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bn_prime.c

/* crypto/bn/bn_prime.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
 * All rights reserved.
 *
 * This package is an SSL implementation written
 * by Eric Young (eay@cryptsoft.com).
 * The implementation was written so as to conform with Netscapes SSL.
 * 
 * This library is free for commercial and non-commercial use as long as
 * the following conditions are aheared to.  The following conditions
 * apply to all code found in this distribution, be it the RC4, RSA,
 * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
 * included with this distribution is covered by the same copyright terms
 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
 * 
 * Copyright remains Eric Young's, and as such any Copyright notices in
 * the code are not to be removed.
 * If this package is used in a product, Eric Young should be given attribution
 * as the author of the parts of the library used.
 * This can be in the form of a textual message at program startup or
 * in documentation (online or textual) provided with the package.
 * 
 * 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 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 acknowledgement:
 *    "This product includes cryptographic software written by
 *     Eric Young (eay@cryptsoft.com)"
 *    The word 'cryptographic' can be left out if the rouines from the library
 *    being used are not cryptographic related :-).
 * 4. If you include any Windows specific code (or a derivative thereof) from 
 *    the apps directory (application code) you must include an acknowledgement:
 *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
 * 
 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
 * ANY EXPRESS 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 AUTHOR OR 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.
 * 
 * The licence and distribution terms for any publically available version or
 * derivative of this code cannot be changed.  i.e. this code cannot simply be
 * copied and put under another distribution licence
 * [including the GNU Public Licence.]
 */
/* ====================================================================
 * Copyright (c) 1998-2001 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
 *    openssl-core@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 <time.h>
#include "cryptlib.h"
#include "bn_lcl.h"
#include <openssl/rand.h>

/* NB: these functions have been "upgraded", the deprecated versions (which are
 * compatibility wrappers using these functions) are in bn_depr.c.
 * - Geoff
 */

/* The quick sieve algorithm approach to weeding out primes is
 * Philip Zimmermann's, as implemented in PGP.  I have had a read of
 * his comments and implemented my own version.
 */
#include "bn_prime.h"

static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
      const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits);
static int probable_prime_dh(BIGNUM *rnd, int bits,
      const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
      const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);

int BN_GENCB_call(BN_GENCB *cb, int a, int b)
      {
      /* No callback means continue */
      if(!cb) return 1;
      switch(cb->ver)
            {
      case 1:
            /* Deprecated-style callbacks */
            if(!cb->cb.cb_1)
                  return 1;
            cb->cb.cb_1(a, b, cb->arg);
            return 1;
      case 2:
            /* New-style callbacks */
            return cb->cb.cb_2(a, b, cb);
      default:
            break;
            }
      /* Unrecognised callback type */
      return 0;
      }

int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
      const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
      {
      BIGNUM *t;
      int found=0;
      int i,j,c1=0;
      BN_CTX *ctx;
      int checks = BN_prime_checks_for_size(bits);

      ctx=BN_CTX_new();
      if (ctx == NULL) goto err;
      BN_CTX_start(ctx);
      t = BN_CTX_get(ctx);
      if(!t) goto err;
loop: 
      /* make a random number and set the top and bottom bits */
      if (add == NULL)
            {
            if (!probable_prime(ret,bits)) goto err;
            }
      else
            {
            if (safe)
                  {
                  if (!probable_prime_dh_safe(ret,bits,add,rem,ctx))
                         goto err;
                  }
            else
                  {
                  if (!probable_prime_dh(ret,bits,add,rem,ctx))
                        goto err;
                  }
            }
      /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
      if(!BN_GENCB_call(cb, 0, c1++))
            /* aborted */
            goto err;

      if (!safe)
            {
            i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb);
            if (i == -1) goto err;
            if (i == 0) goto loop;
            }
      else
            {
            /* for "safe prime" generation,
             * check that (p-1)/2 is prime.
             * Since a prime is odd, We just
             * need to divide by 2 */
            if (!BN_rshift1(t,ret)) goto err;

            for (i=0; i<checks; i++)
                  {
                  j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb);
                  if (j == -1) goto err;
                  if (j == 0) goto loop;

                  j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb);
                  if (j == -1) goto err;
                  if (j == 0) goto loop;

                  if(!BN_GENCB_call(cb, 2, c1-1))
                        goto err;
                  /* We have a safe prime test pass */
                  }
            }
      /* we have a prime :-) */
      found = 1;
err:
      if (ctx != NULL)
            {
            BN_CTX_end(ctx);
            BN_CTX_free(ctx);
            }
      bn_check_top(ret);
      return found;
      }

int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
      {
      return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
      }

int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
            int do_trial_division, BN_GENCB *cb)
      {
      int i, j, ret = -1;
      int k;
      BN_CTX *ctx = NULL;
      BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
      BN_MONT_CTX *mont = NULL;
      const BIGNUM *A = NULL;

      if (BN_cmp(a, BN_value_one()) <= 0)
            return 0;
      
      if (checks == BN_prime_checks)
            checks = BN_prime_checks_for_size(BN_num_bits(a));

      /* first look for small factors */
      if (!BN_is_odd(a))
            return 0;
      if (do_trial_division)
            {
            for (i = 1; i < NUMPRIMES; i++)
                  if (BN_mod_word(a, primes[i]) == 0) 
                        return 0;
            if(!BN_GENCB_call(cb, 1, -1))
                  goto err;
            }

      if (ctx_passed != NULL)
            ctx = ctx_passed;
      else
            if ((ctx=BN_CTX_new()) == NULL)
                  goto err;
      BN_CTX_start(ctx);

      /* A := abs(a) */
      if (a->neg)
            {
            BIGNUM *t;
            if ((t = BN_CTX_get(ctx)) == NULL) goto err;
            BN_copy(t, a);
            t->neg = 0;
            A = t;
            }
      else
            A = a;
      A1 = BN_CTX_get(ctx);
      A1_odd = BN_CTX_get(ctx);
      check = BN_CTX_get(ctx);
      if (check == NULL) goto err;

      /* compute A1 := A - 1 */
      if (!BN_copy(A1, A))
            goto err;
      if (!BN_sub_word(A1, 1))
            goto err;
      if (BN_is_zero(A1))
            {
            ret = 0;
            goto err;
            }

      /* write  A1  as  A1_odd * 2^k */
      k = 1;
      while (!BN_is_bit_set(A1, k))
            k++;
      if (!BN_rshift(A1_odd, A1, k))
            goto err;

      /* Montgomery setup for computations mod A */
      mont = BN_MONT_CTX_new();
      if (mont == NULL)
            goto err;
      if (!BN_MONT_CTX_set(mont, A, ctx))
            goto err;
      
      for (i = 0; i < checks; i++)
            {
            if (!BN_pseudo_rand_range(check, A1))
                  goto err;
            if (!BN_add_word(check, 1))
                  goto err;
            /* now 1 <= check < A */

            j = witness(check, A, A1, A1_odd, k, ctx, mont);
            if (j == -1) goto err;
            if (j)
                  {
                  ret=0;
                  goto err;
                  }
            if(!BN_GENCB_call(cb, 1, i))
                  goto err;
            }
      ret=1;
err:
      if (ctx != NULL)
            {
            BN_CTX_end(ctx);
            if (ctx_passed == NULL)
                  BN_CTX_free(ctx);
            }
      if (mont != NULL)
            BN_MONT_CTX_free(mont);

      return(ret);
      }

static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
      const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
      {
      if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
            return -1;
      if (BN_is_one(w))
            return 0; /* probably prime */
      if (BN_cmp(w, a1) == 0)
            return 0; /* w == -1 (mod a),  'a' is probably prime */
      while (--k)
            {
            if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
                  return -1;
            if (BN_is_one(w))
                  return 1; /* 'a' is composite, otherwise a previous 'w' would
                             * have been == -1 (mod 'a') */
            if (BN_cmp(w, a1) == 0)
                  return 0; /* w == -1 (mod a), 'a' is probably prime */
            }
      /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
       * and it is neither -1 nor +1 -- so 'a' cannot be prime */
      bn_check_top(w);
      return 1;
      }

static int probable_prime(BIGNUM *rnd, int bits)
      {
      int i;
      BN_ULONG mods[NUMPRIMES];
      BN_ULONG delta,d;

again:
      if (!BN_rand(rnd,bits,1,1)) return(0);
      /* we now have a random number 'rand' to test. */
      for (i=1; i<NUMPRIMES; i++)
            mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
      delta=0;
      loop: for (i=1; i<NUMPRIMES; i++)
            {
            /* check that rnd is not a prime and also
             * that gcd(rnd-1,primes) == 1 (except for 2) */
            if (((mods[i]+delta)%primes[i]) <= 1)
                  {
                  d=delta;
                  delta+=2;
                  /* perhaps need to check for overflow of
                   * delta (but delta can be up to 2^32)
                   * 21-May-98 eay - added overflow check */
                  if (delta < d) goto again;
                  goto loop;
                  }
            }
      if (!BN_add_word(rnd,delta)) return(0);
      bn_check_top(rnd);
      return(1);
      }

static int probable_prime_dh(BIGNUM *rnd, int bits,
      const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
      {
      int i,ret=0;
      BIGNUM *t1;

      BN_CTX_start(ctx);
      if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;

      if (!BN_rand(rnd,bits,0,1)) goto err;

      /* we need ((rnd-rem) % add) == 0 */

      if (!BN_mod(t1,rnd,add,ctx)) goto err;
      if (!BN_sub(rnd,rnd,t1)) goto err;
      if (rem == NULL)
            { if (!BN_add_word(rnd,1)) goto err; }
      else
            { if (!BN_add(rnd,rnd,rem)) goto err; }

      /* we now have a random number 'rand' to test. */

      loop: for (i=1; i<NUMPRIMES; i++)
            {
            /* check that rnd is a prime */
            if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
                  {
                  if (!BN_add(rnd,rnd,add)) goto err;
                  goto loop;
                  }
            }
      ret=1;
err:
      BN_CTX_end(ctx);
      bn_check_top(rnd);
      return(ret);
      }

static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
      const BIGNUM *rem, BN_CTX *ctx)
      {
      int i,ret=0;
      BIGNUM *t1,*qadd,*q;

      bits--;
      BN_CTX_start(ctx);
      t1 = BN_CTX_get(ctx);
      q = BN_CTX_get(ctx);
      qadd = BN_CTX_get(ctx);
      if (qadd == NULL) goto err;

      if (!BN_rshift1(qadd,padd)) goto err;
            
      if (!BN_rand(q,bits,0,1)) goto err;

      /* we need ((rnd-rem) % add) == 0 */
      if (!BN_mod(t1,q,qadd,ctx)) goto err;
      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) */
            if (  (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
                  (BN_mod_word(q,(BN_ULONG)primes[i]) == 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);
      }

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