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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;

      }


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