/* elgamal.c - ElGamal Public Key encryption
* Copyright (C) 1998 Free Software Foundation, Inc.
*
* For a description of the algorithm, see:
* Bruce Schneier: Applied Cryptography. John Wiley & Sons, 1996.
* ISBN 0-471-11709-9. Pages 476 ff.
*
* 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 "util.h"
#include "mpi.h"
#include "cipher.h"
#include "elgamal.h"
typedef struct {
MPI p; /* prime */
MPI g; /* group generator */
MPI y; /* g^x mod p */
} ELG_public_key;
typedef struct {
MPI p; /* prime */
MPI g; /* group generator */
MPI y; /* g^x mod p */
MPI x; /* secret exponent */
} ELG_secret_key;
static void test_keys( ELG_secret_key *sk, unsigned nbits );
static MPI gen_k( MPI p );
static void generate( ELG_secret_key *sk, unsigned nbits, MPI **factors );
static int check_secret_key( ELG_secret_key *sk );
static void encrypt(MPI a, MPI b, MPI input, ELG_public_key *pkey );
static void decrypt(MPI output, MPI a, MPI b, ELG_secret_key *skey );
static void sign(MPI a, MPI b, MPI input, ELG_secret_key *skey);
static int verify(MPI a, MPI b, MPI input, ELG_public_key *pkey);
static void
test_keys( ELG_secret_key *sk, unsigned nbits )
{
ELG_public_key pk;
MPI test = mpi_alloc( 0 );
MPI out1_a = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
MPI out1_b = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
MPI out2 = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
pk.p = sk->p;
pk.g = sk->g;
pk.y = sk->y;
/*mpi_set_bytes( test, nbits, get_random_byte, 0 );*/
{ char *p = get_random_bits( nbits, 0, 0 );
mpi_set_buffer( test, p, (nbits+7)/8, 0 );
m_free(p);
}
encrypt( out1_a, out1_b, test, &pk );
decrypt( out2, out1_a, out1_b, sk );
if( mpi_cmp( test, out2 ) )
log_fatal("ElGamal operation: encrypt, decrypt failed\n");
sign( out1_a, out1_b, test, sk );
if( !verify( out1_a, out1_b, test, &pk ) )
log_fatal("ElGamal operation: sign, verify failed\n");
mpi_free( test );
mpi_free( out1_a );
mpi_free( out1_b );
mpi_free( out2 );
}
/****************
* generate a random secret exponent k from prime p, so
* that k is relatively prime to p-1
*/
static MPI
gen_k( MPI p )
{
MPI k = mpi_alloc_secure( 0 );
MPI temp = mpi_alloc( mpi_get_nlimbs(p) );
MPI p_1 = mpi_copy(p);
unsigned nbits = mpi_get_nbits(p);
if( DBG_CIPHER )
log_debug("choosing a random k ");
mpi_sub_ui( p_1, p, 1);
for(;;) {
if( DBG_CIPHER )
fputc('.', stderr);
{ char *p = get_random_bits( nbits, 1, 1 );
mpi_set_buffer( k, p, (nbits+7)/8, 0 );
m_free(p);
/* make sure that the number is of the exact lenght */
if( mpi_test_bit( k, nbits-1 ) )
mpi_set_highbit( k, nbits-1 );
else {
mpi_set_highbit( k, nbits-1 );
mpi_clear_bit( k, nbits-1 );
}
}
if( !(mpi_cmp( k, p_1 ) < 0) ) /* check: k < (p-1) */
continue; /* no */
if( !(mpi_cmp_ui( k, 0 ) > 0) ) /* check: k > 0 */
continue; /* no */
if( mpi_gcd( temp, k, p_1 ) )
break; /* okay, k is relatively prime to (p-1) */
}
if( DBG_CIPHER )
fputc('\n', stderr);
mpi_free(p_1);
mpi_free(temp);
return k;
}
/****************
* Generate a key pair with a key of size NBITS
* Returns: 2 structures filles with all needed values
* and an array with n-1 factors of (p-1)
*/
static void
generate( ELG_secret_key *sk, unsigned nbits, MPI **ret_factors )
{
MPI p; /* the prime */
MPI p_min1;
MPI g;
MPI x; /* the secret exponent */
MPI y;
MPI temp;
unsigned qbits;
byte *rndbuf;
p_min1 = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
temp = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
if( nbits < 512 )
qbits = 120;
else if( nbits <= 1024 )
qbits = 160;
else if( nbits <= 2048 )
qbits = 200;
else
qbits = 240;
g = mpi_alloc(1);
p = generate_elg_prime( 0, nbits, qbits, g, ret_factors );
mpi_sub_ui(p_min1, p, 1);
/* select a random number which has these properties:
* 0 < x < p-1
* This must be a very good random number because this is the
* secret part. The prime is public and may be shared anyway,
* so a random generator level of 1 is used for the prime.
*/
x = mpi_alloc_secure( nbits/BITS_PER_MPI_LIMB );
if( DBG_CIPHER )
log_debug("choosing a random x ");
rndbuf = NULL;
do {
if( DBG_CIPHER )
fputc('.', stderr);
if( rndbuf ) { /* change only some of the higher bits */
if( nbits < 16 ) {/* should never happen ... */
m_free(rndbuf);
rndbuf = get_random_bits( nbits, 2, 1 );
}
else {
char *r = get_random_bits( 16, 2, 1 );
memcpy(rndbuf, r, 16/8 );
m_free(r);
}
}
else
rndbuf = get_random_bits( nbits, 2, 1 );
mpi_set_buffer( x, rndbuf, (nbits+7)/8, 0 );
mpi_clear_highbit( x, nbits+1 );
} while( !( mpi_cmp_ui( x, 0 )>0 && mpi_cmp( x, p_min1 )<0 ) );
m_free(rndbuf);
y = mpi_alloc(nbits/BITS_PER_MPI_LIMB);
mpi_powm( y, g, x, p );
if( DBG_CIPHER ) {
fputc('\n', stderr);
log_mpidump("elg p= ", p );
log_mpidump("elg g= ", g );
log_mpidump("elg y= ", y );
log_mpidump("elg x= ", x );
}
/* copy the stuff to the key structures */
sk->p = p;
sk->g = g;
sk->y = y;
sk->x = x;
/* now we can test our keys (this should never fail!) */
test_keys( sk, nbits - 64 );
mpi_free( p_min1 );
mpi_free( temp );
}
/****************
* Test whether the secret key is valid.
* Returns: if this is a valid key.
*/
static int
check_secret_key( ELG_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;
}
static void
encrypt(MPI a, MPI b, MPI input, ELG_public_key *pkey )
{
MPI k;
k = gen_k( pkey->p );
mpi_powm( a, pkey->g, k, pkey->p );
/* b = (y^k * input) mod p
* = ((y^k mod p) * (input mod p)) mod p
* and because input is < p (FIXME: check this!)
* = ((y^k mod p) * input) mod p
*/
mpi_powm( b, pkey->y, k, pkey->p );
mpi_mulm( b, b, input, pkey->p );
#if 0
if( DBG_CIPHER ) {
log_mpidump("elg encrypted y= ", pkey->y);
log_mpidump("elg encrypted p= ", pkey->p);
log_mpidump("elg encrypted k= ", k);
log_mpidump("elg encrypted M= ", input);
log_mpidump("elg encrypted a= ", a);
log_mpidump("elg encrypted b= ", b);
}
#endif
mpi_free(k);
}
static void
decrypt(MPI output, MPI a, MPI b, ELG_secret_key *skey )
{
MPI t1 = mpi_alloc_secure( mpi_get_nlimbs( skey->p ) );
/* output = b/(a^x) mod p */
mpi_powm( t1, a, skey->x, skey->p );
mpi_invm( t1, t1, skey->p );
mpi_mulm( output, b, t1, skey->p );
#if 0
if( DBG_CIPHER ) {
log_mpidump("elg decrypted x= ", skey->x);
log_mpidump("elg decrypted p= ", skey->p);
log_mpidump("elg decrypted a= ", a);
log_mpidump("elg decrypted b= ", b);
log_mpidump("elg decrypted M= ", output);
}
#endif
mpi_free(t1);
}
/****************
* Make an Elgamal signature out of INPUT
*/
static void
sign(MPI a, MPI b, MPI input, ELG_secret_key *skey )
{
MPI k;
MPI t = mpi_alloc( mpi_get_nlimbs(a) );
MPI inv = mpi_alloc( mpi_get_nlimbs(a) );
MPI p_1 = mpi_copy(skey->p);
/*
* b = (t * inv) mod (p-1)
* b = (t * inv(k,(p-1),(p-1)) mod (p-1)
* b = (((M-x*a) mod (p-1)) * inv(k,(p-1),(p-1))) mod (p-1)
*
*/
mpi_sub_ui(p_1, p_1, 1);
k = gen_k( skey->p );
mpi_powm( a, skey->g, k, skey->p );
mpi_mul(t, skey->x, a );
mpi_subm(t, input, t, p_1 );
while( mpi_is_neg(t) )
mpi_add(t, t, p_1);
mpi_invm(inv, k, p_1 );
mpi_mulm(b, t, inv, p_1 );
#if 0
if( DBG_CIPHER ) {
log_mpidump("elg sign p= ", skey->p);
log_mpidump("elg sign g= ", skey->g);
log_mpidump("elg sign y= ", skey->y);
log_mpidump("elg sign x= ", skey->x);
log_mpidump("elg sign k= ", k);
log_mpidump("elg sign M= ", input);
log_mpidump("elg sign a= ", a);
log_mpidump("elg sign b= ", b);
}
#endif
mpi_free(k);
mpi_free(t);
mpi_free(inv);
mpi_free(p_1);
}
/****************
* Returns true if the signature composed of A and B is valid.
*/
static int
verify(MPI a, MPI b, MPI input, ELG_public_key *pkey )
{
int rc;
MPI t1;
MPI t2;
MPI base[4];
MPI exp[4];
if( !(mpi_cmp_ui( a, 0 ) > 0 && mpi_cmp( a, pkey->p ) < 0) )
return 0; /* assertion 0 < a < p failed */
t1 = mpi_alloc( mpi_get_nlimbs(a) );
t2 = mpi_alloc( mpi_get_nlimbs(a) );
#if 0
/* t1 = (y^a mod p) * (a^b mod p) mod p */
mpi_powm( t1, pkey->y, a, pkey->p );
mpi_powm( t2, a, b, pkey->p );
mpi_mulm( t1, t1, t2, pkey->p );
/* t2 = g ^ input mod p */
mpi_powm( t2, pkey->g, input, pkey->p );
rc = !mpi_cmp( t1, t2 );
#elif 0
/* t1 = (y^a mod p) * (a^b mod p) mod p */
base[0] = pkey->y; exp[0] = a;
base[1] = a; exp[1] = b;
base[2] = NULL; exp[2] = NULL;
mpi_mulpowm( t1, base, exp, pkey->p );
/* t2 = g ^ input mod p */
mpi_powm( t2, pkey->g, input, pkey->p );
rc = !mpi_cmp( t1, t2 );
#else
/* t1 = g ^ - input * y ^ a * a ^ b mod p */
mpi_invm(t2, pkey->g, pkey->p );
base[0] = t2 ; exp[0] = input;
base[1] = pkey->y; exp[1] = a;
base[2] = a; exp[2] = b;
base[3] = NULL; exp[3] = NULL;
mpi_mulpowm( t1, base, exp, pkey->p );
rc = !mpi_cmp_ui( t1, 1 );
#endif
mpi_free(t1);
mpi_free(t2);
return rc;
}
/*********************************************
************** interface ******************
*********************************************/
int
elg_generate( int algo, unsigned nbits, MPI *skey, MPI **retfactors )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
generate( &sk, nbits, retfactors );
skey[0] = sk.p;
skey[1] = sk.g;
skey[2] = sk.y;
skey[3] = sk.x;
return 0;
}
int
elg_check_secret_key( int algo, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
sk.p = skey[0];
sk.g = skey[1];
sk.y = skey[2];
sk.x = skey[3];
if( !check_secret_key( &sk ) )
return G10ERR_BAD_SECKEY;
return 0;
}
int
elg_encrypt( int algo, MPI *resarr, MPI data, MPI *pkey )
{
ELG_public_key pk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
pk.p = pkey[0];
pk.g = pkey[1];
pk.y = pkey[2];
resarr[0] = mpi_alloc( mpi_get_nlimbs( pk.p ) );
resarr[1] = mpi_alloc( mpi_get_nlimbs( pk.p ) );
encrypt( resarr[0], resarr[1], data, &pk );
return 0;
}
int
elg_decrypt( int algo, MPI *result, MPI *data, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
sk.p = skey[0];
sk.g = skey[1];
sk.y = skey[2];
sk.x = skey[3];
*result = mpi_alloc_secure( mpi_get_nlimbs( sk.p ) );
decrypt( *result, data[0], data[1], &sk );
return 0;
}
int
elg_sign( int algo, MPI *resarr, MPI data, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
sk.p = skey[0];
sk.g = skey[1];
sk.y = skey[2];
sk.x = skey[3];
resarr[0] = mpi_alloc( mpi_get_nlimbs( sk.p ) );
resarr[1] = mpi_alloc( mpi_get_nlimbs( sk.p ) );
sign( resarr[0], resarr[1], data, &sk );
return 0;
}
int
elg_verify( int algo, MPI hash, MPI *data, MPI *pkey,
int (*cmp)(void *, MPI), void *opaquev )
{
ELG_public_key pk;
if( !is_ELGAMAL(algo) )
return G10ERR_PUBKEY_ALGO;
pk.p = pkey[0];
pk.g = pkey[1];
pk.y = pkey[2];
if( !verify( data[0], data[1], hash, &pk ) )
return G10ERR_BAD_SIGN;
return 0;
}
unsigned
elg_get_nbits( int algo, MPI *pkey )
{
if( !is_ELGAMAL(algo) )
return 0;
return mpi_get_nbits( pkey[0] );
}
/****************
* Return some information about the algorithm. We need algo here to
* distinguish different flavors of the algorithm.
* Returns: A pointer to string describing the algorithm or NULL if
* the ALGO is invalid.
* Usage: Bit 0 set : allows signing
* 1 set : allows encryption
* NOTE: This function allows signing also for ELG-E, which is not
* okay but a bad hack to allow to work with old gpg keys. The real check
* is done in the gnupg ocde depending on the packet version.
*/
const char *
elg_get_info( int algo, int *npkey, int *nskey, int *nenc, int *nsig,
int *usage )
{
*npkey = 3;
*nskey = 4;
*nenc = 2;
*nsig = 2;
switch( algo ) {
case PUBKEY_ALGO_ELGAMAL:
*usage = PUBKEY_USAGE_SIG|PUBKEY_USAGE_ENC;
return "ELG";
case PUBKEY_ALGO_ELGAMAL_E:
*usage = PUBKEY_USAGE_SIG|PUBKEY_USAGE_ENC;
return "ELG-E";
default: *usage = 0; return NULL;
}
}