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

 /* 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) 1998-2000 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>

 /* 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);

 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
 	const BIGNUM *add, const BIGNUM *rem,
 	void (*callback)(int,int,void *), void *cb_arg)
 	{
 	BIGNUM *rnd=NULL;
 	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;
 	if (ret == NULL)
 		{
 		if ((rnd=BN_new()) == NULL) goto err;
 		}
 	else
 		rnd=ret;
 	BN_init(&t);
 loop:
 	/* make a random number and set the top and bottom bits */
 	if (add == NULL)
 		{
 		if (!probable_prime(rnd,bits)) goto err;
 		}
 	else
 		{
 		if (safe)
 			{
 			if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
 				 goto err;
 			}
 		else
 			{
 			if (!probable_prime_dh(rnd,bits,add,rem,ctx))
 				goto err;
 			}
 		}
 	/* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
 	if (callback != NULL) callback(0,c1++,cb_arg);

 	if (!safe)
 		{
 		i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
 		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,rnd)) goto err;

 		for (i=0; i<checks; i++)
 			{
 			j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
 			if (j == -1) goto err;
 			if (j == 0) goto loop;

 			j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
 			if (j == -1) goto err;
 			if (j == 0) goto loop;

 			if (callback != NULL) callback(2,c1-1,cb_arg);
 			/* We have a safe prime test pass */
 			}
 		}
 	/* we have a prime :-) */
 	found = 1;
 err:
 	if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
 	BN_free(&t);
 	if (ctx != NULL) BN_CTX_free(ctx);
 	return(found ? rnd : NULL);
 	}

 int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
 	BN_CTX *ctx_passed, void *cb_arg)
 	{
 	return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
 	}

 int BN_is_prime_fasttest(const BIGNUM *a, int checks,
 		void (*callback)(int,int,void *),
 		BN_CTX *ctx_passed, void *cb_arg,
 		int do_trial_division)
 	{
 	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 (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 (callback != NULL) callback(1, -1, cb_arg);
 		}

 	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(check, BN_num_bits(A1), 0, 0))
 			goto err;
 		if (BN_cmp(check, A1) >= 0)
 			if (!BN_sub(check, 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 (callback != NULL) callback(1,i,cb_arg);
 		}
 	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 */
 	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);
 	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);
 	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);
 	return(ret);
 	}
	/* 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) 1998-2000 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>

	/* 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);

	BIGNUM BN_generate_prime(BIGNUM ret, int bits, int safe,
	const BIGNUM add, const BIGNUM rem,
	void (callback)(int,int,void ), void *cb_arg)
	{
	BIGNUM *rnd=NULL;
	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;
	if (ret == NULL)
	{
	if ((rnd=BN_new()) == NULL) goto err;
	}
	else
	rnd=ret;
	BN_init(&t);
	loop:
	/* make a random number and set the top and bottom bits */
	if (add == NULL)
	{
	if (!probable_prime(rnd,bits)) goto err;
	}
	else
	{
	if (safe)
	{
	if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
	goto err;
	}
	else
	{
	if (!probable_prime_dh(rnd,bits,add,rem,ctx))
	goto err;
	}
	}
	/* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
	if (callback != NULL) callback(0,c1++,cb_arg);

	if (!safe)
	{
	i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
	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,rnd)) goto err;

	for (i=0; i<checks; i++)
	{
	j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
	if (j == -1) goto err;
	if (j == 0) goto loop;

	j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
	if (j == -1) goto err;
	if (j == 0) goto loop;

	if (callback != NULL) callback(2,c1-1,cb_arg);
	/* We have a safe prime test pass */
	}
	}
	/* we have a prime :-) */
	found = 1;
	err:
	if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
	BN_free(&t);
	if (ctx != NULL) BN_CTX_free(ctx);
	return(found ? rnd : NULL);
	}

	int BN_is_prime(const BIGNUM a, int checks, void (callback)(int,int,void *),
	BN_CTX ctx_passed, void cb_arg)
	{
	return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
	}

	int BN_is_prime_fasttest(const BIGNUM *a, int checks,
	void (callback)(int,int,void ),
	BN_CTX ctx_passed, void cb_arg,
	int do_trial_division)
	{
	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 (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 (callback != NULL) callback(1, -1, cb_arg);
	}

	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(check, BN_num_bits(A1), 0, 0))
	goto err;
	if (BN_cmp(check, A1) >= 0)
	if (!BN_sub(check, 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 (callback != NULL) callback(1,i,cb_arg);
	}
	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 */
	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);
	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);
	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);
	return(ret);
	}