547 lines
15 KiB
C
Executable File
547 lines
15 KiB
C
Executable File
/* $OpenBSD: bn_prime.c,v 1.18 2017/01/29 17:49:22 beck Exp $ */
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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) 1998-2001 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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*
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* 3. All advertising materials mentioning features or use of this
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* software must display the following acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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*
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* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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* endorse or promote products derived from this software without
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* prior written permission. For written permission, please contact
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* openssl-core@openssl.org.
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*
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* 5. Products derived from this software may not be called "OpenSSL"
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* nor may "OpenSSL" appear in their names without prior written
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* permission of the OpenSSL Project.
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*
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* 6. Redistributions of any form whatsoever must retain the following
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* acknowledgment:
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* "This product includes software developed by the OpenSSL Project
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* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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*
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* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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* OF THE POSSIBILITY OF SUCH DAMAGE.
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* ====================================================================
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*
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* This product includes cryptographic software written by Eric Young
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* (eay@cryptsoft.com). This product includes software written by Tim
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* Hudson (tjh@cryptsoft.com).
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*
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*/
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#include <stdio.h>
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#include <time.h>
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#include <openssl/err.h>
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#include "bn_lcl.h"
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/* NB: these functions have been "upgraded", the deprecated versions (which are
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* compatibility wrappers using these functions) are in bn_depr.c.
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* - Geoff
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*/
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/* The quick sieve algorithm approach to weeding out primes is
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* Philip Zimmermann's, as implemented in PGP. I have had a read of
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* his comments and implemented my own version.
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*/
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#include "bn_prime.h"
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static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
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static int probable_prime(BIGNUM *rnd, int bits);
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static int probable_prime_dh(BIGNUM *rnd, int bits,
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const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
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static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
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const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
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int
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BN_GENCB_call(BN_GENCB *cb, int a, int b)
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{
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/* No callback means continue */
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if (!cb)
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return 1;
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switch (cb->ver) {
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case 1:
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/* Deprecated-style callbacks */
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if (!cb->cb.cb_1)
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return 1;
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cb->cb.cb_1(a, b, cb->arg);
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return 1;
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case 2:
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/* New-style callbacks */
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return cb->cb.cb_2(a, b, cb);
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default:
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break;
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}
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/* Unrecognised callback type */
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return 0;
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}
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int
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BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add,
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const BIGNUM *rem, BN_GENCB *cb)
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{
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BIGNUM *t;
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int found = 0;
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int i, j, c1 = 0;
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BN_CTX *ctx;
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int checks;
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if (bits < 2 || (bits == 2 && safe)) {
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/*
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* There are no prime numbers smaller than 2, and the smallest
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* safe prime (7) spans three bits.
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*/
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BNerror(BN_R_BITS_TOO_SMALL);
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return 0;
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}
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ctx = BN_CTX_new();
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if (ctx == NULL)
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goto err;
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BN_CTX_start(ctx);
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if ((t = BN_CTX_get(ctx)) == NULL)
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goto err;
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checks = BN_prime_checks_for_size(bits);
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loop:
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/* make a random number and set the top and bottom bits */
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if (add == NULL) {
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if (!probable_prime(ret, bits))
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goto err;
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} else {
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if (safe) {
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if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
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goto err;
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} else {
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if (!probable_prime_dh(ret, bits, add, rem, ctx))
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goto err;
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}
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}
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/* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
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if (!BN_GENCB_call(cb, 0, c1++))
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/* aborted */
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goto err;
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if (!safe) {
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i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
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if (i == -1)
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goto err;
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if (i == 0)
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goto loop;
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} else {
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/* for "safe prime" generation,
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* check that (p-1)/2 is prime.
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* Since a prime is odd, We just
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* need to divide by 2 */
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if (!BN_rshift1(t, ret))
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goto err;
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for (i = 0; i < checks; i++) {
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j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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if (!BN_GENCB_call(cb, 2, c1 - 1))
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goto err;
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/* We have a safe prime test pass */
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}
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}
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/* we have a prime :-) */
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found = 1;
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err:
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if (ctx != NULL) {
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BN_CTX_end(ctx);
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BN_CTX_free(ctx);
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}
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bn_check_top(ret);
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return found;
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}
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int
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BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
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{
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return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
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}
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int
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BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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int do_trial_division, BN_GENCB *cb)
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{
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int i, j, ret = -1;
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int k;
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BN_CTX *ctx = NULL;
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BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
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BN_MONT_CTX *mont = NULL;
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const BIGNUM *A = NULL;
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if (BN_cmp(a, BN_value_one()) <= 0)
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return 0;
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if (checks == BN_prime_checks)
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checks = BN_prime_checks_for_size(BN_num_bits(a));
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/* first look for small factors */
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if (!BN_is_odd(a))
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/* a is even => a is prime if and only if a == 2 */
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return BN_is_word(a, 2);
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if (do_trial_division) {
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for (i = 1; i < NUMPRIMES; i++) {
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BN_ULONG mod = BN_mod_word(a, primes[i]);
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if (mod == (BN_ULONG)-1)
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goto err;
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if (mod == 0)
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return 0;
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}
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if (!BN_GENCB_call(cb, 1, -1))
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goto err;
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}
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if (ctx_passed != NULL)
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ctx = ctx_passed;
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else if ((ctx = BN_CTX_new()) == NULL)
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goto err;
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BN_CTX_start(ctx);
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/* A := abs(a) */
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if (a->neg) {
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BIGNUM *t;
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if ((t = BN_CTX_get(ctx)) == NULL)
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goto err;
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BN_copy(t, a);
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t->neg = 0;
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A = t;
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} else
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A = a;
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if ((A1 = BN_CTX_get(ctx)) == NULL)
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goto err;
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if ((A1_odd = BN_CTX_get(ctx)) == NULL)
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goto err;
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if ((check = BN_CTX_get(ctx)) == NULL)
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goto err;
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/* compute A1 := A - 1 */
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if (!BN_copy(A1, A))
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goto err;
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if (!BN_sub_word(A1, 1))
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goto err;
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if (BN_is_zero(A1)) {
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ret = 0;
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goto err;
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}
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/* write A1 as A1_odd * 2^k */
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k = 1;
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while (!BN_is_bit_set(A1, k))
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k++;
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if (!BN_rshift(A1_odd, A1, k))
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goto err;
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/* Montgomery setup for computations mod A */
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mont = BN_MONT_CTX_new();
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if (mont == NULL)
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goto err;
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if (!BN_MONT_CTX_set(mont, A, ctx))
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goto err;
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for (i = 0; i < checks; i++) {
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if (!BN_pseudo_rand_range(check, A1))
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goto err;
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if (!BN_add_word(check, 1))
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goto err;
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/* now 1 <= check < A */
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j = witness(check, A, A1, A1_odd, k, ctx, mont);
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if (j == -1)
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goto err;
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if (j) {
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ret = 0;
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goto err;
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}
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if (!BN_GENCB_call(cb, 1, i))
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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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if (ctx != NULL) {
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BN_CTX_end(ctx);
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if (ctx_passed == NULL)
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BN_CTX_free(ctx);
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}
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BN_MONT_CTX_free(mont);
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return (ret);
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}
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static int
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witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd,
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int k, BN_CTX *ctx, BN_MONT_CTX *mont)
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{
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if (!BN_mod_exp_mont_ct(w, w, a1_odd, a, ctx, mont))
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/* w := w^a1_odd mod a */
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return -1;
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if (BN_is_one(w))
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return 0; /* probably prime */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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while (--k) {
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if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
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return -1;
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if (BN_is_one(w))
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return 1; /* 'a' is composite, otherwise a previous 'w' would
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* have been == -1 (mod 'a') */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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}
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/* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
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* and it is neither -1 nor +1 -- so 'a' cannot be prime */
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bn_check_top(w);
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return 1;
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}
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static int
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probable_prime(BIGNUM *rnd, int bits)
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{
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int i;
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prime_t mods[NUMPRIMES];
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BN_ULONG delta, maxdelta;
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again:
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if (!BN_rand(rnd, bits, 1, 1))
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return (0);
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/* we now have a random number 'rand' to test. */
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for (i = 1; i < NUMPRIMES; i++) {
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BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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if (mod == (BN_ULONG)-1)
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return (0);
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mods[i] = (prime_t)mod;
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}
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maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
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delta = 0;
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loop:
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for (i = 1; i < NUMPRIMES; i++) {
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/* check that rnd is not a prime and also
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* that gcd(rnd-1,primes) == 1 (except for 2) */
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if (((mods[i] + delta) % primes[i]) <= 1) {
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delta += 2;
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if (delta > maxdelta)
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goto again;
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goto loop;
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}
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}
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if (!BN_add_word(rnd, delta))
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return (0);
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bn_check_top(rnd);
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return (1);
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}
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static int
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probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem,
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BN_CTX *ctx)
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{
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int i, ret = 0;
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BIGNUM *t1;
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BN_CTX_start(ctx);
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if ((t1 = BN_CTX_get(ctx)) == NULL)
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goto err;
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if (!BN_rand(rnd, bits, 0, 1))
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goto err;
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/* we need ((rnd-rem) % add) == 0 */
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if (!BN_mod_ct(t1, rnd, add, ctx))
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goto err;
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if (!BN_sub(rnd, rnd, t1))
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goto err;
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if (rem == NULL) {
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if (!BN_add_word(rnd, 1))
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goto err;
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} else {
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if (!BN_add(rnd, rnd, rem))
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goto err;
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}
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/* we now have a random number 'rand' to test. */
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loop:
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for (i = 1; i < NUMPRIMES; i++) {
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/* check that rnd is a prime */
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BN_LONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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if (mod == (BN_ULONG)-1)
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goto err;
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if (mod <= 1) {
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if (!BN_add(rnd, rnd, add))
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goto err;
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goto loop;
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}
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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_check_top(rnd);
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return (ret);
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}
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static int
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probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
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const BIGNUM *rem, BN_CTX *ctx)
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{
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int i, ret = 0;
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BIGNUM *t1, *qadd, *q;
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bits--;
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BN_CTX_start(ctx);
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if ((t1 = BN_CTX_get(ctx)) == NULL)
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goto err;
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if ((q = BN_CTX_get(ctx)) == NULL)
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goto err;
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if ((qadd = BN_CTX_get(ctx)) == NULL)
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goto err;
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if (!BN_rshift1(qadd, padd))
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goto err;
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if (!BN_rand(q, bits, 0, 1))
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goto err;
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/* we need ((rnd-rem) % add) == 0 */
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if (!BN_mod_ct(t1, q,qadd, ctx))
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goto err;
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if (!BN_sub(q, q, t1))
|
|
goto err;
|
|
if (rem == NULL) {
|
|
if (!BN_add_word(q, 1))
|
|
goto err;
|
|
} else {
|
|
if (!BN_rshift1(t1, rem))
|
|
goto err;
|
|
if (!BN_add(q, q, t1))
|
|
goto err;
|
|
}
|
|
|
|
/* we now have a random number 'rand' to test. */
|
|
if (!BN_lshift1(p, q))
|
|
goto err;
|
|
if (!BN_add_word(p, 1))
|
|
goto err;
|
|
|
|
loop:
|
|
for (i = 1; i < NUMPRIMES; i++) {
|
|
/* check that p and q are prime */
|
|
/* check that for p and q
|
|
* gcd(p-1,primes) == 1 (except for 2) */
|
|
BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
|
|
BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
|
|
if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
|
|
goto err;
|
|
if (pmod == 0 || qmod == 0) {
|
|
if (!BN_add(p, p, padd))
|
|
goto err;
|
|
if (!BN_add(q, q, qadd))
|
|
goto err;
|
|
goto loop;
|
|
}
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(p);
|
|
return (ret);
|
|
}
|