* bignum-random.c: New file.

(nettle_mpz_random): New function.
(nettle_mpz_random_size): New function, renamed and moved here
from...
* rsa-keygen.c (bignum_random_size): ... here. Updated all
callers.

Rev: src/nettle/bignum-random.c:1.1
Rev: src/nettle/rsa-keygen.c:1.4

bignum-random.c

+/* bignum-random.c
+ *
+ * Generating big random numbers
+ */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2002 Niels Möller
+ *  
+ * The nettle library is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published by
+ * the Free Software Foundation; either version 2.1 of the License, or (at your
+ * option) any later version.
+ * 
+ * The nettle library is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+ * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+ * License for more details.
+ * 
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ */
+
+#if HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#if HAVE_LIBGMP
+
+#include "bignum.h"
+
+#include <stdlib.h>
+
+void
+nettle_mpz_random_size(mpz_t x,
+		       void *ctx, nettle_random_func random,
+		       unsigned bits)
+{
+  unsigned length = (bits + 7) / 8;
+  uint8_t *data = alloca(length);
+
+  random(ctx, length, data);
+
+  nettle_mpz_set_str_256(x, length, data);
+
+  if (bits % 8)
+    mpz_fdiv_r_2exp(x, x, bits);
+}
+
+void
+nettle_mpz_random(mpz_t x,
+		  void *ctx, nettle_random_func random,
+		  const mpz_t n)
+{
+  /* FIXME: This leaves some bias, which may be bad for DSA. A better
+   * way might to generate a random number of mpz_sizeinbase(n, 2)
+   * bits, and loop until one smaller than n is found. */
+
+  /* From Daniel Bleichenbacher (via coderpunks):
+   *
+   * There is still a theoretical attack possible with 8 extra bits.
+   * But, the attack would need about 2^66 signatures 2^66 memory and
+   * 2^66 time (if I remember that correctly). Compare that to DSA,
+   * where the attack requires 2^22 signatures 2^40 memory and 2^64
+   * time. And of course, the numbers above are not a real threat for
+   * PGP. Using 16 extra bits (i.e. generating a 176 bit random number
+   * and reducing it modulo q) will defeat even this theoretical
+   * attack.
+   * 
+   * More generally log_2(q)/8 extra bits are enough to defeat my
+   * attack. NIST also plans to update the standard.
+   */
+
+  /* Add a few bits extra, to decrease the bias from the final modulo
+   * operation. */
+
+  nettle_mpz_random_size(x, 
+			 ctx, random,
+			 mpz_sizeinbase(n, 2) + 16);
+  
+  mpz_fdiv_r(x, x, n);
+}
+
+#endif /* HAVE_LIBGMP */

rsa-keygen.c

@@ -44,21 +44,6 @@
 # include <stdio.h>
 #endif
 
-/* Returns a random number, 0 <= x < 2^bits. */
-static void
-bignum_random_size(mpz_t x, unsigned bits,
-		   void *random_ctx, nettle_random_func random)
-{
-  unsigned length = (bits + 7) / 8;
-  uint8_t *data = alloca(length);
-
-  random(random_ctx, length, data);
-
-  nettle_mpz_set_str_256(x, length, data);
-
-  if (bits % 8)
-    mpz_fdiv_r_2exp(x, x, bits);
-}
 
 #define NUMBER_OF_PRIMES 167
 
@@ -172,7 +157,7 @@ bignum_random_prime(mpz_t x, unsigned bits,
   
   for (;;)
     {
-      bignum_random_size(x, bits, random_ctx, random);
+      nettle_mpz_random_size(x, random_ctx, random, bits);
       mpz_setbit(x, bits - 1);
 
       /* Miller-rabin count of 25 is probably much overkill. */
@@ -307,8 +292,9 @@ rsa_generate_keypair(struct rsa_public_key *pub,
       int retried = 0;
       for (;;)
 	{
-	  bignum_random_size(pub->e, e_size,
-			     random_ctx, random);
+	  nettle_mpz_random_size(pub->e,
+				 random_ctx, random,
+				 e_size);
 	
 	  /* Make sure it's odd and that the most significant bit is
 	   * set */