gnupg/cipher/dsa.c

/* dsa.c  -  DSA signature scheme
 *	Copyright (C) 1998 Free Software Foundation, Inc.
 *
 * This file is part of GNUPG.
 *
 * GNUPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * GNUPG 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 */

#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "util.h"
#include "mpi.h"
#include "cipher.h"
#include "dsa.h"

/****************
 * Generate a random secret exponent k less than q
 */
static MPI
gen_k( MPI q )
{
    MPI k = mpi_alloc_secure( mpi_get_nlimbs(q) );
    unsigned nbits = mpi_get_nbits(q);

    if( DBG_CIPHER )
	log_debug("choosing a random k ");
    for(;;) {
	if( DBG_CIPHER )
	    fputc('.', stderr);
	mpi_set_bytes( k, nbits , get_random_byte, 1 );
	if( !(mpi_cmp( k, q ) < 0) )  /* check: k < q */
	    continue; /* no  */
	if( !(mpi_cmp_ui( k, 0 ) > 0) ) /* check: k > 0 */
	    continue; /* no */
	break;	/* okay */
    }
    if( DBG_CIPHER )
	fputc('\n', stderr);

    return k;
}

void
dsa_free_public_key( DSA_public_key *pk )
{
    mpi_free( pk->p ); pk->p = NULL;
    mpi_free( pk->q ); pk->q = NULL;
    mpi_free( pk->g ); pk->g = NULL;
    mpi_free( pk->y ); pk->y = NULL;
}

void
dsa_free_secret_key( DSA_secret_key *sk )
{
    mpi_free( sk->p ); sk->p = NULL;
    mpi_free( sk->q ); sk->q = NULL;
    mpi_free( sk->g ); sk->g = NULL;
    mpi_free( sk->y ); sk->y = NULL;
    mpi_free( sk->x ); sk->x = NULL;
}


static void
test_keys( DSA_public_key *pk, DSA_secret_key *sk, unsigned qbits )
{
    MPI test = mpi_alloc( qbits / BITS_PER_MPI_LIMB );
    MPI out1_a = mpi_alloc( qbits / BITS_PER_MPI_LIMB );
    MPI out1_b = mpi_alloc( qbits / BITS_PER_MPI_LIMB );

    mpi_set_bytes( test, qbits, get_random_byte, 0 );

    dsa_sign( out1_a, out1_b, test, sk );
    if( !dsa_verify( out1_a, out1_b, test, pk ) )
	log_fatal("DSA:: sign, verify failed\n");

    mpi_free( test );
    mpi_free( out1_a );
    mpi_free( out1_b );
}



/****************
 * Generate a DSA key pair with a key of size NBITS
 * Returns: 2 structures filled with all needed values
 *	    and an array with the n-1 factors of (p-1)
 */
void
dsa_generate( DSA_public_key *pk, DSA_secret_key *sk,
	      unsigned nbits, MPI **ret_factors )
{
    MPI p;    /* the prime */
    MPI q;    /* the 160 bit prime factor */
    MPI g;    /* the generator */
    MPI y;    /* g^x mod p */
    MPI x;    /* the secret exponent */
    MPI h, e;  /* helper */
    unsigned qbits;
    byte *rndbuf;

    assert( nbits >= 512 && nbits <= 1024 );

    qbits = 160;
    p = generate_elg_prime( 1, nbits, qbits, NULL, ret_factors );
    /* get q out of factors */
    q = mpi_copy((*ret_factors)[0]);
    if( mpi_get_nbits(q) != qbits )
	BUG();

    /* find a generator g (h and e are helpers)*/
    /* e = (p-1)/q */
    e = mpi_alloc( mpi_get_nlimbs(p) );
    mpi_sub_ui( e, p, 1 );
    mpi_fdiv_q( e, e, q );
    g = mpi_alloc( mpi_get_nlimbs(p) );
    h = mpi_alloc_set_ui( 1 ); /* we start with 2 */
    do {
	mpi_add_ui( h, h, 1 );
	/* g = h^e mod p */
	mpi_powm( g, h, e, p );
    } while( !mpi_cmp_ui( g, 1 ) );  /* continue until g != 1 */

    /* select a random number which has these properties:
     *	 0 < x < q-1
     * This must be a very good random number because this
     * is the secret part. */
    if( DBG_CIPHER )
	log_debug("choosing a random x ");
    assert( qbits >= 16 );
    x = mpi_alloc_secure( mpi_get_nlimbs(q) );
    mpi_sub_ui( h, q, 1 );  /* put q-1 into h */
    rndbuf = NULL;
    do {
	if( DBG_CIPHER )
	    fputc('.', stderr);
	if( !rndbuf )
	    rndbuf = get_random_bits( qbits, 2, 1 );
	else { /* change only some of the higher bits (= 2 bytes)*/
	    char *r = get_random_bits( 16, 2, 1 );
	    memcpy(rndbuf, r, 16/8 );
	    m_free(r);
	}
	mpi_set_buffer( x, rndbuf, (qbits+7)/8, 0 );
	mpi_clear_highbit( x, qbits+1 );
    } while( !( mpi_cmp_ui( x, 0 )>0 && mpi_cmp( x, h )<0 ) );
    m_free(rndbuf);
    mpi_free( e );
    mpi_free( h );

    /* y = g^x mod p */
    y = mpi_alloc( mpi_get_nlimbs(p) );
    mpi_powm( y, g, x, p );

    if( DBG_CIPHER ) {
	fputc('\n', stderr);
	log_mpidump("dsa  p= ", p );
	log_mpidump("dsa  q= ", q );
	log_mpidump("dsa  g= ", g );
	log_mpidump("dsa  y= ", y );
	log_mpidump("dsa  x= ", x );
    }

    /* copy the stuff to the key structures */
    pk->p = mpi_copy(p);
    pk->q = mpi_copy(q);
    pk->g = mpi_copy(g);
    pk->y = mpi_copy(y);
    sk->p = p;
    sk->q = q;
    sk->g = g;
    sk->y = y;
    sk->x = x;

    /* now we can test our keys (this should never fail!) */
    test_keys( pk, sk, qbits );
}



/****************
 * Test whether the secret key is valid.
 * Returns: if this is a valid key.
 */
int
dsa_check_secret_key( DSA_secret_key *sk )
{
    int rc;
    MPI y = mpi_alloc( mpi_get_nlimbs(sk->y) );

    mpi_powm( y, sk->g, sk->x, sk->p );
    rc = !mpi_cmp( y, sk->y );
    mpi_free( y );
    return rc;
}



/****************
 * Make a DSA signature from HASH and put it into r and s.
 */

void
dsa_sign(MPI r, MPI s, MPI hash, DSA_secret_key *skey )
{
    MPI k;
    MPI kinv;
    MPI tmp;

    /* select a random k with 0 < k < q */
    k = gen_k( skey->q );

    /* r = (a^k mod p) mod q */
    mpi_powm( r, skey->g, k, skey->p );
    mpi_fdiv_r( r, r, skey->q );

    /* kinv = k^(-1) mod q */
    kinv = mpi_alloc( mpi_get_nlimbs(k) );
    mpi_invm(kinv, k, skey->q );

    /* s = (kinv * ( hash + x * r)) mod q */
    tmp = mpi_alloc( mpi_get_nlimbs(skey->p) );
    mpi_mul( tmp, skey->x, r );
    mpi_add( tmp, tmp, hash );
    mpi_mulm( s , kinv, tmp, skey->q );

    mpi_free(k);
    mpi_free(kinv);
    mpi_free(tmp);
}


/****************
 * Returns true if the signature composed from R and S is valid.
 */
int
dsa_verify(MPI r, MPI s, MPI hash, DSA_public_key *pkey )
{
    int rc;
    MPI w, u1, u2, v;
    MPI base[3];
    MPI exp[3];

    if( !(mpi_cmp_ui( r, 0 ) > 0 && mpi_cmp( r, pkey->q ) < 0) )
	return 0; /* assertion	0 < r < q  failed */
    if( !(mpi_cmp_ui( s, 0 ) > 0 && mpi_cmp( s, pkey->q ) < 0) )
	return 0; /* assertion	0 < s < q  failed */

    w  = mpi_alloc( mpi_get_nlimbs(pkey->q) );
    u1 = mpi_alloc( mpi_get_nlimbs(pkey->q) );
    u2 = mpi_alloc( mpi_get_nlimbs(pkey->q) );
    v  = mpi_alloc( mpi_get_nlimbs(pkey->p) );

    /* w = s^(-1) mod q */
    mpi_invm( w, s, pkey->q );

    /* u1 = (hash * w) mod q */
    mpi_mulm( u1, hash, w, pkey->q );

    /* u2 = r * w mod q  */
    mpi_mulm( u2, r, w, pkey->q );

    /* v =  g^u1 * y^u2 mod p mod q */
    base[0] = pkey->g; exp[0] = u1;
    base[1] = pkey->y; exp[1] = u2;
    base[2] = NULL;    exp[2] = NULL;
    mpi_mulpowm( v, base, exp, pkey->p );
    mpi_fdiv_r( v, v, pkey->q );

    rc = !mpi_cmp( v, r );

    mpi_free(w);
    mpi_free(u1);
    mpi_free(u2);
    mpi_free(v);
    return rc;
}