crypto/bn/bn_x931p.c - third_party/openssl - Git at Google

 /* 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>
 #include "bn_lcl.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 parameters Xp, Xq for X9.31 prime generation. Note: nbits
  * parameter 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;

 }
	/* 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>
	#include "bn_lcl.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 parameters Xp, Xq for X9.31 prime generation. Note: nbits
	* parameter 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;

	}