) goto err;
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if (!EC_GROUP_get_order(group, order, ctx)) return 0;
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if (BN_is_zero(order))
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{
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ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
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goto err;
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}
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/* TODO */
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ret = 1;
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err:
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BN_CTX_end(ctx);
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if (new_ctx != NULL)
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BN_CTX_free(new_ctx);
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return ret;
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}
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