bn_x931p.c

/* bn_x931p.c */
/* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL
 * project 2005.
 */
/* ====================================================================
 * Copyright (c) 2005 The OpenSSL Project.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer. 
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in
 *    the documentation and/or other materials provided with the
 *    distribution.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    licensing@OpenSSL.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
 * OF THE POSSIBILITY OF SUCH DAMAGE.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */

#include <stdio.h>
#include <openssl/bn.h>

/* X9.31 routines for prime derivation */

/* X9.31 prime derivation. This is used to generate the primes pi
 * (p1, p2, q1, q2) from a parameter Xpi by checking successive odd
 * integers.
 */

static int bn_x931_derive_pi(BIGNUM *pi, const BIGNUM *Xpi, BN_CTX *ctx,
			BN_GENCB *cb)
	{
	int i = 0;
	if (!BN_copy(pi, Xpi))
		return 0;
	if (!BN_is_odd(pi) && !BN_add_word(pi, 1))
		return 0;
	for(;;)
		{
		i++;
		BN_GENCB_call(cb, 0, i);
		/* NB 27 MR is specificed in X9.31 */
		if (BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb))
			break;
		if (!BN_add_word(pi, 2))
			return 0;
		}
	BN_GENCB_call(cb, 2, i);
	return 1;
	}

/* This is the main X9.31 prime derivation function. From parameters
 * Xp1, Xp2 and Xp derive the prime p. If the parameters p1 or p2 are
 * not NULL they will be returned too: this is needed for testing.
 */

int BN_X931_derive_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
			const BIGNUM *Xp, const BIGNUM *Xp1, const BIGNUM *Xp2,
			const BIGNUM *e, BN_CTX *ctx, BN_GENCB *cb)
	{
	int ret = 0;

	BIGNUM *t, *p1p2, *pm1;

	/* Only even e supported */
	if (!BN_is_odd(e))
		return 0;

	BN_CTX_start(ctx);
	if (!p1)
		p1 = BN_CTX_get(ctx);

	if (!p2)
		p2 = BN_CTX_get(ctx);

	t = BN_CTX_get(ctx);

	p1p2 = BN_CTX_get(ctx);

	pm1 = BN_CTX_get(ctx);

	if (!bn_x931_derive_pi(p1, Xp1, ctx, cb))
		goto err;

	if (!bn_x931_derive_pi(p2, Xp2, ctx, cb))
		goto err;

	if (!BN_mul(p1p2, p1, p2, ctx))
		goto err;

	/* First set p to value of Rp */

	if (!BN_mod_inverse(p, p2, p1, ctx))
		goto err;

	if (!BN_mul(p, p, p2, ctx))
		goto err;

	if (!BN_mod_inverse(t, p1, p2, ctx))
		goto err;

	if (!BN_mul(t, t, p1, ctx))
		goto err;

	if (!BN_sub(p, p, t))
		goto err;

	if (p->neg && !BN_add(p, p, p1p2))
		goto err;

	/* p now equals Rp */

	if (!BN_mod_sub(p, p, Xp, p1p2, ctx))
		goto err;

	if (!BN_add(p, p, Xp))
		goto err;

	/* p now equals Yp0 */

	for (;;)
		{
		int i = 1;
		BN_GENCB_call(cb, 0, i++);
		if (!BN_copy(pm1, p))
			goto err;
		if (!BN_sub_word(pm1, 1))
			goto err;
		if (!BN_gcd(t, pm1, e, ctx))
			goto err;
		if (BN_is_one(t)
		/* X9.31 specifies 8 MR and 1 Lucas test or any prime test
		 * offering similar or better guarantees 50 MR is considerably 
		 * better.
		 */
			&& BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb))
			break;
		if (!BN_add(p, p, p1p2))
			goto err;
		}

	BN_GENCB_call(cb, 3, 0);

	ret = 1;

	err:

	BN_CTX_end(ctx);

	return ret;
	}

/* Generate pair of paramters Xp, Xq for X9.31 prime generation.
 * Note: nbits paramter is sum of number of bits in both.
 */

int BN_X931_generate_Xpq(BIGNUM *Xp, BIGNUM *Xq, int nbits, BN_CTX *ctx)
	{
	BIGNUM *t;
	int i;
	/* Number of bits for each prime is of the form
	 * 512+128s for s = 0, 1, ...
	 */
	if ((nbits < 1024) || (nbits & 0xff))
		return 0;
	nbits >>= 1;
	/* The random value Xp must be between sqrt(2) * 2^(nbits-1) and
	 * 2^nbits - 1. By setting the top two bits we ensure that the lower
	 * bound is exceeded.
	 */
	if (!BN_rand(Xp, nbits, 1, 0))
		return 0;

	BN_CTX_start(ctx);
	t = BN_CTX_get(ctx);

	for (i = 0; i < 1000; i++)
		{
		if (!BN_rand(Xq, nbits, 1, 0))
			return 0;
		/* Check that |Xp - Xq| > 2^(nbits - 100) */
		BN_sub(t, Xp, Xq);
		if (BN_num_bits(t) > (nbits - 100))
			break;
		}

	BN_CTX_end(ctx);

	if (i < 1000)
		return 1;

	return 0;

	}

/* Generate primes using X9.31 algorithm. Of the values p, p1, p2, Xp1
 * and Xp2 only 'p' needs to be non-NULL. If any of the others are not NULL
 * the relevant parameter will be stored in it.
 *
 * Due to the fact that |Xp - Xq| > 2^(nbits - 100) must be satisfied Xp and Xq
 * are generated using the previous function and supplied as input.
 */

int BN_X931_generate_prime_ex(BIGNUM *p, BIGNUM *p1, BIGNUM *p2,
			BIGNUM *Xp1, BIGNUM *Xp2,
			const BIGNUM *Xp,
			const BIGNUM *e, BN_CTX *ctx,
			BN_GENCB *cb)
	{
	int ret = 0;

	BN_CTX_start(ctx);
	if (!Xp1)
		Xp1 = BN_CTX_get(ctx);
	if (!Xp2)
		Xp2 = BN_CTX_get(ctx);

	if (!BN_rand(Xp1, 101, 0, 0))
		goto error;
	if (!BN_rand(Xp2, 101, 0, 0))
		goto error;
	if (!BN_X931_derive_prime_ex(p, p1, p2, Xp, Xp1, Xp2, e, ctx, cb))
		goto error;

	ret = 1;

	error:
	BN_CTX_end(ctx);

	return ret;

	}