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667 lines
17 KiB
C
667 lines
17 KiB
C
/* elgamal.c - ElGamal Public Key encryption
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* Copyright (C) 1998, 2000 Free Software Foundation, Inc.
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*
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* For a description of the algorithm, see:
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* Bruce Schneier: Applied Cryptography. John Wiley & Sons, 1996.
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* ISBN 0-471-11709-9. Pages 476 ff.
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*
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* This file is part of GnuPG.
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*
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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*
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* GnuPG is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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*/
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#include <config.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "util.h"
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#include "mpi.h"
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#include "cipher.h"
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#include "elgamal.h"
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typedef struct {
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MPI p; /* prime */
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MPI g; /* group generator */
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MPI y; /* g^x mod p */
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} ELG_public_key;
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typedef struct {
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MPI p; /* prime */
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MPI g; /* group generator */
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MPI y; /* g^x mod p */
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MPI x; /* secret exponent */
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} ELG_secret_key;
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static void test_keys( ELG_secret_key *sk, unsigned nbits );
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static MPI gen_k( MPI p );
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static void generate( ELG_secret_key *sk, unsigned nbits, MPI **factors );
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static int check_secret_key( ELG_secret_key *sk );
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static void do_encrypt(MPI a, MPI b, MPI input, ELG_public_key *pkey );
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static void decrypt(MPI output, MPI a, MPI b, ELG_secret_key *skey );
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static void sign(MPI a, MPI b, MPI input, ELG_secret_key *skey);
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static int verify(MPI a, MPI b, MPI input, ELG_public_key *pkey);
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static void (*progress_cb) ( void *, int );
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static void *progress_cb_data;
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void
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register_pk_elg_progress ( void (*cb)( void *, int), void *cb_data )
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{
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progress_cb = cb;
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progress_cb_data = cb_data;
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}
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static void
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progress( int c )
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{
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if ( progress_cb )
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progress_cb ( progress_cb_data, c );
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else
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fputc( c, stderr );
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}
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/****************
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* Michael Wiener's table about subgroup sizes to match field sizes
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* (floating around somewhere - Fixme: need a reference)
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*/
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static unsigned int
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wiener_map( unsigned int n )
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{
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static struct { unsigned int p_n, q_n; } t[] =
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{ /* p q attack cost */
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{ 512, 119 }, /* 9 x 10^17 */
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{ 768, 145 }, /* 6 x 10^21 */
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{ 1024, 165 }, /* 7 x 10^24 */
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{ 1280, 183 }, /* 3 x 10^27 */
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{ 1536, 198 }, /* 7 x 10^29 */
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{ 1792, 212 }, /* 9 x 10^31 */
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{ 2048, 225 }, /* 8 x 10^33 */
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{ 2304, 237 }, /* 5 x 10^35 */
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{ 2560, 249 }, /* 3 x 10^37 */
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{ 2816, 259 }, /* 1 x 10^39 */
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{ 3072, 269 }, /* 3 x 10^40 */
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{ 3328, 279 }, /* 8 x 10^41 */
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{ 3584, 288 }, /* 2 x 10^43 */
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{ 3840, 296 }, /* 4 x 10^44 */
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{ 4096, 305 }, /* 7 x 10^45 */
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{ 4352, 313 }, /* 1 x 10^47 */
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{ 4608, 320 }, /* 2 x 10^48 */
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{ 4864, 328 }, /* 2 x 10^49 */
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{ 5120, 335 }, /* 3 x 10^50 */
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{ 0, 0 }
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};
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int i;
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for(i=0; t[i].p_n; i++ ) {
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if( n <= t[i].p_n )
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return t[i].q_n;
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}
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/* not in table - use some arbitrary high number ;-) */
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return n / 8 + 200;
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}
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static void
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test_keys( ELG_secret_key *sk, unsigned nbits )
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{
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ELG_public_key pk;
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MPI test = mpi_alloc( 0 );
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MPI out1_a = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
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MPI out1_b = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
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MPI out2 = mpi_alloc( nbits / BITS_PER_MPI_LIMB );
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pk.p = sk->p;
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pk.g = sk->g;
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pk.y = sk->y;
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/*mpi_set_bytes( test, nbits, get_random_byte, 0 );*/
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{ char *p = get_random_bits( nbits, 0, 0 );
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mpi_set_buffer( test, p, (nbits+7)/8, 0 );
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m_free(p);
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}
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do_encrypt( out1_a, out1_b, test, &pk );
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decrypt( out2, out1_a, out1_b, sk );
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if( mpi_cmp( test, out2 ) )
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log_fatal("ElGamal operation: encrypt, decrypt failed\n");
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sign( out1_a, out1_b, test, sk );
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if( !verify( out1_a, out1_b, test, &pk ) )
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log_fatal("ElGamal operation: sign, verify failed\n");
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mpi_free( test );
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mpi_free( out1_a );
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mpi_free( out1_b );
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mpi_free( out2 );
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}
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/****************
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* generate a random secret exponent k from prime p, so
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* that k is relatively prime to p-1
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*/
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static MPI
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gen_k( MPI p )
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{
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MPI k = mpi_alloc_secure( 0 );
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MPI temp = mpi_alloc( mpi_get_nlimbs(p) );
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MPI p_1 = mpi_copy(p);
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unsigned int orig_nbits = mpi_get_nbits(p);
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unsigned int nbits;
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unsigned int nbytes;
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char *rndbuf = NULL;
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/* IMO using a k much lesser than p is sufficient and it greatly
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* improves the encryption performance. We use Wiener's table
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* and add a large safety margin.
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*/
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nbits = wiener_map( orig_nbits ) * 3 / 2;
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if( nbits >= orig_nbits )
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BUG();
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nbytes = (nbits+7)/8;
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if( DBG_CIPHER )
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log_debug("choosing a random k of %u bits", nbits);
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mpi_sub_ui( p_1, p, 1);
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for(;;) {
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if( !rndbuf || nbits < 32 ) {
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m_free(rndbuf);
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rndbuf = get_random_bits( nbits, 1, 1 );
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}
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else { /* change only some of the higher bits */
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/* we could impprove this by directly requesting more memory
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* at the first call to get_random_bits() and use this the here
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* maybe it is easier to do this directly in random.c
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* Anyway, it is highly inlikely that we will ever reach this code
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*/
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char *pp = get_random_bits( 32, 1, 1 );
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memcpy( rndbuf,pp, 4 );
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m_free(pp);
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log_debug("gen_k: tsss, never expected to reach this\n");
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}
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mpi_set_buffer( k, rndbuf, nbytes, 0 );
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for(;;) {
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/* Hmm, actually we don't need this step here
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* because we use k much smaller than p - we do it anyway
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* just in case the keep on adding a one to k ;) */
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if( !(mpi_cmp( k, p_1 ) < 0) ) { /* check: k < (p-1) */
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if( DBG_CIPHER )
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progress('+');
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break; /* no */
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}
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if( !(mpi_cmp_ui( k, 0 ) > 0) ) { /* check: k > 0 */
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if( DBG_CIPHER )
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progress('-');
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break; /* no */
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}
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if( mpi_gcd( temp, k, p_1 ) )
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goto found; /* okay, k is relatively prime to (p-1) */
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mpi_add_ui( k, k, 1 );
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if( DBG_CIPHER )
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progress('.');
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}
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}
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found:
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m_free(rndbuf);
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if( DBG_CIPHER )
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progress('\n');
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mpi_free(p_1);
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mpi_free(temp);
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return k;
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}
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/****************
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* Generate a key pair with a key of size NBITS
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* Returns: 2 structures filles with all needed values
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* and an array with n-1 factors of (p-1)
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*/
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static void
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generate( ELG_secret_key *sk, unsigned int nbits, MPI **ret_factors )
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{
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MPI p; /* the prime */
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MPI p_min1;
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MPI g;
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MPI x; /* the secret exponent */
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MPI y;
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MPI temp;
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unsigned int qbits;
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unsigned int xbits;
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byte *rndbuf;
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p_min1 = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
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temp = mpi_alloc( (nbits+BITS_PER_MPI_LIMB-1)/BITS_PER_MPI_LIMB );
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qbits = wiener_map( nbits );
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if( qbits & 1 ) /* better have a even one */
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qbits++;
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g = mpi_alloc(1);
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p = generate_elg_prime( 0, nbits, qbits, g, ret_factors );
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mpi_sub_ui(p_min1, p, 1);
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/* select a random number which has these properties:
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* 0 < x < p-1
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* This must be a very good random number because this is the
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* secret part. The prime is public and may be shared anyway,
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* so a random generator level of 1 is used for the prime.
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*
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* I don't see a reason to have a x of about the same size
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* as the p. It should be sufficient to have one about the size
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* of q or the later used k plus a large safety margin. Decryption
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* will be much faster with such an x.
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*/
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xbits = qbits * 3 / 2;
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if( xbits >= nbits )
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BUG();
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x = mpi_alloc_secure( xbits/BITS_PER_MPI_LIMB );
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if( DBG_CIPHER )
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log_debug("choosing a random x of size %u", xbits );
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rndbuf = NULL;
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do {
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if( DBG_CIPHER )
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progress('.');
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if( rndbuf ) { /* change only some of the higher bits */
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if( xbits < 16 ) {/* should never happen ... */
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m_free(rndbuf);
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rndbuf = get_random_bits( xbits, 2, 1 );
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}
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else {
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char *r = get_random_bits( 16, 2, 1 );
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memcpy(rndbuf, r, 16/8 );
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m_free(r);
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}
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}
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else
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rndbuf = get_random_bits( xbits, 2, 1 );
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mpi_set_buffer( x, rndbuf, (xbits+7)/8, 0 );
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mpi_clear_highbit( x, xbits+1 );
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} while( !( mpi_cmp_ui( x, 0 )>0 && mpi_cmp( x, p_min1 )<0 ) );
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m_free(rndbuf);
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y = mpi_alloc(nbits/BITS_PER_MPI_LIMB);
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mpi_powm( y, g, x, p );
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if( DBG_CIPHER ) {
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progress('\n');
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log_mpidump("elg p= ", p );
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log_mpidump("elg g= ", g );
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log_mpidump("elg y= ", y );
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log_mpidump("elg x= ", x );
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}
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/* copy the stuff to the key structures */
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sk->p = p;
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sk->g = g;
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sk->y = y;
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sk->x = x;
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/* now we can test our keys (this should never fail!) */
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test_keys( sk, nbits - 64 );
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mpi_free( p_min1 );
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mpi_free( temp );
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}
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/****************
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* Test whether the secret key is valid.
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* Returns: if this is a valid key.
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*/
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static int
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check_secret_key( ELG_secret_key *sk )
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{
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int rc;
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MPI y = mpi_alloc( mpi_get_nlimbs(sk->y) );
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mpi_powm( y, sk->g, sk->x, sk->p );
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rc = !mpi_cmp( y, sk->y );
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mpi_free( y );
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return rc;
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}
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static void
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do_encrypt(MPI a, MPI b, MPI input, ELG_public_key *pkey )
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{
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MPI k;
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/* Note: maybe we should change the interface, so that it
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* is possible to check that input is < p and return an
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* error code.
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*/
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k = gen_k( pkey->p );
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mpi_powm( a, pkey->g, k, pkey->p );
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/* b = (y^k * input) mod p
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* = ((y^k mod p) * (input mod p)) mod p
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* and because input is < p
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* = ((y^k mod p) * input) mod p
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*/
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mpi_powm( b, pkey->y, k, pkey->p );
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mpi_mulm( b, b, input, pkey->p );
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#if 0
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if( DBG_CIPHER ) {
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log_mpidump("elg encrypted y= ", pkey->y);
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log_mpidump("elg encrypted p= ", pkey->p);
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log_mpidump("elg encrypted k= ", k);
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log_mpidump("elg encrypted M= ", input);
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log_mpidump("elg encrypted a= ", a);
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log_mpidump("elg encrypted b= ", b);
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}
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#endif
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mpi_free(k);
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}
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static void
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decrypt(MPI output, MPI a, MPI b, ELG_secret_key *skey )
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{
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MPI t1 = mpi_alloc_secure( mpi_get_nlimbs( skey->p ) );
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/* output = b/(a^x) mod p */
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mpi_powm( t1, a, skey->x, skey->p );
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mpi_invm( t1, t1, skey->p );
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mpi_mulm( output, b, t1, skey->p );
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#if 0
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if( DBG_CIPHER ) {
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log_mpidump("elg decrypted x= ", skey->x);
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log_mpidump("elg decrypted p= ", skey->p);
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log_mpidump("elg decrypted a= ", a);
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log_mpidump("elg decrypted b= ", b);
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log_mpidump("elg decrypted M= ", output);
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}
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#endif
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mpi_free(t1);
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}
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/****************
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* Make an Elgamal signature out of INPUT
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*/
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static void
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sign(MPI a, MPI b, MPI input, ELG_secret_key *skey )
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{
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MPI k;
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MPI t = mpi_alloc( mpi_get_nlimbs(a) );
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MPI inv = mpi_alloc( mpi_get_nlimbs(a) );
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MPI p_1 = mpi_copy(skey->p);
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/*
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* b = (t * inv) mod (p-1)
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* b = (t * inv(k,(p-1),(p-1)) mod (p-1)
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* b = (((M-x*a) mod (p-1)) * inv(k,(p-1),(p-1))) mod (p-1)
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*
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*/
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mpi_sub_ui(p_1, p_1, 1);
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k = gen_k( skey->p );
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mpi_powm( a, skey->g, k, skey->p );
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mpi_mul(t, skey->x, a );
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mpi_subm(t, input, t, p_1 );
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while( mpi_is_neg(t) ) {
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BUG(); /* That is nonsense code - left over from a very early test?*/
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mpi_add(t, t, p_1);
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}
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mpi_invm(inv, k, p_1 );
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mpi_mulm(b, t, inv, p_1 );
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#if 0
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if( DBG_CIPHER ) {
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log_mpidump("elg sign p= ", skey->p);
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log_mpidump("elg sign g= ", skey->g);
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log_mpidump("elg sign y= ", skey->y);
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log_mpidump("elg sign x= ", skey->x);
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log_mpidump("elg sign k= ", k);
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log_mpidump("elg sign M= ", input);
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log_mpidump("elg sign a= ", a);
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log_mpidump("elg sign b= ", b);
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}
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#endif
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mpi_free(k);
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mpi_free(t);
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mpi_free(inv);
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mpi_free(p_1);
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}
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/****************
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* Returns true if the signature composed of A and B is valid.
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*/
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static int
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verify(MPI a, MPI b, MPI input, ELG_public_key *pkey )
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{
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int rc;
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MPI t1;
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MPI t2;
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MPI base[4];
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MPI exp[4];
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if( !(mpi_cmp_ui( a, 0 ) > 0 && mpi_cmp( a, pkey->p ) < 0) )
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return 0; /* assertion 0 < a < p failed */
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t1 = mpi_alloc( mpi_get_nlimbs(a) );
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t2 = mpi_alloc( mpi_get_nlimbs(a) );
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#if 0
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/* t1 = (y^a mod p) * (a^b mod p) mod p */
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mpi_powm( t1, pkey->y, a, pkey->p );
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mpi_powm( t2, a, b, pkey->p );
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mpi_mulm( t1, t1, t2, pkey->p );
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/* t2 = g ^ input mod p */
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mpi_powm( t2, pkey->g, input, pkey->p );
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rc = !mpi_cmp( t1, t2 );
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#elif 0
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/* t1 = (y^a mod p) * (a^b mod p) mod p */
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base[0] = pkey->y; exp[0] = a;
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base[1] = a; exp[1] = b;
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base[2] = NULL; exp[2] = NULL;
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mpi_mulpowm( t1, base, exp, pkey->p );
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/* t2 = g ^ input mod p */
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mpi_powm( t2, pkey->g, input, pkey->p );
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|
|
|
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;
|
|
if( !skey[0] || !skey[1] || !skey[2] || !skey[3] )
|
|
return G10ERR_BAD_MPI;
|
|
|
|
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;
|
|
if( !data || !pkey[0] || !pkey[1] || !pkey[2] )
|
|
return G10ERR_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
|
|
elg_decrypt( int algo, MPI *result, MPI *data, MPI *skey )
|
|
{
|
|
ELG_secret_key sk;
|
|
|
|
if( !is_ELGAMAL(algo) )
|
|
return G10ERR_PUBKEY_ALGO;
|
|
if( !data[0] || !data[1]
|
|
|| !skey[0] || !skey[1] || !skey[2] || !skey[3] )
|
|
return G10ERR_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
|
|
elg_sign( int algo, MPI *resarr, MPI data, MPI *skey )
|
|
{
|
|
ELG_secret_key sk;
|
|
|
|
if( !is_ELGAMAL(algo) )
|
|
return G10ERR_PUBKEY_ALGO;
|
|
if( !data || !skey[0] || !skey[1] || !skey[2] || !skey[3] )
|
|
return G10ERR_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
|
|
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;
|
|
if( !data[0] || !data[1] || !hash
|
|
|| !pkey[0] || !pkey[1] || !pkey[2] )
|
|
return G10ERR_BAD_MPI;
|
|
|
|
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 int
|
|
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 *use )
|
|
{
|
|
*npkey = 3;
|
|
*nskey = 4;
|
|
*nenc = 2;
|
|
*nsig = 2;
|
|
|
|
switch( algo ) {
|
|
case PUBKEY_ALGO_ELGAMAL:
|
|
*use = PUBKEY_USAGE_SIG|PUBKEY_USAGE_ENC;
|
|
return "ELG";
|
|
case PUBKEY_ALGO_ELGAMAL_E:
|
|
*use = PUBKEY_USAGE_SIG|PUBKEY_USAGE_ENC;
|
|
return "ELG-E";
|
|
default: *use = 0; return NULL;
|
|
}
|
|
}
|
|
|
|
|