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41 results

des3.c

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  • dsa-sign.c 3.33 KiB
    /* 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(const struct dsa_public_key *pub,
    	 const 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, 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, pub->g, k, pub->p);
      mpz_fdiv_r(signature->r, tmp, pub->q);
    
      /* Compute hash */
      mpz_init(h);
      _dsa_hash(h, hash);
    
      /* Compute k^-1 (mod q) */
      if (!mpz_invert(k, k, 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, pub->q);
      mpz_add(tmp, tmp, h);
      mpz_mul(tmp, tmp, k);
      mpz_fdiv_r(signature->s, tmp, pub->q);
    
      mpz_clear(k);
      mpz_clear(h);
      mpz_clear(tmp);
    }
    
    #endif /* WITH_PUBLIC_KEY */