495 lines
14 KiB
C
495 lines
14 KiB
C
/* crypto/bn/bn_prime.c */
|
|
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
|
|
* All rights reserved.
|
|
*
|
|
* This package is an SSL implementation written
|
|
* by Eric Young (eay@cryptsoft.com).
|
|
* The implementation was written so as to conform with Netscapes SSL.
|
|
*
|
|
* This library is free for commercial and non-commercial use as long as
|
|
* the following conditions are aheared to. The following conditions
|
|
* apply to all code found in this distribution, be it the RC4, RSA,
|
|
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
|
|
* included with this distribution is covered by the same copyright terms
|
|
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
|
|
*
|
|
* Copyright remains Eric Young's, and as such any Copyright notices in
|
|
* the code are not to be removed.
|
|
* If this package is used in a product, Eric Young should be given attribution
|
|
* as the author of the parts of the library used.
|
|
* This can be in the form of a textual message at program startup or
|
|
* in documentation (online or textual) provided with the package.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
* 3. All advertising materials mentioning features or use of this software
|
|
* must display the following acknowledgement:
|
|
* "This product includes cryptographic software written by
|
|
* Eric Young (eay@cryptsoft.com)"
|
|
* The word 'cryptographic' can be left out if the rouines from the library
|
|
* being used are not cryptographic related :-).
|
|
* 4. If you include any Windows specific code (or a derivative thereof) from
|
|
* the apps directory (application code) you must include an acknowledgement:
|
|
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
|
* SUCH DAMAGE.
|
|
*
|
|
* The licence and distribution terms for any publically available version or
|
|
* derivative of this code cannot be changed. i.e. this code cannot simply be
|
|
* copied and put under another distribution licence
|
|
* [including the GNU Public Licence.]
|
|
*/
|
|
/* ====================================================================
|
|
* Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
*
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
*
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in
|
|
* the documentation and/or other materials provided with the
|
|
* distribution.
|
|
*
|
|
* 3. All advertising materials mentioning features or use of this
|
|
* software must display the following acknowledgment:
|
|
* "This product includes software developed by the OpenSSL Project
|
|
* for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
|
|
*
|
|
* 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
|
|
* endorse or promote products derived from this software without
|
|
* prior written permission. For written permission, please contact
|
|
* openssl-core@openssl.org.
|
|
*
|
|
* 5. Products derived from this software may not be called "OpenSSL"
|
|
* nor may "OpenSSL" appear in their names without prior written
|
|
* permission of the OpenSSL Project.
|
|
*
|
|
* 6. Redistributions of any form whatsoever must retain the following
|
|
* acknowledgment:
|
|
* "This product includes software developed by the OpenSSL Project
|
|
* for use in the OpenSSL Toolkit (http://www.openssl.org/)"
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
|
|
* EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
|
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
|
|
* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
|
|
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
|
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
|
|
* OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
* ====================================================================
|
|
*
|
|
* This product includes cryptographic software written by Eric Young
|
|
* (eay@cryptsoft.com). This product includes software written by Tim
|
|
* Hudson (tjh@cryptsoft.com).
|
|
*
|
|
*/
|
|
|
|
#include <stdio.h>
|
|
#include <time.h>
|
|
#include "cryptlib.h"
|
|
#include "bn_lcl.h"
|
|
#include <openssl/rand.h>
|
|
|
|
/* NB: these functions have been "upgraded", the deprecated versions (which are
|
|
* compatibility wrappers using these functions) are in bn_depr.c.
|
|
* - Geoff
|
|
*/
|
|
|
|
/* The quick sieve algorithm approach to weeding out primes is
|
|
* Philip Zimmermann's, as implemented in PGP. I have had a read of
|
|
* his comments and implemented my own version.
|
|
*/
|
|
#include "bn_prime.h"
|
|
|
|
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
|
|
const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
|
|
static int probable_prime(BIGNUM *rnd, int bits);
|
|
static int probable_prime_dh(BIGNUM *rnd, int bits,
|
|
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
|
|
static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
|
|
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
|
|
|
|
int BN_GENCB_call(BN_GENCB *cb, int a, int b)
|
|
{
|
|
/* No callback means continue */
|
|
if(!cb) return 1;
|
|
switch(cb->ver)
|
|
{
|
|
case 1:
|
|
/* Deprecated-style callbacks */
|
|
if(!cb->cb.cb_1)
|
|
return 1;
|
|
cb->cb.cb_1(a, b, cb->arg);
|
|
return 1;
|
|
case 2:
|
|
/* New-style callbacks */
|
|
return cb->cb.cb_2(a, b, cb);
|
|
default:
|
|
break;
|
|
}
|
|
/* Unrecognised callback type */
|
|
return 0;
|
|
}
|
|
|
|
int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
|
|
const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
|
|
{
|
|
BIGNUM *t;
|
|
int found=0;
|
|
int i,j,c1=0;
|
|
BN_CTX *ctx;
|
|
int checks = BN_prime_checks_for_size(bits);
|
|
|
|
ctx=BN_CTX_new();
|
|
if (ctx == NULL) goto err;
|
|
BN_CTX_start(ctx);
|
|
t = BN_CTX_get(ctx);
|
|
if(!t) goto err;
|
|
loop:
|
|
/* make a random number and set the top and bottom bits */
|
|
if (add == NULL)
|
|
{
|
|
if (!probable_prime(ret,bits)) goto err;
|
|
}
|
|
else
|
|
{
|
|
if (safe)
|
|
{
|
|
if (!probable_prime_dh_safe(ret,bits,add,rem,ctx))
|
|
goto err;
|
|
}
|
|
else
|
|
{
|
|
if (!probable_prime_dh(ret,bits,add,rem,ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
/* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
|
|
if(!BN_GENCB_call(cb, 0, c1++))
|
|
/* aborted */
|
|
goto err;
|
|
|
|
if (!safe)
|
|
{
|
|
i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb);
|
|
if (i == -1) goto err;
|
|
if (i == 0) goto loop;
|
|
}
|
|
else
|
|
{
|
|
/* for "safe prime" generation,
|
|
* check that (p-1)/2 is prime.
|
|
* Since a prime is odd, We just
|
|
* need to divide by 2 */
|
|
if (!BN_rshift1(t,ret)) goto err;
|
|
|
|
for (i=0; i<checks; i++)
|
|
{
|
|
j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb);
|
|
if (j == -1) goto err;
|
|
if (j == 0) goto loop;
|
|
|
|
j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb);
|
|
if (j == -1) goto err;
|
|
if (j == 0) goto loop;
|
|
|
|
if(!BN_GENCB_call(cb, 2, c1-1))
|
|
goto err;
|
|
/* We have a safe prime test pass */
|
|
}
|
|
}
|
|
/* we have a prime :-) */
|
|
found = 1;
|
|
err:
|
|
if (ctx != NULL)
|
|
{
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(ctx);
|
|
}
|
|
bn_check_top(ret);
|
|
return found;
|
|
}
|
|
|
|
int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
|
|
{
|
|
return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
|
|
}
|
|
|
|
int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
|
|
int do_trial_division, BN_GENCB *cb)
|
|
{
|
|
int i, j, ret = -1;
|
|
int k;
|
|
BN_CTX *ctx = NULL;
|
|
BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
|
|
BN_MONT_CTX *mont = NULL;
|
|
const BIGNUM *A = NULL;
|
|
|
|
if (BN_cmp(a, BN_value_one()) <= 0)
|
|
return 0;
|
|
|
|
if (checks == BN_prime_checks)
|
|
checks = BN_prime_checks_for_size(BN_num_bits(a));
|
|
|
|
/* first look for small factors */
|
|
if (!BN_is_odd(a))
|
|
/* a is even => a is prime if and only if a == 2 */
|
|
return BN_is_word(a, 2);
|
|
if (do_trial_division)
|
|
{
|
|
for (i = 1; i < NUMPRIMES; i++)
|
|
if (BN_mod_word(a, primes[i]) == 0)
|
|
return 0;
|
|
if(!BN_GENCB_call(cb, 1, -1))
|
|
goto err;
|
|
}
|
|
|
|
if (ctx_passed != NULL)
|
|
ctx = ctx_passed;
|
|
else
|
|
if ((ctx=BN_CTX_new()) == NULL)
|
|
goto err;
|
|
BN_CTX_start(ctx);
|
|
|
|
/* A := abs(a) */
|
|
if (a->neg)
|
|
{
|
|
BIGNUM *t;
|
|
if ((t = BN_CTX_get(ctx)) == NULL) goto err;
|
|
BN_copy(t, a);
|
|
t->neg = 0;
|
|
A = t;
|
|
}
|
|
else
|
|
A = a;
|
|
A1 = BN_CTX_get(ctx);
|
|
A1_odd = BN_CTX_get(ctx);
|
|
check = BN_CTX_get(ctx);
|
|
if (check == NULL) goto err;
|
|
|
|
/* compute A1 := A - 1 */
|
|
if (!BN_copy(A1, A))
|
|
goto err;
|
|
if (!BN_sub_word(A1, 1))
|
|
goto err;
|
|
if (BN_is_zero(A1))
|
|
{
|
|
ret = 0;
|
|
goto err;
|
|
}
|
|
|
|
/* write A1 as A1_odd * 2^k */
|
|
k = 1;
|
|
while (!BN_is_bit_set(A1, k))
|
|
k++;
|
|
if (!BN_rshift(A1_odd, A1, k))
|
|
goto err;
|
|
|
|
/* Montgomery setup for computations mod A */
|
|
mont = BN_MONT_CTX_new();
|
|
if (mont == NULL)
|
|
goto err;
|
|
if (!BN_MONT_CTX_set(mont, A, ctx))
|
|
goto err;
|
|
|
|
for (i = 0; i < checks; i++)
|
|
{
|
|
if (!BN_pseudo_rand_range(check, A1))
|
|
goto err;
|
|
if (!BN_add_word(check, 1))
|
|
goto err;
|
|
/* now 1 <= check < A */
|
|
|
|
j = witness(check, A, A1, A1_odd, k, ctx, mont);
|
|
if (j == -1) goto err;
|
|
if (j)
|
|
{
|
|
ret=0;
|
|
goto err;
|
|
}
|
|
if(!BN_GENCB_call(cb, 1, i))
|
|
goto err;
|
|
}
|
|
ret=1;
|
|
err:
|
|
if (ctx != NULL)
|
|
{
|
|
BN_CTX_end(ctx);
|
|
if (ctx_passed == NULL)
|
|
BN_CTX_free(ctx);
|
|
}
|
|
if (mont != NULL)
|
|
BN_MONT_CTX_free(mont);
|
|
|
|
return(ret);
|
|
}
|
|
|
|
static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
|
|
const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
|
|
{
|
|
if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
|
|
return -1;
|
|
if (BN_is_one(w))
|
|
return 0; /* probably prime */
|
|
if (BN_cmp(w, a1) == 0)
|
|
return 0; /* w == -1 (mod a), 'a' is probably prime */
|
|
while (--k)
|
|
{
|
|
if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
|
|
return -1;
|
|
if (BN_is_one(w))
|
|
return 1; /* 'a' is composite, otherwise a previous 'w' would
|
|
* have been == -1 (mod 'a') */
|
|
if (BN_cmp(w, a1) == 0)
|
|
return 0; /* w == -1 (mod a), 'a' is probably prime */
|
|
}
|
|
/* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
|
|
* and it is neither -1 nor +1 -- so 'a' cannot be prime */
|
|
bn_check_top(w);
|
|
return 1;
|
|
}
|
|
|
|
static int probable_prime(BIGNUM *rnd, int bits)
|
|
{
|
|
int i;
|
|
prime_t mods[NUMPRIMES];
|
|
BN_ULONG delta,maxdelta;
|
|
|
|
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]=(prime_t)BN_mod_word(rnd,(BN_ULONG)primes[i]);
|
|
maxdelta=BN_MASK2 - primes[NUMPRIMES-1];
|
|
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)
|
|
{
|
|
delta+=2;
|
|
if (delta > maxdelta) goto again;
|
|
goto loop;
|
|
}
|
|
}
|
|
if (!BN_add_word(rnd,delta)) return(0);
|
|
bn_check_top(rnd);
|
|
return(1);
|
|
}
|
|
|
|
static int probable_prime_dh(BIGNUM *rnd, int bits,
|
|
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
|
|
{
|
|
int i,ret=0;
|
|
BIGNUM *t1;
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
|
|
|
|
if (!BN_rand(rnd,bits,0,1)) goto err;
|
|
|
|
/* we need ((rnd-rem) % add) == 0 */
|
|
|
|
if (!BN_mod(t1,rnd,add,ctx)) goto err;
|
|
if (!BN_sub(rnd,rnd,t1)) goto err;
|
|
if (rem == NULL)
|
|
{ if (!BN_add_word(rnd,1)) goto err; }
|
|
else
|
|
{ if (!BN_add(rnd,rnd,rem)) goto err; }
|
|
|
|
/* we now have a random number 'rand' to test. */
|
|
|
|
loop: for (i=1; i<NUMPRIMES; i++)
|
|
{
|
|
/* check that rnd is a prime */
|
|
if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
|
|
{
|
|
if (!BN_add(rnd,rnd,add)) goto err;
|
|
goto loop;
|
|
}
|
|
}
|
|
ret=1;
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rnd);
|
|
return(ret);
|
|
}
|
|
|
|
static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
|
|
const BIGNUM *rem, BN_CTX *ctx)
|
|
{
|
|
int i,ret=0;
|
|
BIGNUM *t1,*qadd,*q;
|
|
|
|
bits--;
|
|
BN_CTX_start(ctx);
|
|
t1 = BN_CTX_get(ctx);
|
|
q = BN_CTX_get(ctx);
|
|
qadd = BN_CTX_get(ctx);
|
|
if (qadd == NULL) goto err;
|
|
|
|
if (!BN_rshift1(qadd,padd)) goto err;
|
|
|
|
if (!BN_rand(q,bits,0,1)) goto err;
|
|
|
|
/* we need ((rnd-rem) % add) == 0 */
|
|
if (!BN_mod(t1,q,qadd,ctx)) goto err;
|
|
if (!BN_sub(q,q,t1)) goto err;
|
|
if (rem == NULL)
|
|
{ if (!BN_add_word(q,1)) goto err; }
|
|
else
|
|
{
|
|
if (!BN_rshift1(t1,rem)) goto err;
|
|
if (!BN_add(q,q,t1)) goto err;
|
|
}
|
|
|
|
/* we now have a random number 'rand' to test. */
|
|
if (!BN_lshift1(p,q)) goto err;
|
|
if (!BN_add_word(p,1)) goto err;
|
|
|
|
loop: for (i=1; i<NUMPRIMES; i++)
|
|
{
|
|
/* check that p and q are prime */
|
|
/* check that for p and q
|
|
* gcd(p-1,primes) == 1 (except for 2) */
|
|
if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
|
|
(BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
|
|
{
|
|
if (!BN_add(p,p,padd)) goto err;
|
|
if (!BN_add(q,q,qadd)) goto err;
|
|
goto loop;
|
|
}
|
|
}
|
|
ret=1;
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(p);
|
|
return(ret);
|
|
}
|