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/* 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;
}
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