bignum-random.c 2.63 KB
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/* bignum-random.c
 *
 * Generating big random numbers
 */

/* nettle, low-level cryptographics library
 *
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 * Copyright (C) 2002 Niels Möller
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 *  
 * 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
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 * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 * MA 02111-1301, USA.
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 */

#if HAVE_CONFIG_H
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# include "config.h"
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#endif

#include <stdlib.h>

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#include "bignum.h"
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#include "gmp-glue.h"
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void
nettle_mpz_random_size(mpz_t x,
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		       void *ctx, nettle_random_func *random,
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		       unsigned bits)
{
  unsigned length = (bits + 7) / 8;
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  TMP_GMP_DECL(data, uint8_t);
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  TMP_GMP_ALLOC(data, length);
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  random(ctx, length, data);
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  nettle_mpz_set_str_256_u(x, length, data);
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  if (bits % 8)
    mpz_fdiv_r_2exp(x, x, bits);
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  TMP_GMP_FREE(data);
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}

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/* Returns a random number x, 0 <= x < n */
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void
nettle_mpz_random(mpz_t x,
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		  void *ctx, nettle_random_func *random,
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		  const mpz_t n)
{
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  /* NOTE: This leaves some bias, which may be bad for DSA. A better
   * way might be to generate a random number of mpz_sizeinbase(n, 2)
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   * 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
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   * operation. NIST FIPS 186-3 specifies 64 extra bits, for use with
   * DSA. */
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  nettle_mpz_random_size(x, 
			 ctx, random,
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			 mpz_sizeinbase(n, 2) + 64);
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  mpz_fdiv_r(x, x, n);
}