/* 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>/* 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);	BN_init(&t);	ctx=BN_CTX_new();	if (ctx == NULL) goto err;	if (ret == NULL)		{		if ((rnd=BN_new()) == NULL) goto err;		}	else		rnd=ret;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 (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 (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_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 (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);	}