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/* elgamal.c - ElGamal Public Key encryption
* Copyright (C) 1998, 2000, 2001, 2002 Free Software Foundation, Inc.
*
* This file is part of Libgcrypt.
*
* Libgcrypt 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.
*
* Libgcrypt 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 this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
*
* For a description of the algorithm, see:
* Bruce Schneier: Applied Cryptography. John Wiley & Sons, 1996.
* ISBN 0-471-11709-9. Pages 476 ff.
*/
#include <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "g10lib.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 do_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 (*progress_cb) ( void *, int );
static void *progress_cb_data;
void
_gcry_register_pk_elg_progress ( void (*cb)( void *,const char*, int,int,int),
void *cb_data )
{
progress_cb = cb;
progress_cb_data = cb_data;
}
static void
progress( int c )
{
if (progress_cb)
progress_cb (progress_cb_data, "pk_elg", c, 0, 0);
}
/****************
* Michael Wiener's table on subgroup sizes to match field sizes
* (floating around somewhere - Fixme: need a reference)
*/
static unsigned int
wiener_map( unsigned int n )
{
static struct { unsigned int p_n, q_n; } t[] =
{ /* p q attack cost */
{ 512, 119 }, /* 9 x 10^17 */
{ 768, 145 }, /* 6 x 10^21 */
{ 1024, 165 }, /* 7 x 10^24 */
{ 1280, 183 }, /* 3 x 10^27 */
{ 1536, 198 }, /* 7 x 10^29 */
{ 1792, 212 }, /* 9 x 10^31 */
{ 2048, 225 }, /* 8 x 10^33 */
{ 2304, 237 }, /* 5 x 10^35 */
{ 2560, 249 }, /* 3 x 10^37 */
{ 2816, 259 }, /* 1 x 10^39 */
{ 3072, 269 }, /* 3 x 10^40 */
{ 3328, 279 }, /* 8 x 10^41 */
{ 3584, 288 }, /* 2 x 10^43 */
{ 3840, 296 }, /* 4 x 10^44 */
{ 4096, 305 }, /* 7 x 10^45 */
{ 4352, 313 }, /* 1 x 10^47 */
{ 4608, 320 }, /* 2 x 10^48 */
{ 4864, 328 }, /* 2 x 10^49 */
{ 5120, 335 }, /* 3 x 10^50 */
{ 0, 0 }
};
int i;
for(i=0; t[i].p_n; i++ ) {
if( n <= t[i].p_n )
return t[i].q_n;
}
/* not in table - use some arbitrary high number ;-) */
return n / 8 + 200;
}
static void
test_keys( ELG_secret_key *sk, unsigned nbits )
{
ELG_public_key pk;
MPI test = gcry_mpi_new ( 0 );
MPI out1_a = gcry_mpi_new ( nbits );
MPI out1_b = gcry_mpi_new ( nbits );
MPI out2 = gcry_mpi_new ( nbits );
pk.p = sk->p;
pk.g = sk->g;
pk.y = sk->y;
gcry_mpi_randomize( test, nbits, GCRY_WEAK_RANDOM );
do_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");
gcry_mpi_release ( test );
gcry_mpi_release ( out1_a );
gcry_mpi_release ( out1_b );
gcry_mpi_release ( 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 int orig_nbits = mpi_get_nbits(p);
unsigned int nbits, nbytes;
char *rndbuf = NULL;
/* IMO using a k much lesser than p is sufficient and it greatly
* improves the encryption performance. We use Wiener's table
* and add a large safety margin.
*/
nbits = wiener_map( orig_nbits ) * 3 / 2;
if( nbits >= orig_nbits )
BUG();
nbytes = (nbits+7)/8;
if( DBG_CIPHER )
log_debug("choosing a random k ");
mpi_sub_ui( p_1, p, 1);
for(;;) {
if( !rndbuf || nbits < 32 ) {
gcry_free(rndbuf);
rndbuf = gcry_random_bytes_secure( nbytes, GCRY_STRONG_RANDOM );
}
else { /* change only some of the higher bits */
/* we could improve this by directly requesting more memory
* at the first call to get_random_bytes() and use this the here
* maybe it is easier to do this directly in random.c
* Anyway, it is highly inlikely that we will ever reach this code
*/
char *pp = gcry_random_bytes_secure( 4, GCRY_STRONG_RANDOM );
memcpy( rndbuf, pp, 4 );
gcry_free(pp);
log_debug("gen_k: tsss, never expected to reach this\n");
}
_gcry_mpi_set_buffer( k, rndbuf, nbytes, 0 );
for(;;) {
/* Hmm, actually we don't need this step here
* because we use k much smaller than p - we do it anyway
* just in case the keep on adding a one to k ;) */
if( !(mpi_cmp( k, p_1 ) < 0) ) { /* check: k < (p-1) */
if( DBG_CIPHER )
progress('+');
break; /* no */
}
if( !(mpi_cmp_ui( k, 0 ) > 0) ) { /* check: k > 0 */
if( DBG_CIPHER )
progress('-');
break; /* no */
}
if( gcry_mpi_gcd( temp, k, p_1 ) )
goto found; /* okay, k is relatively prime to (p-1) */
mpi_add_ui( k, k, 1 );
if( DBG_CIPHER )
progress('.');
}
}
found:
gcry_free(rndbuf);
if( DBG_CIPHER )
progress('\n');
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 int nbits, MPI **ret_factors )
{
MPI p; /* the prime */
MPI p_min1;
MPI g;
MPI x; /* the secret exponent */
MPI y;
MPI temp;
unsigned int qbits;
unsigned int xbits;
byte *rndbuf;
p_min1 = gcry_mpi_new ( nbits );
temp = gcry_mpi_new( nbits );
qbits = wiener_map( nbits );
if( qbits & 1 ) /* better have a even one */
qbits++;
g = mpi_alloc(1);
p = _gcry_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.
*
* I don't see a reason to have a x of about the same size
* as the p. It should be sufficient to have one about the size
* of q or the later used k plus a large safety margin. Decryption
* will be much faster with such an x.
*/
xbits = qbits * 3 / 2;
if( xbits >= nbits )
BUG();
x = gcry_mpi_snew ( xbits );
if( DBG_CIPHER )
log_debug("choosing a random x of size %u", xbits );
rndbuf = NULL;
do {
if( DBG_CIPHER )
progress('.');
if( rndbuf ) { /* change only some of the higher bits */
if( xbits < 16 ) {/* should never happen ... */
gcry_free(rndbuf);
rndbuf = gcry_random_bytes_secure( (xbits+7)/8,
GCRY_VERY_STRONG_RANDOM );
}
else {
char *r = gcry_random_bytes_secure( 2,
GCRY_VERY_STRONG_RANDOM );
memcpy(rndbuf, r, 2 );
gcry_free(r);
}
}
else {
rndbuf = gcry_random_bytes_secure( (xbits+7)/8,
GCRY_VERY_STRONG_RANDOM );
}
_gcry_mpi_set_buffer( x, rndbuf, (xbits+7)/8, 0 );
mpi_clear_highbit( x, xbits+1 );
} while( !( mpi_cmp_ui( x, 0 )>0 && mpi_cmp( x, p_min1 )<0 ) );
gcry_free(rndbuf);
y = gcry_mpi_new (nbits);
gcry_mpi_powm( y, g, x, p );
if( DBG_CIPHER ) {
progress('\n');
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 );
gcry_mpi_release ( p_min1 );
gcry_mpi_release ( 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) );
gcry_mpi_powm( y, sk->g, sk->x, sk->p );
rc = !mpi_cmp( y, sk->y );
mpi_free( y );
return rc;
}
static void
do_encrypt(MPI a, MPI b, MPI input, ELG_public_key *pkey )
{
MPI k;
/* Note: maybe we should change the interface, so that it
* is possible to check that input is < p and return an
* error code.
*/
k = gen_k( pkey->p );
gcry_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
* = ((y^k mod p) * input) mod p
*/
gcry_mpi_powm( b, pkey->y, k, pkey->p );
gcry_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 */
gcry_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 );
gcry_mpi_powm( a, skey->g, k, skey->p );
mpi_mul(t, skey->x, a );
mpi_subm(t, input, 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 */
gcry_mpi_powm( t1, pkey->y, a, pkey->p );
gcry_mpi_powm( t2, a, b, pkey->p );
mpi_mulm( t1, t1, t2, pkey->p );
/* t2 = g ^ input mod p */
gcry_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 */
gcry_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
_gcry_elg_generate( int algo, unsigned nbits, MPI *skey, MPI **retfactors )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return GCRYERR_INV_PK_ALGO;
generate( &sk, nbits, retfactors );
skey[0] = sk.p;
skey[1] = sk.g;
skey[2] = sk.y;
skey[3] = sk.x;
return 0;
}
int
_gcry_elg_check_secret_key( int algo, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return GCRYERR_INV_PK_ALGO;
if( !skey[0] || !skey[1] || !skey[2] || !skey[3] )
return GCRYERR_BAD_MPI;
sk.p = skey[0];
sk.g = skey[1];
sk.y = skey[2];
sk.x = skey[3];
if( !check_secret_key( &sk ) )
return GCRYERR_BAD_SECRET_KEY;
return 0;
}
int
_gcry_elg_encrypt( int algo, MPI *resarr, MPI data, MPI *pkey )
{
ELG_public_key pk;
if( !is_ELGAMAL(algo) )
return GCRYERR_INV_PK_ALGO;
if( !data || !pkey[0] || !pkey[1] || !pkey[2] )
return GCRYERR_BAD_MPI;
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 ) );
do_encrypt( resarr[0], resarr[1], data, &pk );
return 0;
}
int
_gcry_elg_decrypt( int algo, MPI *result, MPI *data, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return GCRYERR_INV_PK_ALGO;
if( !data[0] || !data[1]
|| !skey[0] || !skey[1] || !skey[2] || !skey[3] )
return GCRYERR_BAD_MPI;
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
_gcry_elg_sign( int algo, MPI *resarr, MPI data, MPI *skey )
{
ELG_secret_key sk;
if( !is_ELGAMAL(algo) )
return GCRYERR_INV_PK_ALGO;
if( !data || !skey[0] || !skey[1] || !skey[2] || !skey[3] )
return GCRYERR_BAD_MPI;
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
_gcry_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 GCRYERR_INV_PK_ALGO;
if( !data[0] || !data[1] || !hash
|| !pkey[0] || !pkey[1] || !pkey[2] )
return GCRYERR_BAD_MPI;
pk.p = pkey[0];
pk.g = pkey[1];
pk.y = pkey[2];
if( !verify( data[0], data[1], hash, &pk ) )
return GCRYERR_BAD_SIGNATURE;
return 0;
}
unsigned int
_gcry_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 *
_gcry_elg_get_info( int algo, int *npkey, int *nskey, int *nenc, int *nsig,
int *use )
{
*npkey = 3;
*nskey = 4;
*nenc = 2;
*nsig = 2;
switch( algo ) {
case GCRY_PK_ELG:
*use = GCRY_PK_USAGE_SIGN|GCRY_PK_USAGE_ENCR;
return "ELG";
case GCRY_PK_ELG_E:
*use = GCRY_PK_USAGE_SIGN|GCRY_PK_USAGE_ENCR;
return "ELG-E";
default: *use = 0; return NULL;
}
}

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