/* elgamal.c - ElGamal Public Key encryption * Copyright (C) 1998, 2000, 2001 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 #include #include #include #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 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 register_pk_elg_progress ( void (*cb)( void *, 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, c ); else fputc( c, stderr ); } /**************** * Michael Wiener's table about 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 = 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); } 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"); 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 int orig_nbits = mpi_get_nbits(p); unsigned int nbits; unsigned int 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 of %u bits", nbits); mpi_sub_ui( p_1, p, 1); for(;;) { if( !rndbuf || nbits < 32 ) { m_free(rndbuf); rndbuf = get_random_bits( nbits, 1, 1 ); } else { /* change only some of the higher bits */ /* we could impprove this by directly requesting more memory * at the first call to get_random_bits() 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 = get_random_bits( 32, 1, 1 ); memcpy( rndbuf,pp, 4 ); m_free(pp); log_debug("gen_k: tsss, never expected to reach this\n"); } 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( 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: m_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 = 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 ); qbits = wiener_map( nbits ); if( qbits & 1 ) /* better have a even one */ qbits++; 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. * * 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 = mpi_alloc_secure( xbits/BITS_PER_MPI_LIMB ); 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 ... */ m_free(rndbuf); rndbuf = get_random_bits( xbits, 2, 1 ); } else { char *r = get_random_bits( 16, 2, 1 ); memcpy(rndbuf, r, 16/8 ); m_free(r); } } else rndbuf = get_random_bits( xbits, 2, 1 ); 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 ) ); m_free(rndbuf); y = mpi_alloc(nbits/BITS_PER_MPI_LIMB); 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 ); 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 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 ); 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 */ 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) ) { BUG(); /* That is nonsense code - left over from a very early test?*/ 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; 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; } }