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.]
  */

 #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"

 /* number of Miller-Rabin iterations for an error rate  of less than 2^-80
  * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
  * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
  * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
  * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
 #define BN_prime_checks_size(b) ((b) >= 1300 ?  2 : \
                                 (b) >=  850 ?  3 : \
                                 (b) >=  650 ?  4 : \
                                 (b) >=  550 ?  5 : \
                                 (b) >=  450 ?  6 : \
                                 (b) >=  400 ?  7 : \
                                 (b) >=  350 ?  8 : \
                                 (b) >=  300 ?  9 : \
                                 (b) >=  250 ? 12 : \
                                 (b) >=  200 ? 15 : \
                                 (b) >=  150 ? 18 : \
                                 /* b >= 100 */ 27)

 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
 	BN_MONT_CTX *mont);
 static int probable_prime(BIGNUM *rnd, int bits);
 static int probable_prime_dh(BIGNUM *rnd, int bits,
 	BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
 	BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);

 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
 	     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_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(rnd,checks,callback,ctx,cb_arg);
 		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(rnd,1,callback,ctx,cb_arg);
 			if (j == -1) goto err;
 			if (j == 0) goto loop;

 			j=BN_is_prime(&t,1,callback,ctx,cb_arg);
 			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(BIGNUM *a, int checks, void (*callback)(int,int,void *),
 	     BN_CTX *ctx_passed, void *cb_arg)
 	{
 	int i,j,c2=0,ret= -1;
 	BIGNUM *check;
 	BN_CTX *ctx=NULL,*ctx2=NULL;
 	BN_MONT_CTX *mont=NULL;

 	if (checks == BN_prime_checks)
 		{
 		int bits = BN_num_bits(a);
 		checks = BN_prime_checks_size(bits);
 		}

 	if (!BN_is_odd(a))
 		return(0);
 	if (ctx_passed != NULL)
 		ctx=ctx_passed;
 	else
 		if ((ctx=BN_CTX_new()) == NULL) goto err;

 	if ((ctx2=BN_CTX_new()) == NULL) goto err;
 	if ((mont=BN_MONT_CTX_new()) == NULL) goto err;

 	check= &(ctx->bn[ctx->tos++]);

 	/* Setup the montgomery structure */
 	if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;

 	for (i=0; i<checks; i++)
 		{
 		if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
 		j=witness(check,a,ctx,ctx2,mont);
 		if (j == -1) goto err;
 		if (j)
 			{
 			ret=0;
 			goto err;
 			}
 		if (callback != NULL) callback(1,c2++,cb_arg);
 		}
 	ret=1;
 err:
 	ctx->tos--;
 	if ((ctx_passed == NULL) && (ctx != NULL))
 		BN_CTX_free(ctx);
 	if (ctx2 != NULL)
 		BN_CTX_free(ctx2);
 	if (mont != NULL) BN_MONT_CTX_free(mont);

 	return(ret);
 	}

 #define RECP_MUL_MOD

 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx, BN_CTX *ctx2,
 	     BN_MONT_CTX *mont)
 	{
 	int k,i,ret= -1,good;
 	BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
 	BIGNUM *mont_one,*mont_n1,*mont_a;

 	d1= &(ctx->bn[ctx->tos]);
 	d2= &(ctx->bn[ctx->tos+1]);
 	n1= &(ctx->bn[ctx->tos+2]);
 	ctx->tos+=3;

 	mont_one= &(ctx2->bn[ctx2->tos]);
 	mont_n1= &(ctx2->bn[ctx2->tos+1]);
 	mont_a= &(ctx2->bn[ctx2->tos+2]);
 	ctx2->tos+=3;

 	d=d1;
 	dd=d2;
 	if (!BN_one(d)) goto err;
 	if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
 	k=BN_num_bits(n1);

 	if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
 	if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
 	if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;

 	BN_copy(d,mont_one);
 	for (i=k-1; i>=0; i--)
 		{
 		if (	(BN_cmp(d,mont_one) != 0) &&
 			(BN_cmp(d,mont_n1) != 0))
 			good=1;
 		else
 			good=0;

 		BN_mod_mul_montgomery(dd,d,d,mont,ctx2);

 		if (good && (BN_cmp(dd,mont_one) == 0))
 			{
 			ret=1;
 			goto err;
 			}
 		if (BN_is_bit_set(n1,i))
 			{
 			BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
 			}
 		else
 			{
 			tmp=d;
 			d=dd;
 			dd=tmp;
 			}
 		}
 	if (BN_cmp(d,mont_one) == 0)
 		i=0;
 	else	i=1;
 	ret=i;
 err:
 	ctx->tos-=3;
 	ctx2->tos-=3;
 	return(ret);
 	}

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

 	t1= &(ctx->bn[ctx->tos++]);

 	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:
 	ctx->tos--;
 	return(ret);
 	}

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

 	bits--;
 	t1= &(ctx->bn[ctx->tos++]);
 	q= &(ctx->bn[ctx->tos++]);
 	qadd= &(ctx->bn[ctx->tos++]);

 	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:
 	ctx->tos-=3;
 	return(ret);
 	}

 #if 0
 static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx)
 	{
 	int k,i,nb,ret= -1;
 	BIGNUM *d,*dd,*tmp;
 	BIGNUM *d1,*d2,*x,*n1,*inv;

 	d1= &(ctx->bn[ctx->tos]);
 	d2= &(ctx->bn[ctx->tos+1]);
 	x=  &(ctx->bn[ctx->tos+2]);
 	n1= &(ctx->bn[ctx->tos+3]);
 	inv=&(ctx->bn[ctx->tos+4]);
 	ctx->tos+=5;

 	d=d1;
 	dd=d2;
 	if (!BN_one(d)) goto err;
 	if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
 	k=BN_num_bits(n1);

 	/* i=BN_num_bits(n); */
 #ifdef RECP_MUL_MOD
 	nb=BN_reciprocal(inv,n,ctx); /**/
 	if (nb == -1) goto err;
 #endif

 	for (i=k-1; i>=0; i--)
 		{
 		if (BN_copy(x,d) == NULL) goto err;
 #ifndef RECP_MUL_MOD
 		if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
 #else
 		if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
 #endif
 		if (	BN_is_one(dd) &&
 			!BN_is_one(x) &&
 			(BN_cmp(x,n1) != 0))
 			{
 			ret=1;
 			goto err;
 			}
 		if (BN_is_bit_set(n1,i))
 			{
 #ifndef RECP_MUL_MOD
 			if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
 #else
 			if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
 #endif
 			}
 		else
 			{
 			tmp=d;
 			d=dd;
 			dd=tmp;
 			}
 		}
 	if (BN_is_one(d))
 		i=0;
 	else	i=1;
 	ret=i;
 err:
 	ctx->tos-=5;
 	return(ret);
 	}
 #endif
	/* 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.]
	*/

	#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"

	/* number of Miller-Rabin iterations for an error rate of less than 2^-80
	* for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
	* of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
	* original paper: Damgaard, Landrock, Pomerance: Average case error estimates
	* for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
	#define BN_prime_checks_size(b) ((b) >= 1300 ? 2 : \
	(b) >= 850 ? 3 : \
	(b) >= 650 ? 4 : \
	(b) >= 550 ? 5 : \
	(b) >= 450 ? 6 : \
	(b) >= 400 ? 7 : \
	(b) >= 350 ? 8 : \
	(b) >= 300 ? 9 : \
	(b) >= 250 ? 12 : \
	(b) >= 200 ? 15 : \
	(b) >= 150 ? 18 : \
	/* b >= 100 */ 27)

	static int witness(BIGNUM a, BIGNUM n, BN_CTX ctx,BN_CTX ctx2,
	BN_MONT_CTX *mont);
	static int probable_prime(BIGNUM *rnd, int bits);
	static int probable_prime_dh(BIGNUM *rnd, int bits,
	BIGNUM add, BIGNUM rem, BN_CTX *ctx);
	static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
	BIGNUM add, BIGNUM rem, BN_CTX *ctx);

	BIGNUM BN_generate_prime(BIGNUM ret, int bits, int safe, BIGNUM *add,
	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_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(rnd,checks,callback,ctx,cb_arg);
	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(rnd,1,callback,ctx,cb_arg);
	if (j == -1) goto err;
	if (j == 0) goto loop;

	j=BN_is_prime(&t,1,callback,ctx,cb_arg);
	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(BIGNUM a, int checks, void (callback)(int,int,void *),
	BN_CTX ctx_passed, void cb_arg)
	{
	int i,j,c2=0,ret= -1;
	BIGNUM *check;
	BN_CTX ctx=NULL,ctx2=NULL;
	BN_MONT_CTX *mont=NULL;

	if (checks == BN_prime_checks)
	{
	int bits = BN_num_bits(a);
	checks = BN_prime_checks_size(bits);
	}

	if (!BN_is_odd(a))
	return(0);
	if (ctx_passed != NULL)
	ctx=ctx_passed;
	else
	if ((ctx=BN_CTX_new()) == NULL) goto err;

	if ((ctx2=BN_CTX_new()) == NULL) goto err;
	if ((mont=BN_MONT_CTX_new()) == NULL) goto err;

	check= &(ctx->bn[ctx->tos++]);

	/* Setup the montgomery structure */
	if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;

	for (i=0; i<checks; i++)
	{
	if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
	j=witness(check,a,ctx,ctx2,mont);
	if (j == -1) goto err;
	if (j)
	{
	ret=0;
	goto err;
	}
	if (callback != NULL) callback(1,c2++,cb_arg);
	}
	ret=1;
	err:
	ctx->tos--;
	if ((ctx_passed == NULL) && (ctx != NULL))
	BN_CTX_free(ctx);
	if (ctx2 != NULL)
	BN_CTX_free(ctx2);
	if (mont != NULL) BN_MONT_CTX_free(mont);

	return(ret);
	}

	#define RECP_MUL_MOD

	static int witness(BIGNUM a, BIGNUM n, BN_CTX ctx, BN_CTX ctx2,
	BN_MONT_CTX *mont)
	{
	int k,i,ret= -1,good;
	BIGNUM d,dd,tmp,d1,d2,n1;
	BIGNUM mont_one,mont_n1,*mont_a;

	d1= &(ctx->bn[ctx->tos]);
	d2= &(ctx->bn[ctx->tos+1]);
	n1= &(ctx->bn[ctx->tos+2]);
	ctx->tos+=3;

	mont_one= &(ctx2->bn[ctx2->tos]);
	mont_n1= &(ctx2->bn[ctx2->tos+1]);
	mont_a= &(ctx2->bn[ctx2->tos+2]);
	ctx2->tos+=3;

	d=d1;
	dd=d2;
	if (!BN_one(d)) goto err;
	if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
	k=BN_num_bits(n1);

	if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
	if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
	if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;

	BN_copy(d,mont_one);
	for (i=k-1; i>=0; i--)
	{
	if ( (BN_cmp(d,mont_one) != 0) &&
	(BN_cmp(d,mont_n1) != 0))
	good=1;
	else
	good=0;

	BN_mod_mul_montgomery(dd,d,d,mont,ctx2);

	if (good && (BN_cmp(dd,mont_one) == 0))
	{
	ret=1;
	goto err;
	}
	if (BN_is_bit_set(n1,i))
	{
	BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
	}
	else
	{
	tmp=d;
	d=dd;
	dd=tmp;
	}
	}
	if (BN_cmp(d,mont_one) == 0)
	i=0;
	else i=1;
	ret=i;
	err:
	ctx->tos-=3;
	ctx2->tos-=3;
	return(ret);
	}

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

	t1= &(ctx->bn[ctx->tos++]);

	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:
	ctx->tos--;
	return(ret);
	}

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

	bits--;
	t1= &(ctx->bn[ctx->tos++]);
	q= &(ctx->bn[ctx->tos++]);
	qadd= &(ctx->bn[ctx->tos++]);

	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:
	ctx->tos-=3;
	return(ret);
	}

	#if 0
	static int witness(BIGNUM a, BIGNUM n, BN_CTX *ctx)
	{
	int k,i,nb,ret= -1;
	BIGNUM d,dd,*tmp;
	BIGNUM d1,d2,x,n1,*inv;

	d1= &(ctx->bn[ctx->tos]);
	d2= &(ctx->bn[ctx->tos+1]);
	x= &(ctx->bn[ctx->tos+2]);
	n1= &(ctx->bn[ctx->tos+3]);
	inv=&(ctx->bn[ctx->tos+4]);
	ctx->tos+=5;

	d=d1;
	dd=d2;
	if (!BN_one(d)) goto err;
	if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
	k=BN_num_bits(n1);

	/* i=BN_num_bits(n); */
	#ifdef RECP_MUL_MOD
	nb=BN_reciprocal(inv,n,ctx); /**/
	if (nb == -1) goto err;
	#endif

	for (i=k-1; i>=0; i--)
	{
	if (BN_copy(x,d) == NULL) goto err;
	#ifndef RECP_MUL_MOD
	if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
	#else
	if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
	#endif
	if ( BN_is_one(dd) &&
	!BN_is_one(x) &&
	(BN_cmp(x,n1) != 0))
	{
	ret=1;
	goto err;
	}
	if (BN_is_bit_set(n1,i))
	{
	#ifndef RECP_MUL_MOD
	if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
	#else
	if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
	#endif
	}
	else
	{
	tmp=d;
	d=dd;
	dd=tmp;
	}
	}
	if (BN_is_one(d))
	i=0;
	else i=1;
	ret=i;
	err:
	ctx->tos-=5;
	return(ret);
	}
	#endif