text: /*
   * Copyright 2011-2018 The OpenSSL Project Authors. All Rights Reserved.
   *
   * Licensed under the Apache License 2.0 (the "License").  You may not use
   * this file except in compliance with the License.  You can obtain a copy
   * in the file LICENSE in the source distribution or at
   * https://www.openssl.org/source/license.html
   */
  
  #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, is_prime;
      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 specified in X9.31 */
          is_prime = BN_is_prime_fasttest_ex(pi, 27, ctx, 1, cb);
          if (is_prime < 0)
              return 0;
          if (is_prime)
              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 == NULL)
          p1 = BN_CTX_get(ctx);
  
      if (p2 == NULL)
          p2 = BN_CTX_get(ctx);
  
      t = BN_CTX_get(ctx);
  
      p1p2 = BN_CTX_get(ctx);
  
      pm1 = BN_CTX_get(ctx);
  
      if (pm1 == NULL)
          goto err;
  
      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.
               */
              int r = BN_is_prime_fasttest_ex(p, 50, ctx, 1, cb);
              if (r < 0)
                  goto err;
              if (r)
                  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_priv_rand(Xp, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
          goto err;
  
      BN_CTX_start(ctx);
      t = BN_CTX_get(ctx);
      if (t == NULL)
          goto err;
  
      for (i = 0; i < 1000; i++) {
          if (!BN_priv_rand(Xq, nbits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ANY))
              goto err;
  
          /* Check that |Xp - Xq| > 2^(nbits - 100) */
          if (!BN_sub(t, Xp, Xq))
              goto err;
          if (BN_num_bits(t) > (nbits - 100))
              break;
      }
  
      BN_CTX_end(ctx);
  
      if (i < 1000)
          return 1;
  
      return 0;
  
   err:
      BN_CTX_end(ctx);
      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 == NULL)
          Xp1 = BN_CTX_get(ctx);
      if (Xp2 == NULL)
          Xp2 = BN_CTX_get(ctx);
      if (Xp1 == NULL || Xp2 == NULL)
          goto error;
  
      if (!BN_priv_rand(Xp1, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
          goto error;
      if (!BN_priv_rand(Xp2, 101, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY))
          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;
  
  }
  