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/* 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., 51 Franklin Street, Fifth Floor, Boston,
* MA 02111-1301, USA.
*/
#if HAVE_CONFIG_H
# include "config.h"
#endif
#include <stdlib.h>
#include "bignum.h"
#include "gmp-glue.h"
void
nettle_mpz_random_size(mpz_t x,
void *ctx, nettle_random_func *random,
unsigned bits)
{
unsigned length = (bits + 7) / 8;
TMP_GMP_DECL(data, uint8_t);
TMP_GMP_ALLOC(data, length);
random(ctx, length, data);
nettle_mpz_set_str_256_u(x, length, data);
if (bits % 8)
mpz_fdiv_r_2exp(x, x, bits);
TMP_GMP_FREE(data);
}
/* Returns a random number x, 0 <= x < n */
void
nettle_mpz_random(mpz_t x,
void *ctx, nettle_random_func *random,
const mpz_t n)
{
/* 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)
* 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. NIST FIPS 186-3 specifies 64 extra bits, for use with
* DSA. */
nettle_mpz_random_size(x,
ctx, random,
mpz_sizeinbase(n, 2) + 64);
mpz_fdiv_r(x, x, n);
}
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