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Use uniformly chosen witnesses for Miller-Rabin test

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(by using new BN_pseudo_rand_range function)
This commit is contained in:
Bodo Möller 2001-09-03 12:58:16 +00:00
parent 931a23a5a5
commit 983495c4b2
6 changed files with 89 additions and 8 deletions
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9
CHANGES
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@ -12,6 +12,15 @@
*) applies to 0.9.6a/0.9.6b/0.9.6c and 0.9.7
+) applies to 0.9.7 only
*) Rabin-Miller test analyses assume uniformly distributed witnesses,
so use BN_pseudo_rand_range() instead of using BN_pseudo_rand()
followed by modular reduction.
[Bodo Moeller; pointed out by Adam Young <AYoung1@NCSUS.JNJ.COM>]
*) Add BN_pseudo_rand_range() with obvious functionality: BN_rand_range()
requivalent based on BN_pseudo_rand() instead of BN_rand().
[Bodo Moeller]
+) Add a copy() function to EVP_MD.
[Ben Laurie]

1
crypto/bn/bn.h
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@ -321,6 +321,7 @@ void BN_CTX_end(BN_CTX *ctx);
int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
int BN_pseudo_rand(BIGNUM *rnd, int bits, int top,int bottom);
int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
int BN_num_bits(const BIGNUM *a);
int BN_num_bits_word(BN_ULONG);
BIGNUM *BN_new(void);

10
crypto/bn/bn_prime.c
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@ -226,12 +226,15 @@ int BN_is_prime_fasttest(const BIGNUM *a, int checks,
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);
return 0;
if (do_trial_division)
{
for (i = 1; i < NUMPRIMES; i++)
@ -290,11 +293,8 @@ int BN_is_prime_fasttest(const BIGNUM *a, int checks,
for (i = 0; i < checks; i++)
{
if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0))
if (!BN_pseudo_rand_range(check, A1))
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 */

71
crypto/bn/bn_rand.c
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@ -55,6 +55,59 @@
* 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>
@ -173,8 +226,9 @@ int BN_bntest_rand(BIGNUM *rnd, int bits, int top, int bottom)
/* random number r: 0 <= r < range */
int BN_rand_range(BIGNUM *r, BIGNUM *range)
static int bn_rand_range(int pseudo, BIGNUM *r, BIGNUM *range)
{
int (*bn_rand)(BIGNUM *, int, int, int) = pseudo ? BN_pseudo_rand : BN_rand;
int n;
if (range->neg || BN_is_zero(range))
@ -194,7 +248,7 @@ int BN_rand_range(BIGNUM *r, BIGNUM *range)
do
{
/* range = 11..._2, so each iteration succeeds with probability >= .75 */
if (!BN_rand(r, n, -1, 0)) return 0;
if (!bn_rand(r, n, -1, 0)) return 0;
}
while (BN_cmp(r, range) >= 0);
}
@ -204,7 +258,7 @@ int BN_rand_range(BIGNUM *r, BIGNUM *range)
* so 3*range (= 11..._2) is exactly one bit longer than range */
do
{
if (!BN_rand(r, n + 1, -1, 0)) return 0;
if (!bn_rand(r, n + 1, -1, 0)) return 0;
/* If r < 3*range, use r := r MOD range
* (which is either r, r - range, or r - 2*range).
* Otherwise, iterate once more.
@ -222,3 +276,14 @@ int BN_rand_range(BIGNUM *r, BIGNUM *range)
return 1;
}
int BN_rand_range(BIGNUM *r, BIGNUM *range)
{
return bn_rand_range(0, r, range);
}
int BN_pseudo_rand_range(BIGNUM *r, BIGNUM *range)
{
return bn_rand_range(1, r, range);
}

5
doc/crypto/BN_rand.pod
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@ -14,6 +14,8 @@ BN_rand, BN_pseudo_rand - generate pseudo-random number
int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
int BN_pseudo_rand_range(BIGNUM *rnd, int bits, int top, int bottom);
=head1 DESCRIPTION
BN_rand() generates a cryptographically strong pseudo-random number of
@ -31,6 +33,8 @@ protocols, but usually not for key generation etc.
BN_rand_range() generates a cryptographically strong pseudo-random
number B<rnd> in the range 0 <lt>= B<rnd> E<lt> B<range>.
BN_pseudo_rand_range() does the same, but is based on BN_pseudo_rand(),
and hence numbers generated by it are not necessarily unpredictable.
The PRNG must be seeded prior to calling BN_rand() or BN_rand_range().
@ -49,5 +53,6 @@ L<RAND_add(3)|RAND_add(3)>, L<RAND_bytes(3)|RAND_bytes(3)>
BN_rand() is available in all versions of SSLeay and OpenSSL.
BN_pseudo_rand() was added in OpenSSL 0.9.5. The B<top> == -1 case
and the function BN_rand_range() were added in OpenSSL 0.9.6a.
BN_pseudo_rand_range() was added in OpenSSL 0.9.6c.
=cut

1
doc/crypto/bn.pod
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@ -69,6 +69,7 @@ bn - multiprecision integer arithmetics
int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);