1457 lines
48 KiB
C
1457 lines
48 KiB
C
/* crypto/bn/bn_exp.c */
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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* All rights reserved.
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*
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* This package is an SSL implementation written
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* by Eric Young (eay@cryptsoft.com).
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* The implementation was written so as to conform with Netscapes SSL.
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*
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* This library is free for commercial and non-commercial use as long as
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* the following conditions are aheared to. The following conditions
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* apply to all code found in this distribution, be it the RC4, RSA,
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation
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* included with this distribution is covered by the same copyright terms
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* except that the holder is Tim Hudson (tjh@cryptsoft.com).
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*
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* Copyright remains Eric Young's, and as such any Copyright notices in
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* the code are not to be removed.
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* If this package is used in a product, Eric Young should be given attribution
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* as the author of the parts of the library used.
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* This can be in the form of a textual message at program startup or
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* in documentation (online or textual) provided with the package.
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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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* 1. Redistributions of source code must retain the copyright
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* notice, this list of conditions and the following disclaimer.
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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 the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* "This product includes cryptographic software written by
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* Eric Young (eay@cryptsoft.com)"
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* The word 'cryptographic' can be left out if the rouines from the library
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* being used are not cryptographic related :-).
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* 4. If you include any Windows specific code (or a derivative thereof) from
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* the apps directory (application code) you must include an acknowledgement:
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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*
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* The licence and distribution terms for any publically available version or
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* derivative of this code cannot be changed. i.e. this code cannot simply be
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* copied and put under another distribution licence
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* [including the GNU Public Licence.]
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*/
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/* ====================================================================
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* Copyright (c) 1998-2005 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 "cryptlib.h"
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#include "constant_time_locl.h"
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#include "bn_lcl.h"
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#include <stdlib.h>
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#ifdef _WIN32
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# include <malloc.h>
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# ifndef alloca
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# define alloca _alloca
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# endif
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#elif defined(__GNUC__)
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# ifndef alloca
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# define alloca(s) __builtin_alloca((s))
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# endif
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#elif defined(__sun)
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# include <alloca.h>
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#endif
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#include "rsaz_exp.h"
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#undef SPARC_T4_MONT
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#if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
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# include "sparc_arch.h"
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extern unsigned int OPENSSL_sparcv9cap_P[];
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# define SPARC_T4_MONT
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#endif
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/* maximum precomputation table size for *variable* sliding windows */
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#define TABLE_SIZE 32
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/* this one works - simple but works */
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int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
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{
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int i, bits, ret = 0;
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BIGNUM *v, *rr;
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if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
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/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
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BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
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return -1;
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}
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BN_CTX_start(ctx);
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if ((r == a) || (r == p))
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rr = BN_CTX_get(ctx);
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else
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rr = r;
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v = BN_CTX_get(ctx);
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if (rr == NULL || v == NULL)
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goto err;
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if (BN_copy(v, a) == NULL)
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goto err;
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bits = BN_num_bits(p);
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if (BN_is_odd(p)) {
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if (BN_copy(rr, a) == NULL)
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goto err;
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} else {
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if (!BN_one(rr))
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goto err;
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}
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for (i = 1; i < bits; i++) {
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if (!BN_sqr(v, v, ctx))
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goto err;
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if (BN_is_bit_set(p, i)) {
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if (!BN_mul(rr, rr, v, ctx))
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goto err;
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}
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}
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if (r != rr)
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BN_copy(r, rr);
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ret = 1;
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err:
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BN_CTX_end(ctx);
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bn_check_top(r);
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return (ret);
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}
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int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
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BN_CTX *ctx)
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{
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int ret;
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bn_check_top(a);
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bn_check_top(p);
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bn_check_top(m);
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/*-
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* For even modulus m = 2^k*m_odd, it might make sense to compute
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* a^p mod m_odd and a^p mod 2^k separately (with Montgomery
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* exponentiation for the odd part), using appropriate exponent
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* reductions, and combine the results using the CRT.
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*
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* For now, we use Montgomery only if the modulus is odd; otherwise,
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* exponentiation using the reciprocal-based quick remaindering
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* algorithm is used.
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*
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* (Timing obtained with expspeed.c [computations a^p mod m
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* where a, p, m are of the same length: 256, 512, 1024, 2048,
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* 4096, 8192 bits], compared to the running time of the
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* standard algorithm:
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*
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* BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
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* 55 .. 77 % [UltraSparc processor, but
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* debug-solaris-sparcv8-gcc conf.]
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*
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* BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
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* 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
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*
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* On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
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* at 2048 and more bits, but at 512 and 1024 bits, it was
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* slower even than the standard algorithm!
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*
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* "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
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* should be obtained when the new Montgomery reduction code
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* has been integrated into OpenSSL.)
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*/
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#define MONT_MUL_MOD
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#define MONT_EXP_WORD
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#define RECP_MUL_MOD
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#ifdef MONT_MUL_MOD
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/*
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* I have finally been able to take out this pre-condition of the top bit
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* being set. It was caused by an error in BN_div with negatives. There
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* was also another problem when for a^b%m a >= m. eay 07-May-97
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*/
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/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
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if (BN_is_odd(m)) {
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# ifdef MONT_EXP_WORD
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if (a->top == 1 && !a->neg
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&& (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
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BN_ULONG A = a->d[0];
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ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
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} else
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# endif
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ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
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} else
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#endif
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#ifdef RECP_MUL_MOD
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{
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ret = BN_mod_exp_recp(r, a, p, m, ctx);
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}
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#else
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{
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ret = BN_mod_exp_simple(r, a, p, m, ctx);
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}
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#endif
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bn_check_top(r);
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return (ret);
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}
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int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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const BIGNUM *m, BN_CTX *ctx)
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{
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int i, j, bits, ret = 0, wstart, wend, window, wvalue;
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int start = 1;
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BIGNUM *aa;
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/* Table of variables obtained from 'ctx' */
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BIGNUM *val[TABLE_SIZE];
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BN_RECP_CTX recp;
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if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
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/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
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BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
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return -1;
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}
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bits = BN_num_bits(p);
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if (bits == 0) {
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/* x**0 mod 1 is still zero. */
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if (BN_is_one(m)) {
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ret = 1;
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BN_zero(r);
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} else {
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ret = BN_one(r);
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}
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return ret;
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}
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BN_CTX_start(ctx);
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aa = BN_CTX_get(ctx);
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val[0] = BN_CTX_get(ctx);
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if (!aa || !val[0])
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goto err;
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BN_RECP_CTX_init(&recp);
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if (m->neg) {
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/* ignore sign of 'm' */
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if (!BN_copy(aa, m))
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goto err;
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aa->neg = 0;
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if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
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goto err;
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} else {
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if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
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goto err;
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}
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if (!BN_nnmod(val[0], a, m, ctx))
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goto err; /* 1 */
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if (BN_is_zero(val[0])) {
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BN_zero(r);
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ret = 1;
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goto err;
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}
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window = BN_window_bits_for_exponent_size(bits);
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if (window > 1) {
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if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
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goto err; /* 2 */
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j = 1 << (window - 1);
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for (i = 1; i < j; i++) {
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if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
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!BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
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goto err;
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}
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}
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start = 1; /* This is used to avoid multiplication etc
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* when there is only the value '1' in the
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* buffer. */
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wvalue = 0; /* The 'value' of the window */
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wstart = bits - 1; /* The top bit of the window */
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wend = 0; /* The bottom bit of the window */
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if (!BN_one(r))
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goto err;
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for (;;) {
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if (BN_is_bit_set(p, wstart) == 0) {
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if (!start)
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if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
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goto err;
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if (wstart == 0)
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break;
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wstart--;
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continue;
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}
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/*
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* We now have wstart on a 'set' bit, we now need to work out how bit
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* a window to do. To do this we need to scan forward until the last
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* set bit before the end of the window
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*/
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j = wstart;
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wvalue = 1;
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wend = 0;
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for (i = 1; i < window; i++) {
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if (wstart - i < 0)
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break;
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if (BN_is_bit_set(p, wstart - i)) {
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wvalue <<= (i - wend);
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wvalue |= 1;
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wend = i;
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}
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}
|
|
|
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/* wend is the size of the current window */
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j = wend + 1;
|
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/* add the 'bytes above' */
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if (!start)
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for (i = 0; i < j; i++) {
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if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
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goto err;
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}
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/* wvalue will be an odd number < 2^window */
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if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
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goto err;
|
|
|
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/* move the 'window' down further */
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wstart -= wend + 1;
|
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wvalue = 0;
|
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start = 0;
|
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if (wstart < 0)
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break;
|
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}
|
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ret = 1;
|
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err:
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BN_CTX_end(ctx);
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BN_RECP_CTX_free(&recp);
|
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bn_check_top(r);
|
|
return (ret);
|
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}
|
|
|
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int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
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const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
|
{
|
|
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
|
int start = 1;
|
|
BIGNUM *d, *r;
|
|
const BIGNUM *aa;
|
|
/* Table of variables obtained from 'ctx' */
|
|
BIGNUM *val[TABLE_SIZE];
|
|
BN_MONT_CTX *mont = NULL;
|
|
|
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if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
|
return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
|
|
}
|
|
|
|
bn_check_top(a);
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (!BN_is_odd(m)) {
|
|
BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
|
|
return (0);
|
|
}
|
|
bits = BN_num_bits(p);
|
|
if (bits == 0) {
|
|
/* x**0 mod 1 is still zero. */
|
|
if (BN_is_one(m)) {
|
|
ret = 1;
|
|
BN_zero(rr);
|
|
} else {
|
|
ret = BN_one(rr);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
d = BN_CTX_get(ctx);
|
|
r = BN_CTX_get(ctx);
|
|
val[0] = BN_CTX_get(ctx);
|
|
if (!d || !r || !val[0])
|
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goto err;
|
|
|
|
/*
|
|
* If this is not done, things will break in the montgomery part
|
|
*/
|
|
|
|
if (in_mont != NULL)
|
|
mont = in_mont;
|
|
else {
|
|
if ((mont = BN_MONT_CTX_new()) == NULL)
|
|
goto err;
|
|
if (!BN_MONT_CTX_set(mont, m, ctx))
|
|
goto err;
|
|
}
|
|
|
|
if (a->neg || BN_ucmp(a, m) >= 0) {
|
|
if (!BN_nnmod(val[0], a, m, ctx))
|
|
goto err;
|
|
aa = val[0];
|
|
} else
|
|
aa = a;
|
|
if (BN_is_zero(aa)) {
|
|
BN_zero(rr);
|
|
ret = 1;
|
|
goto err;
|
|
}
|
|
if (!BN_to_montgomery(val[0], aa, mont, ctx))
|
|
goto err; /* 1 */
|
|
|
|
window = BN_window_bits_for_exponent_size(bits);
|
|
if (window > 1) {
|
|
if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
|
|
goto err; /* 2 */
|
|
j = 1 << (window - 1);
|
|
for (i = 1; i < j; i++) {
|
|
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
|
!BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
start = 1; /* This is used to avoid multiplication etc
|
|
* when there is only the value '1' in the
|
|
* buffer. */
|
|
wvalue = 0; /* The 'value' of the window */
|
|
wstart = bits - 1; /* The top bit of the window */
|
|
wend = 0; /* The bottom bit of the window */
|
|
|
|
#if 1 /* by Shay Gueron's suggestion */
|
|
j = m->top; /* borrow j */
|
|
if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
|
if (bn_wexpand(r, j) == NULL)
|
|
goto err;
|
|
/* 2^(top*BN_BITS2) - m */
|
|
r->d[0] = (0 - m->d[0]) & BN_MASK2;
|
|
for (i = 1; i < j; i++)
|
|
r->d[i] = (~m->d[i]) & BN_MASK2;
|
|
r->top = j;
|
|
/*
|
|
* Upper words will be zero if the corresponding words of 'm' were
|
|
* 0xfff[...], so decrement r->top accordingly.
|
|
*/
|
|
bn_correct_top(r);
|
|
} else
|
|
#endif
|
|
if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
|
|
goto err;
|
|
for (;;) {
|
|
if (BN_is_bit_set(p, wstart) == 0) {
|
|
if (!start) {
|
|
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
|
goto err;
|
|
}
|
|
if (wstart == 0)
|
|
break;
|
|
wstart--;
|
|
continue;
|
|
}
|
|
/*
|
|
* We now have wstart on a 'set' bit, we now need to work out how bit
|
|
* a window to do. To do this we need to scan forward until the last
|
|
* set bit before the end of the window
|
|
*/
|
|
j = wstart;
|
|
wvalue = 1;
|
|
wend = 0;
|
|
for (i = 1; i < window; i++) {
|
|
if (wstart - i < 0)
|
|
break;
|
|
if (BN_is_bit_set(p, wstart - i)) {
|
|
wvalue <<= (i - wend);
|
|
wvalue |= 1;
|
|
wend = i;
|
|
}
|
|
}
|
|
|
|
/* wend is the size of the current window */
|
|
j = wend + 1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i = 0; i < j; i++) {
|
|
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
|
goto err;
|
|
}
|
|
|
|
/* wvalue will be an odd number < 2^window */
|
|
if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
|
|
goto err;
|
|
|
|
/* move the 'window' down further */
|
|
wstart -= wend + 1;
|
|
wvalue = 0;
|
|
start = 0;
|
|
if (wstart < 0)
|
|
break;
|
|
}
|
|
#if defined(SPARC_T4_MONT)
|
|
if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
|
j = mont->N.top; /* borrow j */
|
|
val[0]->d[0] = 1; /* borrow val[0] */
|
|
for (i = 1; i < j; i++)
|
|
val[0]->d[i] = 0;
|
|
val[0]->top = j;
|
|
if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
|
|
goto err;
|
|
} else
|
|
#endif
|
|
if (!BN_from_montgomery(rr, r, mont, ctx))
|
|
goto err;
|
|
ret = 1;
|
|
err:
|
|
if ((in_mont == NULL) && (mont != NULL))
|
|
BN_MONT_CTX_free(mont);
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rr);
|
|
return (ret);
|
|
}
|
|
|
|
#if defined(SPARC_T4_MONT)
|
|
static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
|
|
{
|
|
BN_ULONG ret = 0;
|
|
int wordpos;
|
|
|
|
wordpos = bitpos / BN_BITS2;
|
|
bitpos %= BN_BITS2;
|
|
if (wordpos >= 0 && wordpos < a->top) {
|
|
ret = a->d[wordpos] & BN_MASK2;
|
|
if (bitpos) {
|
|
ret >>= bitpos;
|
|
if (++wordpos < a->top)
|
|
ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
|
|
}
|
|
}
|
|
|
|
return ret & BN_MASK2;
|
|
}
|
|
#endif
|
|
|
|
/*
|
|
* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
|
|
* layout so that accessing any of these table values shows the same access
|
|
* pattern as far as cache lines are concerned. The following functions are
|
|
* used to transfer a BIGNUM from/to that table.
|
|
*/
|
|
|
|
static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
|
|
unsigned char *buf, int idx,
|
|
int window)
|
|
{
|
|
int i, j;
|
|
int width = 1 << window;
|
|
BN_ULONG *table = (BN_ULONG *)buf;
|
|
|
|
if (top > b->top)
|
|
top = b->top; /* this works because 'buf' is explicitly
|
|
* zeroed */
|
|
for (i = 0, j = idx; i < top; i++, j += width) {
|
|
table[j] = b->d[i];
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
|
|
unsigned char *buf, int idx,
|
|
int window)
|
|
{
|
|
int i, j;
|
|
int width = 1 << window;
|
|
volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
|
|
|
|
if (bn_wexpand(b, top) == NULL)
|
|
return 0;
|
|
|
|
if (window <= 3) {
|
|
for (i = 0; i < top; i++, table += width) {
|
|
BN_ULONG acc = 0;
|
|
|
|
for (j = 0; j < width; j++) {
|
|
acc |= table[j] &
|
|
((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
|
}
|
|
|
|
b->d[i] = acc;
|
|
}
|
|
} else {
|
|
int xstride = 1 << (window - 2);
|
|
BN_ULONG y0, y1, y2, y3;
|
|
|
|
i = idx >> (window - 2); /* equivalent of idx / xstride */
|
|
idx &= xstride - 1; /* equivalent of idx % xstride */
|
|
|
|
y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
|
|
y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
|
|
y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
|
|
y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
|
|
|
|
for (i = 0; i < top; i++, table += width) {
|
|
BN_ULONG acc = 0;
|
|
|
|
for (j = 0; j < xstride; j++) {
|
|
acc |= ( (table[j + 0 * xstride] & y0) |
|
|
(table[j + 1 * xstride] & y1) |
|
|
(table[j + 2 * xstride] & y2) |
|
|
(table[j + 3 * xstride] & y3) )
|
|
& ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
|
|
}
|
|
|
|
b->d[i] = acc;
|
|
}
|
|
}
|
|
|
|
b->top = top;
|
|
bn_correct_top(b);
|
|
return 1;
|
|
}
|
|
|
|
/*
|
|
* Given a pointer value, compute the next address that is a cache line
|
|
* multiple.
|
|
*/
|
|
#define MOD_EXP_CTIME_ALIGN(x_) \
|
|
((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
|
|
|
|
/*
|
|
* This variant of BN_mod_exp_mont() uses fixed windows and the special
|
|
* precomputation memory layout to limit data-dependency to a minimum to
|
|
* protect secret exponents (cf. the hyper-threading timing attacks pointed
|
|
* out by Colin Percival,
|
|
* http://www.daemonology.net/hyperthreading-considered-harmful/)
|
|
*/
|
|
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
|
|
const BIGNUM *m, BN_CTX *ctx,
|
|
BN_MONT_CTX *in_mont)
|
|
{
|
|
int i, bits, ret = 0, window, wvalue;
|
|
int top;
|
|
BN_MONT_CTX *mont = NULL;
|
|
|
|
int numPowers;
|
|
unsigned char *powerbufFree = NULL;
|
|
int powerbufLen = 0;
|
|
unsigned char *powerbuf = NULL;
|
|
BIGNUM tmp, am;
|
|
#if defined(SPARC_T4_MONT)
|
|
unsigned int t4 = 0;
|
|
#endif
|
|
|
|
bn_check_top(a);
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (!BN_is_odd(m)) {
|
|
BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
|
|
return (0);
|
|
}
|
|
|
|
top = m->top;
|
|
|
|
bits = BN_num_bits(p);
|
|
if (bits == 0) {
|
|
/* x**0 mod 1 is still zero. */
|
|
if (BN_is_one(m)) {
|
|
ret = 1;
|
|
BN_zero(rr);
|
|
} else {
|
|
ret = BN_one(rr);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
|
|
/*
|
|
* Allocate a montgomery context if it was not supplied by the caller. If
|
|
* this is not done, things will break in the montgomery part.
|
|
*/
|
|
if (in_mont != NULL)
|
|
mont = in_mont;
|
|
else {
|
|
if ((mont = BN_MONT_CTX_new()) == NULL)
|
|
goto err;
|
|
if (!BN_MONT_CTX_set(mont, m, ctx))
|
|
goto err;
|
|
}
|
|
|
|
#ifdef RSAZ_ENABLED
|
|
/*
|
|
* If the size of the operands allow it, perform the optimized
|
|
* RSAZ exponentiation. For further information see
|
|
* crypto/bn/rsaz_exp.c and accompanying assembly modules.
|
|
*/
|
|
if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
|
|
&& rsaz_avx2_eligible()) {
|
|
if (NULL == bn_wexpand(rr, 16))
|
|
goto err;
|
|
RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
|
|
mont->n0[0]);
|
|
rr->top = 16;
|
|
rr->neg = 0;
|
|
bn_correct_top(rr);
|
|
ret = 1;
|
|
goto err;
|
|
} else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
|
|
if (NULL == bn_wexpand(rr, 8))
|
|
goto err;
|
|
RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
|
|
rr->top = 8;
|
|
rr->neg = 0;
|
|
bn_correct_top(rr);
|
|
ret = 1;
|
|
goto err;
|
|
}
|
|
#endif
|
|
|
|
/* Get the window size to use with size of p. */
|
|
window = BN_window_bits_for_ctime_exponent_size(bits);
|
|
#if defined(SPARC_T4_MONT)
|
|
if (window >= 5 && (top & 15) == 0 && top <= 64 &&
|
|
(OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
|
|
(CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
|
|
window = 5;
|
|
else
|
|
#endif
|
|
#if defined(OPENSSL_BN_ASM_MONT5)
|
|
if (window >= 5) {
|
|
window = 5; /* ~5% improvement for RSA2048 sign, and even
|
|
* for RSA4096 */
|
|
/* reserve space for mont->N.d[] copy */
|
|
powerbufLen += top * sizeof(mont->N.d[0]);
|
|
}
|
|
#endif
|
|
(void)0;
|
|
|
|
/*
|
|
* Allocate a buffer large enough to hold all of the pre-computed powers
|
|
* of am, am itself and tmp.
|
|
*/
|
|
numPowers = 1 << window;
|
|
powerbufLen += sizeof(m->d[0]) * (top * numPowers +
|
|
((2 * top) >
|
|
numPowers ? (2 * top) : numPowers));
|
|
#ifdef alloca
|
|
if (powerbufLen < 3072)
|
|
powerbufFree =
|
|
alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
|
|
else
|
|
#endif
|
|
if ((powerbufFree =
|
|
(unsigned char *)OPENSSL_malloc(powerbufLen +
|
|
MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
|
|
== NULL)
|
|
goto err;
|
|
|
|
powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
|
|
memset(powerbuf, 0, powerbufLen);
|
|
|
|
#ifdef alloca
|
|
if (powerbufLen < 3072)
|
|
powerbufFree = NULL;
|
|
#endif
|
|
|
|
/* lay down tmp and am right after powers table */
|
|
tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
|
|
am.d = tmp.d + top;
|
|
tmp.top = am.top = 0;
|
|
tmp.dmax = am.dmax = top;
|
|
tmp.neg = am.neg = 0;
|
|
tmp.flags = am.flags = BN_FLG_STATIC_DATA;
|
|
|
|
/* prepare a^0 in Montgomery domain */
|
|
#if 1 /* by Shay Gueron's suggestion */
|
|
if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
|
|
/* 2^(top*BN_BITS2) - m */
|
|
tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
|
|
for (i = 1; i < top; i++)
|
|
tmp.d[i] = (~m->d[i]) & BN_MASK2;
|
|
tmp.top = top;
|
|
} else
|
|
#endif
|
|
if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
|
|
goto err;
|
|
|
|
/* prepare a^1 in Montgomery domain */
|
|
if (a->neg || BN_ucmp(a, m) >= 0) {
|
|
if (!BN_mod(&am, a, m, ctx))
|
|
goto err;
|
|
if (!BN_to_montgomery(&am, &am, mont, ctx))
|
|
goto err;
|
|
} else if (!BN_to_montgomery(&am, a, mont, ctx))
|
|
goto err;
|
|
|
|
#if defined(SPARC_T4_MONT)
|
|
if (t4) {
|
|
typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, const void *table,
|
|
int power, int bits);
|
|
int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, const void *table,
|
|
int power, int bits);
|
|
int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, const void *table,
|
|
int power, int bits);
|
|
int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, const void *table,
|
|
int power, int bits);
|
|
int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, const void *table,
|
|
int power, int bits);
|
|
static const bn_pwr5_mont_f pwr5_funcs[4] = {
|
|
bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
|
|
bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
|
|
};
|
|
bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
|
|
|
|
typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0);
|
|
int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
|
|
const BN_ULONG *np, const BN_ULONG *n0);
|
|
int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0);
|
|
int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0);
|
|
int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0);
|
|
static const bn_mul_mont_f mul_funcs[4] = {
|
|
bn_mul_mont_t4_8, bn_mul_mont_t4_16,
|
|
bn_mul_mont_t4_24, bn_mul_mont_t4_32
|
|
};
|
|
bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
|
|
|
|
void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num);
|
|
void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *bp, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num);
|
|
void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *table, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num, int power);
|
|
void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
|
|
void *table, size_t power);
|
|
void bn_gather5_t4(BN_ULONG *out, size_t num,
|
|
void *table, size_t power);
|
|
void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
|
|
|
|
BN_ULONG *np = mont->N.d, *n0 = mont->n0;
|
|
int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
|
|
* than 32 */
|
|
|
|
/*
|
|
* BN_to_montgomery can contaminate words above .top [in
|
|
* BN_DEBUG[_DEBUG] build]...
|
|
*/
|
|
for (i = am.top; i < top; i++)
|
|
am.d[i] = 0;
|
|
for (i = tmp.top; i < top; i++)
|
|
tmp.d[i] = 0;
|
|
|
|
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
|
|
bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
|
|
if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
|
|
!(*mul_worker) (tmp.d, am.d, am.d, np, n0))
|
|
bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
|
|
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
|
|
|
|
for (i = 3; i < 32; i++) {
|
|
/* Calculate a^i = a^(i-1) * a */
|
|
if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
|
|
!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
|
|
bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
|
|
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
|
|
}
|
|
|
|
/* switch to 64-bit domain */
|
|
np = alloca(top * sizeof(BN_ULONG));
|
|
top /= 2;
|
|
bn_flip_t4(np, mont->N.d, top);
|
|
|
|
bits--;
|
|
for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
|
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
|
bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
|
|
|
|
/*
|
|
* Scan the exponent one window at a time starting from the most
|
|
* significant bits.
|
|
*/
|
|
while (bits >= 0) {
|
|
if (bits < stride)
|
|
stride = bits + 1;
|
|
bits -= stride;
|
|
wvalue = bn_get_bits(p, bits + 1);
|
|
|
|
if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
|
continue;
|
|
/* retry once and fall back */
|
|
if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
|
|
continue;
|
|
|
|
bits += stride - 5;
|
|
wvalue >>= stride - 5;
|
|
wvalue &= 31;
|
|
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
|
|
wvalue);
|
|
}
|
|
|
|
bn_flip_t4(tmp.d, tmp.d, top);
|
|
top *= 2;
|
|
/* back to 32-bit domain */
|
|
tmp.top = top;
|
|
bn_correct_top(&tmp);
|
|
OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
|
|
} else
|
|
#endif
|
|
#if defined(OPENSSL_BN_ASM_MONT5)
|
|
if (window == 5 && top > 1) {
|
|
/*
|
|
* This optimization uses ideas from http://eprint.iacr.org/2011/239,
|
|
* specifically optimization of cache-timing attack countermeasures
|
|
* and pre-computation optimization.
|
|
*/
|
|
|
|
/*
|
|
* Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
|
|
* 512-bit RSA is hardly relevant, we omit it to spare size...
|
|
*/
|
|
void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *table, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num, int power);
|
|
void bn_scatter5(const BN_ULONG *inp, size_t num,
|
|
void *table, size_t power);
|
|
void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
|
|
void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const void *table, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num, int power);
|
|
int bn_get_bits5(const BN_ULONG *ap, int off);
|
|
int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
|
|
const BN_ULONG *not_used, const BN_ULONG *np,
|
|
const BN_ULONG *n0, int num);
|
|
|
|
BN_ULONG *n0 = mont->n0, *np;
|
|
|
|
/*
|
|
* BN_to_montgomery can contaminate words above .top [in
|
|
* BN_DEBUG[_DEBUG] build]...
|
|
*/
|
|
for (i = am.top; i < top; i++)
|
|
am.d[i] = 0;
|
|
for (i = tmp.top; i < top; i++)
|
|
tmp.d[i] = 0;
|
|
|
|
/*
|
|
* copy mont->N.d[] to improve cache locality
|
|
*/
|
|
for (np = am.d + top, i = 0; i < top; i++)
|
|
np[i] = mont->N.d[i];
|
|
|
|
bn_scatter5(tmp.d, top, powerbuf, 0);
|
|
bn_scatter5(am.d, am.top, powerbuf, 1);
|
|
bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
|
|
bn_scatter5(tmp.d, top, powerbuf, 2);
|
|
|
|
# if 0
|
|
for (i = 3; i < 32; i++) {
|
|
/* Calculate a^i = a^(i-1) * a */
|
|
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
|
bn_scatter5(tmp.d, top, powerbuf, i);
|
|
}
|
|
# else
|
|
/* same as above, but uses squaring for 1/2 of operations */
|
|
for (i = 4; i < 32; i *= 2) {
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_scatter5(tmp.d, top, powerbuf, i);
|
|
}
|
|
for (i = 3; i < 8; i += 2) {
|
|
int j;
|
|
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
|
bn_scatter5(tmp.d, top, powerbuf, i);
|
|
for (j = 2 * i; j < 32; j *= 2) {
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_scatter5(tmp.d, top, powerbuf, j);
|
|
}
|
|
}
|
|
for (; i < 16; i += 2) {
|
|
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
|
bn_scatter5(tmp.d, top, powerbuf, i);
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_scatter5(tmp.d, top, powerbuf, 2 * i);
|
|
}
|
|
for (; i < 32; i += 2) {
|
|
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
|
|
bn_scatter5(tmp.d, top, powerbuf, i);
|
|
}
|
|
# endif
|
|
bits--;
|
|
for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
|
|
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
|
bn_gather5(tmp.d, top, powerbuf, wvalue);
|
|
|
|
/*
|
|
* Scan the exponent one window at a time starting from the most
|
|
* significant bits.
|
|
*/
|
|
if (top & 7)
|
|
while (bits >= 0) {
|
|
for (wvalue = 0, i = 0; i < 5; i++, bits--)
|
|
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
|
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
|
|
bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
|
|
wvalue);
|
|
} else {
|
|
while (bits >= 0) {
|
|
wvalue = bn_get_bits5(p->d, bits - 4);
|
|
bits -= 5;
|
|
bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
|
|
}
|
|
}
|
|
|
|
ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
|
|
tmp.top = top;
|
|
bn_correct_top(&tmp);
|
|
if (ret) {
|
|
if (!BN_copy(rr, &tmp))
|
|
ret = 0;
|
|
goto err; /* non-zero ret means it's not error */
|
|
}
|
|
} else
|
|
#endif
|
|
{
|
|
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
|
|
goto err;
|
|
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
|
|
goto err;
|
|
|
|
/*
|
|
* If the window size is greater than 1, then calculate
|
|
* val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
|
|
* powers could instead be computed as (a^(i/2))^2 to use the slight
|
|
* performance advantage of sqr over mul).
|
|
*/
|
|
if (window > 1) {
|
|
if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
|
|
goto err;
|
|
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
|
|
window))
|
|
goto err;
|
|
for (i = 3; i < numPowers; i++) {
|
|
/* Calculate a^i = a^(i-1) * a */
|
|
if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
|
|
goto err;
|
|
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
|
|
window))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
bits--;
|
|
for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
|
|
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
|
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
|
|
window))
|
|
goto err;
|
|
|
|
/*
|
|
* Scan the exponent one window at a time starting from the most
|
|
* significant bits.
|
|
*/
|
|
while (bits >= 0) {
|
|
wvalue = 0; /* The 'value' of the window */
|
|
|
|
/* Scan the window, squaring the result as we go */
|
|
for (i = 0; i < window; i++, bits--) {
|
|
if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
|
|
goto err;
|
|
wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
|
|
}
|
|
|
|
/*
|
|
* Fetch the appropriate pre-computed value from the pre-buf
|
|
*/
|
|
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
|
|
window))
|
|
goto err;
|
|
|
|
/* Multiply the result into the intermediate result */
|
|
if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
/* Convert the final result from montgomery to standard format */
|
|
#if defined(SPARC_T4_MONT)
|
|
if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
|
|
am.d[0] = 1; /* borrow am */
|
|
for (i = 1; i < top; i++)
|
|
am.d[i] = 0;
|
|
if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
|
|
goto err;
|
|
} else
|
|
#endif
|
|
if (!BN_from_montgomery(rr, &tmp, mont, ctx))
|
|
goto err;
|
|
ret = 1;
|
|
err:
|
|
if ((in_mont == NULL) && (mont != NULL))
|
|
BN_MONT_CTX_free(mont);
|
|
if (powerbuf != NULL) {
|
|
OPENSSL_cleanse(powerbuf, powerbufLen);
|
|
if (powerbufFree)
|
|
OPENSSL_free(powerbufFree);
|
|
}
|
|
BN_CTX_end(ctx);
|
|
return (ret);
|
|
}
|
|
|
|
int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
|
|
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
|
|
{
|
|
BN_MONT_CTX *mont = NULL;
|
|
int b, bits, ret = 0;
|
|
int r_is_one;
|
|
BN_ULONG w, next_w;
|
|
BIGNUM *d, *r, *t;
|
|
BIGNUM *swap_tmp;
|
|
#define BN_MOD_MUL_WORD(r, w, m) \
|
|
(BN_mul_word(r, (w)) && \
|
|
(/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
|
|
(BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
|
|
/*
|
|
* BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
|
|
* probably more overhead than always using BN_mod (which uses BN_copy if
|
|
* a similar test returns true).
|
|
*/
|
|
/*
|
|
* We can use BN_mod and do not need BN_nnmod because our accumulator is
|
|
* never negative (the result of BN_mod does not depend on the sign of
|
|
* the modulus).
|
|
*/
|
|
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
|
|
(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
|
|
|
|
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
|
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
|
BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
|
return -1;
|
|
}
|
|
|
|
bn_check_top(p);
|
|
bn_check_top(m);
|
|
|
|
if (!BN_is_odd(m)) {
|
|
BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
|
|
return (0);
|
|
}
|
|
if (m->top == 1)
|
|
a %= m->d[0]; /* make sure that 'a' is reduced */
|
|
|
|
bits = BN_num_bits(p);
|
|
if (bits == 0) {
|
|
/* x**0 mod 1 is still zero. */
|
|
if (BN_is_one(m)) {
|
|
ret = 1;
|
|
BN_zero(rr);
|
|
} else {
|
|
ret = BN_one(rr);
|
|
}
|
|
return ret;
|
|
}
|
|
if (a == 0) {
|
|
BN_zero(rr);
|
|
ret = 1;
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
d = BN_CTX_get(ctx);
|
|
r = BN_CTX_get(ctx);
|
|
t = BN_CTX_get(ctx);
|
|
if (d == NULL || r == NULL || t == NULL)
|
|
goto err;
|
|
|
|
if (in_mont != NULL)
|
|
mont = in_mont;
|
|
else {
|
|
if ((mont = BN_MONT_CTX_new()) == NULL)
|
|
goto err;
|
|
if (!BN_MONT_CTX_set(mont, m, ctx))
|
|
goto err;
|
|
}
|
|
|
|
r_is_one = 1; /* except for Montgomery factor */
|
|
|
|
/* bits-1 >= 0 */
|
|
|
|
/* The result is accumulated in the product r*w. */
|
|
w = a; /* bit 'bits-1' of 'p' is always set */
|
|
for (b = bits - 2; b >= 0; b--) {
|
|
/* First, square r*w. */
|
|
next_w = w * w;
|
|
if ((next_w / w) != w) { /* overflow */
|
|
if (r_is_one) {
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
|
goto err;
|
|
r_is_one = 0;
|
|
} else {
|
|
if (!BN_MOD_MUL_WORD(r, w, m))
|
|
goto err;
|
|
}
|
|
next_w = 1;
|
|
}
|
|
w = next_w;
|
|
if (!r_is_one) {
|
|
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
|
|
goto err;
|
|
}
|
|
|
|
/* Second, multiply r*w by 'a' if exponent bit is set. */
|
|
if (BN_is_bit_set(p, b)) {
|
|
next_w = w * a;
|
|
if ((next_w / a) != w) { /* overflow */
|
|
if (r_is_one) {
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
|
goto err;
|
|
r_is_one = 0;
|
|
} else {
|
|
if (!BN_MOD_MUL_WORD(r, w, m))
|
|
goto err;
|
|
}
|
|
next_w = a;
|
|
}
|
|
w = next_w;
|
|
}
|
|
}
|
|
|
|
/* Finally, set r:=r*w. */
|
|
if (w != 1) {
|
|
if (r_is_one) {
|
|
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
|
|
goto err;
|
|
r_is_one = 0;
|
|
} else {
|
|
if (!BN_MOD_MUL_WORD(r, w, m))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
if (r_is_one) { /* can happen only if a == 1 */
|
|
if (!BN_one(rr))
|
|
goto err;
|
|
} else {
|
|
if (!BN_from_montgomery(rr, r, mont, ctx))
|
|
goto err;
|
|
}
|
|
ret = 1;
|
|
err:
|
|
if ((in_mont == NULL) && (mont != NULL))
|
|
BN_MONT_CTX_free(mont);
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rr);
|
|
return (ret);
|
|
}
|
|
|
|
/* The old fallback, simple version :-) */
|
|
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
|
|
const BIGNUM *m, BN_CTX *ctx)
|
|
{
|
|
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
|
|
int start = 1;
|
|
BIGNUM *d;
|
|
/* Table of variables obtained from 'ctx' */
|
|
BIGNUM *val[TABLE_SIZE];
|
|
|
|
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
|
|
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
|
|
BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
|
|
return -1;
|
|
}
|
|
|
|
bits = BN_num_bits(p);
|
|
if (bits == 0) {
|
|
/* x**0 mod 1 is still zero. */
|
|
if (BN_is_one(m)) {
|
|
ret = 1;
|
|
BN_zero(r);
|
|
} else {
|
|
ret = BN_one(r);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
d = BN_CTX_get(ctx);
|
|
val[0] = BN_CTX_get(ctx);
|
|
if (!d || !val[0])
|
|
goto err;
|
|
|
|
if (!BN_nnmod(val[0], a, m, ctx))
|
|
goto err; /* 1 */
|
|
if (BN_is_zero(val[0])) {
|
|
BN_zero(r);
|
|
ret = 1;
|
|
goto err;
|
|
}
|
|
|
|
window = BN_window_bits_for_exponent_size(bits);
|
|
if (window > 1) {
|
|
if (!BN_mod_mul(d, val[0], val[0], m, ctx))
|
|
goto err; /* 2 */
|
|
j = 1 << (window - 1);
|
|
for (i = 1; i < j; i++) {
|
|
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
|
|
!BN_mod_mul(val[i], val[i - 1], d, m, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
|
|
start = 1; /* This is used to avoid multiplication etc
|
|
* when there is only the value '1' in the
|
|
* buffer. */
|
|
wvalue = 0; /* The 'value' of the window */
|
|
wstart = bits - 1; /* The top bit of the window */
|
|
wend = 0; /* The bottom bit of the window */
|
|
|
|
if (!BN_one(r))
|
|
goto err;
|
|
|
|
for (;;) {
|
|
if (BN_is_bit_set(p, wstart) == 0) {
|
|
if (!start)
|
|
if (!BN_mod_mul(r, r, r, m, ctx))
|
|
goto err;
|
|
if (wstart == 0)
|
|
break;
|
|
wstart--;
|
|
continue;
|
|
}
|
|
/*
|
|
* We now have wstart on a 'set' bit, we now need to work out how bit
|
|
* a window to do. To do this we need to scan forward until the last
|
|
* set bit before the end of the window
|
|
*/
|
|
j = wstart;
|
|
wvalue = 1;
|
|
wend = 0;
|
|
for (i = 1; i < window; i++) {
|
|
if (wstart - i < 0)
|
|
break;
|
|
if (BN_is_bit_set(p, wstart - i)) {
|
|
wvalue <<= (i - wend);
|
|
wvalue |= 1;
|
|
wend = i;
|
|
}
|
|
}
|
|
|
|
/* wend is the size of the current window */
|
|
j = wend + 1;
|
|
/* add the 'bytes above' */
|
|
if (!start)
|
|
for (i = 0; i < j; i++) {
|
|
if (!BN_mod_mul(r, r, r, m, ctx))
|
|
goto err;
|
|
}
|
|
|
|
/* wvalue will be an odd number < 2^window */
|
|
if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
|
|
goto err;
|
|
|
|
/* move the 'window' down further */
|
|
wstart -= wend + 1;
|
|
wvalue = 0;
|
|
start = 0;
|
|
if (wstart < 0)
|
|
break;
|
|
}
|
|
ret = 1;
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(r);
|
|
return (ret);
|
|
}
|