[thirdparty/openssl.git] / crypto / bn / 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 */
		cb->cb_1(a, b, cb->arg);
		return 1;
	case 2:
		/* New-style callbacks */
		return 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_init(&t);
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:
	BN_free(&t);
	if (ctx != NULL) BN_CTX_free(ctx);
	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 */
	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);
	}
Commit	Line	Data
d02b48c6	1	/* crypto/bn/bn_prime.c */
58964a49	2	/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
d02b48c6 RE	3	* All rights reserved.
	4	*
	5	* This package is an SSL implementation written
	6	* by Eric Young (eay@cryptsoft.com).
	7	* The implementation was written so as to conform with Netscapes SSL.
	8	*
	9	* This library is free for commercial and non-commercial use as long as
	10	* the following conditions are aheared to. The following conditions
	11	* apply to all code found in this distribution, be it the RC4, RSA,
	12	* lhash, DES, etc., code; not just the SSL code. The SSL documentation
	13	* included with this distribution is covered by the same copyright terms
	14	* except that the holder is Tim Hudson (tjh@cryptsoft.com).
	15	*
	16	* Copyright remains Eric Young's, and as such any Copyright notices in
	17	* the code are not to be removed.
	18	* If this package is used in a product, Eric Young should be given attribution
	19	* as the author of the parts of the library used.
	20	* This can be in the form of a textual message at program startup or
	21	* in documentation (online or textual) provided with the package.
	22	*
	23	* Redistribution and use in source and binary forms, with or without
	24	* modification, are permitted provided that the following conditions
	25	* are met:
	26	* 1. Redistributions of source code must retain the copyright
	27	* notice, this list of conditions and the following disclaimer.
	28	* 2. Redistributions in binary form must reproduce the above copyright
	29	* notice, this list of conditions and the following disclaimer in the
	30	* documentation and/or other materials provided with the distribution.
	31	* 3. All advertising materials mentioning features or use of this software
	32	* must display the following acknowledgement:
	33	* "This product includes cryptographic software written by
	34	* Eric Young (eay@cryptsoft.com)"
	35	* The word 'cryptographic' can be left out if the rouines from the library
	36	* being used are not cryptographic related :-).
	37	* 4. If you include any Windows specific code (or a derivative thereof) from
	38	* the apps directory (application code) you must include an acknowledgement:
	39	* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
	40	*
	41	* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
	42	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	43	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	44	* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
	45	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	46	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	47	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	48	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	49	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	50	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	51	* SUCH DAMAGE.
	52	*
	53	* The licence and distribution terms for any publically available version or
	54	* derivative of this code cannot be changed. i.e. this code cannot simply be
	55	* copied and put under another distribution licence
	56	* [including the GNU Public Licence.]
	57	*/
bfe30e4d	58	/* ====================================================================
435037d4	59	* Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
bfe30e4d BM	60	*
	61	* Redistribution and use in source and binary forms, with or without
	62	* modification, are permitted provided that the following conditions
	63	* are met:
	64	*
	65	* 1. Redistributions of source code must retain the above copyright
	66	* notice, this list of conditions and the following disclaimer.
	67	*
	68	* 2. Redistributions in binary form must reproduce the above copyright
	69	* notice, this list of conditions and the following disclaimer in
	70	* the documentation and/or other materials provided with the
	71	* distribution.
	72	*
	73	* 3. All advertising materials mentioning features or use of this
	74	* software must display the following acknowledgment:
	75	* "This product includes software developed by the OpenSSL Project
	76	* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
	77	*
	78	* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
	79	* endorse or promote products derived from this software without
	80	* prior written permission. For written permission, please contact
	81	* openssl-core@openssl.org.
	82	*
	83	* 5. Products derived from this software may not be called "OpenSSL"
	84	* nor may "OpenSSL" appear in their names without prior written
	85	* permission of the OpenSSL Project.
	86	*
	87	* 6. Redistributions of any form whatsoever must retain the following
	88	* acknowledgment:
	89	* "This product includes software developed by the OpenSSL Project
	90	* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
	91	*
	92	* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
	93	* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	94	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
	95	* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
	96	* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
	97	* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
	98	* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
	99	* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	100	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
	101	* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
	102	* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
	103	* OF THE POSSIBILITY OF SUCH DAMAGE.
	104	* ====================================================================
	105	*
	106	* This product includes cryptographic software written by Eric Young
	107	* (eay@cryptsoft.com). This product includes software written by Tim
	108	* Hudson (tjh@cryptsoft.com).
	109	*
	110	*/
d02b48c6 RE	111
	112	#include <stdio.h>
	113	#include <time.h>
	114	#include "cryptlib.h"
	115	#include "bn_lcl.h"
ec577822	116	#include <openssl/rand.h>
d02b48c6	117
e9224c71 GT	118	/* NB: these functions have been "upgraded", the deprecated versions (which are
	119	* compatibility wrappers using these functions) are in bn_depr.c.
	120	* - Geoff
	121	*/
	122
4486d0cd	123	/* The quick sieve algorithm approach to weeding out primes is
d02b48c6 RE	124	* Philip Zimmermann's, as implemented in PGP. I have had a read of
	125	* his comments and implemented my own version.
	126	*/
	127	#include "bn_prime.h"
	128
7999c65c BM	129	static int witness(BIGNUM w, const BIGNUM a, const BIGNUM *a1,
7999c65c BM	130	const BIGNUM a1_odd, int k, BN_CTX ctx, BN_MONT_CTX *mont);
d02b48c6 RE	131	static int probable_prime(BIGNUM *rnd, int bits);
d02b48c6 RE	132	static int probable_prime_dh(BIGNUM *rnd, int bits,
020fc820	133	const BIGNUM add, const BIGNUM rem, BN_CTX *ctx);
76aa0ddc	134	static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
020fc820	135	const BIGNUM add, const BIGNUM rem, BN_CTX *ctx);
eb952088	136
e9224c71 GT	137	int BN_GENCB_call(BN_GENCB *cb, int a, int b)
	138	{
	139	/* No callback means continue */
	140	if(!cb) return 1;
	141	switch(cb->ver)
	142	{
	143	case 1:
	144	/* Deprecated-style callbacks */
	145	cb->cb_1(a, b, cb->arg);
	146	return 1;
	147	case 2:
	148	/* New-style callbacks */
	149	return cb->cb_2(a, b, cb);
	150	default:
	151	break;
	152	}
	153	/* Unrecognised callback type */
	154	return 0;
	155	}
	156
	157	int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
	158	const BIGNUM add, const BIGNUM rem, BN_GENCB *cb)
d02b48c6	159	{
dfeab068	160	BIGNUM t;
4486d0cd	161	int found=0;
d02b48c6	162	int i,j,c1=0;
e74231ed	163	BN_CTX *ctx;
a87030a1	164	int checks = BN_prime_checks_for_size(bits);
d02b48c6 RE	165
	166	ctx=BN_CTX_new();
	167	if (ctx == NULL) goto err;
dfeab068	168	BN_init(&t);
d02b48c6 RE	169	loop:
	170	/* make a random number and set the top and bottom bits */
	171	if (add == NULL)
	172	{
e9224c71	173	if (!probable_prime(ret,bits)) goto err;
d02b48c6 RE	174	}
	175	else
	176	{
76aa0ddc	177	if (safe)
d02b48c6	178	{
e9224c71	179	if (!probable_prime_dh_safe(ret,bits,add,rem,ctx))
d02b48c6 RE	180	goto err;
	181	}
	182	else
	183	{
e9224c71	184	if (!probable_prime_dh(ret,bits,add,rem,ctx))
d02b48c6 RE	185	goto err;
	186	}
	187	}
e9224c71 GT	188	/* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
	189	if(!BN_GENCB_call(cb, 0, c1++))
	190	/* aborted */
	191	goto err;
d02b48c6	192
76aa0ddc	193	if (!safe)
d02b48c6	194	{
e9224c71	195	i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb);
d02b48c6 RE	196	if (i == -1) goto err;
	197	if (i == 0) goto loop;
	198	}
	199	else
	200	{
76aa0ddc	201	/* for "safe prime" generation,
d02b48c6 RE	202	* check that (p-1)/2 is prime.
	203	* Since a prime is odd, We just
	204	* need to divide by 2 */
e9224c71	205	if (!BN_rshift1(&t,ret)) goto err;
d02b48c6	206
76aa0ddc	207	for (i=0; i<checks; i++)
d02b48c6	208	{
e9224c71	209	j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb);
d02b48c6 RE	210	if (j == -1) goto err;
	211	if (j == 0) goto loop;
	212
e9224c71	213	j=BN_is_prime_fasttest_ex(&t,1,ctx,0,cb);
d02b48c6 RE	214	if (j == -1) goto err;
	215	if (j == 0) goto loop;
	216
e9224c71 GT	217	if(!BN_GENCB_call(cb, 2, c1-1))
e9224c71 GT	218	goto err;
76aa0ddc	219	/* We have a safe prime test pass */
d02b48c6 RE	220	}
	221	}
	222	/* we have a prime :-) */
4486d0cd	223	found = 1;
d02b48c6	224	err:
dfeab068	225	BN_free(&t);
d02b48c6	226	if (ctx != NULL) BN_CTX_free(ctx);
e9224c71	227	return found;
d02b48c6 RE	228	}
d02b48c6 RE	229
e9224c71	230	int BN_is_prime_ex(const BIGNUM a, int checks, BN_CTX ctx_passed, BN_GENCB *cb)
e74231ed	231	{
e9224c71	232	return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
e74231ed BM	233	}
e74231ed BM	234
e9224c71 GT	235	int BN_is_prime_fasttest_ex(const BIGNUM a, int checks, BN_CTX ctx_passed,
e9224c71 GT	236	int do_trial_division, BN_GENCB *cb)
d02b48c6	237	{
e74231ed BM	238	int i, j, ret = -1;
	239	int k;
	240	BN_CTX *ctx = NULL;
aff0825c	241	BIGNUM A1, A1_odd, check; / taken from ctx */
e74231ed	242	BN_MONT_CTX *mont = NULL;
657e60fa	243	const BIGNUM *A = NULL;
d02b48c6	244
91b3f0e6	245	if (BN_cmp(a, BN_value_one()) <= 0)
983495c4 BM	246	return 0;
983495c4 BM	247
4486d0cd	248	if (checks == BN_prime_checks)
e74231ed BM	249	checks = BN_prime_checks_for_size(BN_num_bits(a));
e74231ed BM	250
e74231ed	251	/* first look for small factors */
58964a49	252	if (!BN_is_odd(a))
983495c4	253	return 0;
a87030a1	254	if (do_trial_division)
1baa9490	255	{
a87030a1 BM	256	for (i = 1; i < NUMPRIMES; i++)
	257	if (BN_mod_word(a, primes[i]) == 0)
	258	return 0;
e9224c71 GT	259	if(!BN_GENCB_call(cb, 1, -1))
e9224c71 GT	260	goto err;
1baa9490	261	}
a87030a1	262
d02b48c6	263	if (ctx_passed != NULL)
e74231ed	264	ctx = ctx_passed;
d02b48c6	265	else
e74231ed BM	266	if ((ctx=BN_CTX_new()) == NULL)
e74231ed BM	267	goto err;
9b141126 UM	268	BN_CTX_start(ctx);
9b141126 UM	269
aff0825c BM	270	/* A := abs(a) */
	271	if (a->neg)
	272	{
9b141126 UM	273	BIGNUM *t;
9b141126 UM	274	if ((t = BN_CTX_get(ctx)) == NULL) goto err;
7999c65c BM	275	BN_copy(t, a);
	276	t->neg = 0;
	277	A = t;
aff0825c BM	278	}
	279	else
	280	A = a;
9b141126 UM	281	A1 = BN_CTX_get(ctx);
	282	A1_odd = BN_CTX_get(ctx);
	283	check = BN_CTX_get(ctx);
	284	if (check == NULL) goto err;
e74231ed	285
aff0825c BM	286	/* compute A1 := A - 1 */
aff0825c BM	287	if (!BN_copy(A1, A))
e74231ed	288	goto err;
aff0825c	289	if (!BN_sub_word(A1, 1))
e74231ed	290	goto err;
aff0825c	291	if (BN_is_zero(A1))
e74231ed BM	292	{
	293	ret = 0;
	294	goto err;
	295	}
58964a49	296
aff0825c	297	/* write A1 as A1_odd * 2^k */
e74231ed	298	k = 1;
aff0825c	299	while (!BN_is_bit_set(A1, k))
e74231ed	300	k++;
aff0825c	301	if (!BN_rshift(A1_odd, A1, k))
e74231ed BM	302	goto err;
e74231ed BM	303
aff0825c	304	/* Montgomery setup for computations mod A */
e74231ed BM	305	mont = BN_MONT_CTX_new();
	306	if (mont == NULL)
	307	goto err;
aff0825c	308	if (!BN_MONT_CTX_set(mont, A, ctx))
e74231ed BM	309	goto err;
	310
	311	for (i = 0; i < checks; i++)
d02b48c6	312	{
983495c4	313	if (!BN_pseudo_rand_range(check, A1))
e74231ed	314	goto err;
e74231ed BM	315	if (!BN_add_word(check, 1))
e74231ed BM	316	goto err;
aff0825c	317	/* now 1 <= check < A */
e74231ed	318
aff0825c	319	j = witness(check, A, A1, A1_odd, k, ctx, mont);
d02b48c6 RE	320	if (j == -1) goto err;
	321	if (j)
	322	{
	323	ret=0;
	324	goto err;
	325	}
e9224c71 GT	326	if(!BN_GENCB_call(cb, 1, i))
e9224c71 GT	327	goto err;
d02b48c6 RE	328	}
	329	ret=1;
	330	err:
9b141126	331	if (ctx != NULL)
aff0825c	332	{
9b141126 UM	333	BN_CTX_end(ctx);
	334	if (ctx_passed == NULL)
	335	BN_CTX_free(ctx);
aff0825c	336	}
e74231ed BM	337	if (mont != NULL)
e74231ed BM	338	BN_MONT_CTX_free(mont);
d02b48c6	339
e74231ed	340	return(ret);
a87030a1 BM	341	}
a87030a1 BM	342
7999c65c BM	343	static int witness(BIGNUM w, const BIGNUM a, const BIGNUM *a1,
7999c65c BM	344	const BIGNUM a1_odd, int k, BN_CTX ctx, BN_MONT_CTX *mont)
d02b48c6	345	{
e74231ed BM	346	if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
	347	return -1;
	348	if (BN_is_one(w))
	349	return 0; /* probably prime */
	350	if (BN_cmp(w, a1) == 0)
	351	return 0; /* w == -1 (mod a), 'a' is probably prime */
	352	while (--k)
d02b48c6	353	{
e74231ed BM	354	if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
	355	return -1;
	356	if (BN_is_one(w))
	357	return 1; /* 'a' is composite, otherwise a previous 'w' would
	358	* have been == -1 (mod 'a') */
	359	if (BN_cmp(w, a1) == 0)
	360	return 0; /* w == -1 (mod a), 'a' is probably prime */
d02b48c6	361	}
e74231ed BM	362	/* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
	363	* and it is neither -1 nor +1 -- so 'a' cannot be prime */
	364	return 1;
d02b48c6 RE	365	}
d02b48c6 RE	366
6b691a5c	367	static int probable_prime(BIGNUM *rnd, int bits)
d02b48c6 RE	368	{
d02b48c6 RE	369	int i;
a87030a1	370	BN_ULONG mods[NUMPRIMES];
dfeab068	371	BN_ULONG delta,d;
d02b48c6	372
dfeab068	373	again:
d02b48c6 RE	374	if (!BN_rand(rnd,bits,1,1)) return(0);
	375	/* we now have a random number 'rand' to test. */
	376	for (i=1; i<NUMPRIMES; i++)
	377	mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
	378	delta=0;
	379	loop: for (i=1; i<NUMPRIMES; i++)
	380	{
	381	/* check that rnd is not a prime and also
	382	* that gcd(rnd-1,primes) == 1 (except for 2) */
	383	if (((mods[i]+delta)%primes[i]) <= 1)
	384	{
dfeab068	385	d=delta;
d02b48c6 RE	386	delta+=2;
d02b48c6 RE	387	/* perhaps need to check for overflow of
657e60fa	388	* delta (but delta can be up to 2^32)
dfeab068 RE	389	* 21-May-98 eay - added overflow check */
dfeab068 RE	390	if (delta < d) goto again;
d02b48c6 RE	391	goto loop;
	392	}
	393	}
	394	if (!BN_add_word(rnd,delta)) return(0);
	395	return(1);
	396	}
	397
020fc820 RL	398	static int probable_prime_dh(BIGNUM *rnd, int bits,
020fc820 RL	399	const BIGNUM add, const BIGNUM rem, BN_CTX *ctx)
d02b48c6 RE	400	{
	401	int i,ret=0;
	402	BIGNUM *t1;
	403
9b141126 UM	404	BN_CTX_start(ctx);
9b141126 UM	405	if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
d02b48c6 RE	406
	407	if (!BN_rand(rnd,bits,0,1)) goto err;
	408
	409	/* we need ((rnd-rem) % add) == 0 */
	410
	411	if (!BN_mod(t1,rnd,add,ctx)) goto err;
	412	if (!BN_sub(rnd,rnd,t1)) goto err;
	413	if (rem == NULL)
	414	{ if (!BN_add_word(rnd,1)) goto err; }
	415	else
	416	{ if (!BN_add(rnd,rnd,rem)) goto err; }
	417
	418	/* we now have a random number 'rand' to test. */
	419
	420	loop: for (i=1; i<NUMPRIMES; i++)
	421	{
	422	/* check that rnd is a prime */
e14d4443	423	if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
d02b48c6 RE	424	{
	425	if (!BN_add(rnd,rnd,add)) goto err;
	426	goto loop;
	427	}
	428	}
	429	ret=1;
	430	err:
9b141126	431	BN_CTX_end(ctx);
d02b48c6 RE	432	return(ret);
	433	}
	434
020fc820 RL	435	static int probable_prime_dh_safe(BIGNUM p, int bits, const BIGNUM padd,
020fc820 RL	436	const BIGNUM rem, BN_CTX ctx)
d02b48c6 RE	437	{
d02b48c6 RE	438	int i,ret=0;
9b141126	439	BIGNUM t1,qadd,*q;
d02b48c6 RE	440
d02b48c6 RE	441	bits--;
9b141126 UM	442	BN_CTX_start(ctx);
	443	t1 = BN_CTX_get(ctx);
	444	q = BN_CTX_get(ctx);
	445	qadd = BN_CTX_get(ctx);
	446	if (qadd == NULL) goto err;
d02b48c6 RE	447
	448	if (!BN_rshift1(qadd,padd)) goto err;
	449
	450	if (!BN_rand(q,bits,0,1)) goto err;
	451
	452	/* we need ((rnd-rem) % add) == 0 */
	453	if (!BN_mod(t1,q,qadd,ctx)) goto err;
	454	if (!BN_sub(q,q,t1)) goto err;
	455	if (rem == NULL)
	456	{ if (!BN_add_word(q,1)) goto err; }
	457	else
	458	{
	459	if (!BN_rshift1(t1,rem)) goto err;
	460	if (!BN_add(q,q,t1)) goto err;
	461	}
	462
	463	/* we now have a random number 'rand' to test. */
	464	if (!BN_lshift1(p,q)) goto err;
	465	if (!BN_add_word(p,1)) goto err;
	466
	467	loop: for (i=1; i<NUMPRIMES; i++)
	468	{
	469	/* check that p and q are prime */
	470	/* check that for p and q
	471	* gcd(p-1,primes) == 1 (except for 2) */
e14d4443 UM	472	if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) \|\|
e14d4443 UM	473	(BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
d02b48c6 RE	474	{
	475	if (!BN_add(p,p,padd)) goto err;
	476	if (!BN_add(q,q,qadd)) goto err;
	477	goto loop;
	478	}
	479	}
	480	ret=1;
	481	err:
9b141126	482	BN_CTX_end(ctx);
d02b48c6 RE	483	return(ret);
d02b48c6 RE	484	}