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/* dsa-sign.c
*
* The DSA publickey algorithm.
*/
/* nettle, low-level cryptographics library
*
* Copyright (C) 2002 Niels Mller
*
* 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 WITH_PUBLIC_KEY
#include "dsa.h"
#include "bignum.h"
#include <stdlib.h>
/* Returns a number x, almost uniformly random in the range
* 0 <= x < n. */
static void
nettle_mpz_random(mpz_t x, const mpz_t n,
void *ctx, nettle_random_func random)
{
/* 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. */
unsigned ndigits = (mpz_sizeinbase(n, 2) + 7) / 8 + 2;
uint8_t *digits = alloca(ndigits);
random(ctx, ndigits, digits);
nettle_mpz_set_str_256(x, ndigits, digits);
mpz_fdiv_r(x, x, n);
}
void
dsa_sign(struct dsa_private_key *key,
void *random_ctx, nettle_random_func random,
struct sha1_ctx *hash,
struct dsa_signature *signature)
{
mpz_t k;
mpz_t h;
mpz_t tmp;
/* Select k, 0<k<q, randomly */
mpz_init_set(tmp, key->pub.q);
mpz_sub_ui(tmp, tmp, 1);
mpz_init(k);
nettle_mpz_random(k, tmp, random_ctx, random);
mpz_add_ui(k, k, 1);
/* Compute r = (g^k (mod p)) (mod q) */
mpz_powm(tmp, key->pub.g, k, key->pub.p);
mpz_fdiv_r(signature->r, tmp, key->pub.q);
/* Compute hash */
mpz_init(h);
_dsa_hash(h, hash);
/* Compute k^-1 (mod q) */
if (!mpz_invert(k, k, key->pub.q))
/* What do we do now? The key is invalid. */
abort();
/* Compute signature s = k^-1(h + xr) (mod q) */
mpz_mul(tmp, signature->r, key->x);
mpz_fdiv_r(tmp, tmp, key->pub.q);
mpz_add(tmp, tmp, h);
mpz_mul(tmp, tmp, k);
mpz_fdiv_r(signature->s, tmp, key->pub.q);
mpz_clear(k);
mpz_clear(h);
mpz_clear(tmp);
}
#endif /* WITH_PUBLIC_KEY */