/* dsa-sign.c * * The DSA publickey algorithm. */ /* nettle, low-level cryptographics library * * Copyright (C) 2002 Niels M�ller * * 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 */ _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 */