Use uniformly chosen witnesses for Miller-Rabin test

(by using new BN_pseudo_rand_range function)

CHANGES

@@ -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]
 

crypto/bn/bn.h

@@ -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);

crypto/bn/bn_prime.c

@@ -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 */

crypto/bn/bn_rand.c

@@ -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);
+	}

doc/crypto/BN_rand.pod

@@ -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

doc/crypto/bn.pod

@@ -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);