202f7c5659
The secret point R can be recovered from S using the equation R = S - P.
The X and Z coordinates should be sufficient for that.
Reviewed-by: Paul Dale <paul.dale@oracle.com>
(Merged from https://github.com/openssl/openssl/pull/8504)
(cherry picked from commit 8a74bb5c7b)
970 lines
30 KiB
C
970 lines
30 KiB
C
/*
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* Copyright 2001-2018 The OpenSSL Project Authors. All Rights Reserved.
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* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <string.h>
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#include <openssl/err.h>
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#include "internal/cryptlib.h"
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#include "internal/bn_int.h"
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#include "ec_lcl.h"
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#include "internal/refcount.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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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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CRYPTO_REF_COUNT references;
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CRYPTO_RWLOCK *lock;
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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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if (!group)
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return NULL;
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ret = OPENSSL_zalloc(sizeof(*ret));
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if (ret == NULL) {
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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->w = 4; /* default */
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ret->references = 1;
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ret->lock = CRYPTO_THREAD_lock_new();
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if (ret->lock == NULL) {
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ECerr(EC_F_EC_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
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OPENSSL_free(ret);
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return NULL;
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}
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return ret;
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}
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EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_COMP *pre)
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{
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int i;
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if (pre != NULL)
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CRYPTO_UP_REF(&pre->references, &i, pre->lock);
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return pre;
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}
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void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
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{
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int i;
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if (pre == NULL)
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return;
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CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
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REF_PRINT_COUNT("EC_ec", pre);
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if (i > 0)
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return;
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REF_ASSERT_ISNT(i < 0);
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if (pre->points != NULL) {
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EC_POINT **pts;
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for (pts = pre->points; *pts != NULL; pts++)
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EC_POINT_free(*pts);
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OPENSSL_free(pre->points);
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}
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CRYPTO_THREAD_lock_free(pre->lock);
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OPENSSL_free(pre);
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}
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#define EC_POINT_BN_set_flags(P, flags) do { \
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BN_set_flags((P)->X, (flags)); \
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BN_set_flags((P)->Y, (flags)); \
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BN_set_flags((P)->Z, (flags)); \
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} while(0)
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/*-
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* This functions computes a single point multiplication over the EC group,
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* using, at a high level, a Montgomery ladder with conditional swaps, with
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* various timing attack defenses.
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*
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* It performs either a fixed point multiplication
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* (scalar * generator)
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* when point is NULL, or a variable point multiplication
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* (scalar * point)
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* when point is not NULL.
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*
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* `scalar` cannot be NULL and should be in the range [0,n) otherwise all
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* constant time bets are off (where n is the cardinality of the EC group).
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*
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* This function expects `group->order` and `group->cardinality` to be well
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* defined and non-zero: it fails with an error code otherwise.
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*
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* NB: This says nothing about the constant-timeness of the ladder step
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* implementation (i.e., the default implementation is based on EC_POINT_add and
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* EC_POINT_dbl, which of course are not constant time themselves) or the
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* underlying multiprecision arithmetic.
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*
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* The product is stored in `r`.
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*
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* This is an internal function: callers are in charge of ensuring that the
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* input parameters `group`, `r`, `scalar` and `ctx` are not NULL.
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*
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* Returns 1 on success, 0 otherwise.
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*/
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int ec_scalar_mul_ladder(const EC_GROUP *group, EC_POINT *r,
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const BIGNUM *scalar, const EC_POINT *point,
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BN_CTX *ctx)
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{
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int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
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EC_POINT *p = NULL;
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EC_POINT *s = NULL;
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BIGNUM *k = NULL;
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BIGNUM *lambda = NULL;
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BIGNUM *cardinality = NULL;
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int ret = 0;
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/* early exit if the input point is the point at infinity */
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if (point != NULL && EC_POINT_is_at_infinity(group, point))
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return EC_POINT_set_to_infinity(group, r);
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if (BN_is_zero(group->order)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_ORDER);
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return 0;
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}
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if (BN_is_zero(group->cofactor)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_UNKNOWN_COFACTOR);
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return 0;
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}
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BN_CTX_start(ctx);
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if (((p = EC_POINT_new(group)) == NULL)
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|| ((s = EC_POINT_new(group)) == NULL)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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if (point == NULL) {
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if (!EC_POINT_copy(p, group->generator)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
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goto err;
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}
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} else {
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if (!EC_POINT_copy(p, point)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_EC_LIB);
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goto err;
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}
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}
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EC_POINT_BN_set_flags(p, BN_FLG_CONSTTIME);
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EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
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EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
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cardinality = BN_CTX_get(ctx);
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lambda = BN_CTX_get(ctx);
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k = BN_CTX_get(ctx);
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if (k == NULL) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_MALLOC_FAILURE);
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goto err;
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}
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if (!BN_mul(cardinality, group->order, group->cofactor, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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/*
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* Group cardinalities are often on a word boundary.
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* So when we pad the scalar, some timing diff might
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* pop if it needs to be expanded due to carries.
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* So expand ahead of time.
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*/
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cardinality_bits = BN_num_bits(cardinality);
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group_top = bn_get_top(cardinality);
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if ((bn_wexpand(k, group_top + 2) == NULL)
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|| (bn_wexpand(lambda, group_top + 2) == NULL)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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if (!BN_copy(k, scalar)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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BN_set_flags(k, BN_FLG_CONSTTIME);
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if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
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/*-
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* this is an unusual input, and we don't guarantee
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* constant-timeness
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*/
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if (!BN_nnmod(k, k, cardinality, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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}
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if (!BN_add(lambda, k, cardinality)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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BN_set_flags(lambda, BN_FLG_CONSTTIME);
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if (!BN_add(k, lambda, cardinality)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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/*
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* lambda := scalar + cardinality
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* k := scalar + 2*cardinality
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*/
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kbit = BN_is_bit_set(lambda, cardinality_bits);
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BN_consttime_swap(kbit, k, lambda, group_top + 2);
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group_top = bn_get_top(group->field);
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if ((bn_wexpand(s->X, group_top) == NULL)
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|| (bn_wexpand(s->Y, group_top) == NULL)
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|| (bn_wexpand(s->Z, group_top) == NULL)
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|| (bn_wexpand(r->X, group_top) == NULL)
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|| (bn_wexpand(r->Y, group_top) == NULL)
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|| (bn_wexpand(r->Z, group_top) == NULL)
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|| (bn_wexpand(p->X, group_top) == NULL)
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|| (bn_wexpand(p->Y, group_top) == NULL)
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|| (bn_wexpand(p->Z, group_top) == NULL)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, ERR_R_BN_LIB);
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goto err;
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}
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/*-
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* Apply coordinate blinding for EC_POINT.
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*
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* The underlying EC_METHOD can optionally implement this function:
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* ec_point_blind_coordinates() returns 0 in case of errors or 1 on
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* success or if coordinate blinding is not implemented for this
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* group.
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*/
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if (!ec_point_blind_coordinates(group, p, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_POINT_COORDINATES_BLIND_FAILURE);
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goto err;
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}
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/* Initialize the Montgomery ladder */
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if (!ec_point_ladder_pre(group, r, s, p, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_PRE_FAILURE);
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goto err;
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}
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/* top bit is a 1, in a fixed pos */
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pbit = 1;
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#define EC_POINT_CSWAP(c, a, b, w, t) do { \
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BN_consttime_swap(c, (a)->X, (b)->X, w); \
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BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
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BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
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t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
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(a)->Z_is_one ^= (t); \
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(b)->Z_is_one ^= (t); \
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} while(0)
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/*-
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* The ladder step, with branches, is
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*
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* k[i] == 0: S = add(R, S), R = dbl(R)
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* k[i] == 1: R = add(S, R), S = dbl(S)
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*
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* Swapping R, S conditionally on k[i] leaves you with state
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*
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* k[i] == 0: T, U = R, S
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* k[i] == 1: T, U = S, R
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*
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* Then perform the ECC ops.
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*
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* U = add(T, U)
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* T = dbl(T)
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*
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* Which leaves you with state
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*
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* k[i] == 0: U = add(R, S), T = dbl(R)
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* k[i] == 1: U = add(S, R), T = dbl(S)
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*
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* Swapping T, U conditionally on k[i] leaves you with state
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*
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* k[i] == 0: R, S = T, U
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* k[i] == 1: R, S = U, T
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*
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* Which leaves you with state
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*
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* k[i] == 0: S = add(R, S), R = dbl(R)
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* k[i] == 1: R = add(S, R), S = dbl(S)
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*
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* So we get the same logic, but instead of a branch it's a
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* conditional swap, followed by ECC ops, then another conditional swap.
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*
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* Optimization: The end of iteration i and start of i-1 looks like
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*
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* ...
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* CSWAP(k[i], R, S)
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* ECC
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* CSWAP(k[i], R, S)
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* (next iteration)
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* CSWAP(k[i-1], R, S)
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* ECC
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* CSWAP(k[i-1], R, S)
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* ...
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*
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* So instead of two contiguous swaps, you can merge the condition
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* bits and do a single swap.
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*
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* k[i] k[i-1] Outcome
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* 0 0 No Swap
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* 0 1 Swap
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* 1 0 Swap
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* 1 1 No Swap
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*
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* This is XOR. pbit tracks the previous bit of k.
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*/
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for (i = cardinality_bits - 1; i >= 0; i--) {
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kbit = BN_is_bit_set(k, i) ^ pbit;
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EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
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/* Perform a single step of the Montgomery ladder */
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if (!ec_point_ladder_step(group, r, s, p, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_STEP_FAILURE);
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goto err;
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}
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/*
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* pbit logic merges this cswap with that of the
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* next iteration
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*/
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pbit ^= kbit;
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}
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/* one final cswap to move the right value into r */
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EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
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#undef EC_POINT_CSWAP
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/* Finalize ladder (and recover full point coordinates) */
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if (!ec_point_ladder_post(group, r, s, p, ctx)) {
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ECerr(EC_F_EC_SCALAR_MUL_LADDER, EC_R_LADDER_POST_FAILURE);
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goto err;
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}
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ret = 1;
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err:
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EC_POINT_free(p);
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EC_POINT_clear_free(s);
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BN_CTX_end(ctx);
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return ret;
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}
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#undef EC_POINT_BN_set_flags
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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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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 (!BN_is_zero(group->order) && !BN_is_zero(group->cofactor)) {
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/*-
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* Handle the common cases where the scalar is secret, enforcing a
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* scalar multiplication implementation based on a Montgomery ladder,
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* with various timing attack defenses.
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*/
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if ((scalar != NULL) && (num == 0)) {
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/*-
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* In this case we want to compute scalar * GeneratorPoint: this
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* codepath is reached most prominently by (ephemeral) key
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* generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
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* ECDH keygen/first half), where the scalar is always secret. This
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* is why we ignore if BN_FLG_CONSTTIME is actually set and we
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* always call the ladder version.
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*/
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return ec_scalar_mul_ladder(group, r, scalar, NULL, ctx);
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}
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if ((scalar == NULL) && (num == 1)) {
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/*-
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* In this case we want to compute scalar * VariablePoint: this
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* codepath is reached most prominently by the second half of ECDH,
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* where the secret scalar is multiplied by the peer's public point.
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* To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
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* actually set and we always call the ladder version.
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*/
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return ec_scalar_mul_ladder(group, r, scalars[0], points[0], ctx);
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}
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}
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|
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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 = group->pre_comp.ec;
|
|
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]));
|
|
/* include space for pivot */
|
|
wNAF = OPENSSL_malloc((totalnum + 1) * sizeof(wNAF[0]));
|
|
val_sub = OPENSSL_malloc(totalnum * sizeof(val_sub[0]));
|
|
|
|
/* Ensure wNAF is initialised in case we end up going to err */
|
|
if (wNAF != NULL)
|
|
wNAF[0] = NULL; /* preliminary pivot */
|
|
|
|
if (wsize == NULL || wNAF_len == NULL || wNAF == NULL || val_sub == NULL) {
|
|
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] =
|
|
bn_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 = bn_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;
|
|
/*
|
|
* 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);
|
|
OPENSSL_free(tmp_wNAF);
|
|
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);
|
|
OPENSSL_free(tmp_wNAF);
|
|
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)) == NULL)
|
|
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 (!EC_POINTs_make_affine(group, num_val, val, ctx))
|
|
goto err;
|
|
|
|
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:
|
|
EC_POINT_free(tmp);
|
|
OPENSSL_free(wsize);
|
|
OPENSSL_free(wNAF_len);
|
|
if (wNAF != NULL) {
|
|
signed char **w;
|
|
|
|
for (w = wNAF; *w != NULL; w++)
|
|
OPENSSL_free(*w);
|
|
|
|
OPENSSL_free(wNAF);
|
|
}
|
|
if (val != NULL) {
|
|
for (v = val; *v != NULL; v++)
|
|
EC_POINT_clear_free(*v);
|
|
|
|
OPENSSL_free(val);
|
|
}
|
|
OPENSSL_free(val_sub);
|
|
return ret;
|
|
}
|
|
|
|
/*-
|
|
* 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;
|
|
const 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_pre_comp_free(group);
|
|
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 = EC_GROUP_get0_order(group);
|
|
if (order == NULL)
|
|
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(*points) * (num + 1));
|
|
if (points == NULL) {
|
|
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)) == NULL
|
|
|| (base = EC_POINT_new(group)) == NULL) {
|
|
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;
|
|
SETPRECOMP(group, ec, pre_comp);
|
|
pre_comp = NULL;
|
|
ret = 1;
|
|
|
|
err:
|
|
if (ctx != NULL)
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(new_ctx);
|
|
EC_ec_pre_comp_free(pre_comp);
|
|
if (points) {
|
|
EC_POINT **p;
|
|
|
|
for (p = points; *p != NULL; p++)
|
|
EC_POINT_free(*p);
|
|
OPENSSL_free(points);
|
|
}
|
|
EC_POINT_free(tmp_point);
|
|
EC_POINT_free(base);
|
|
return ret;
|
|
}
|
|
|
|
int ec_wNAF_have_precompute_mult(const EC_GROUP *group)
|
|
{
|
|
return HAVEPRECOMP(group, ec);
|
|
}
|