/* Elgamal.c - Elgamal Public Key encryption * Copyright (C) 1998, 2000, 2001, 2002, 2003 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 #include #include #include #include "g10lib.h" #include "mpi.h" #include "cipher.h" typedef struct { gcry_mpi_t p; /* prime */ gcry_mpi_t g; /* group generator */ gcry_mpi_t y; /* g^x mod p */ } ELG_public_key; typedef struct { gcry_mpi_t p; /* prime */ gcry_mpi_t g; /* group generator */ gcry_mpi_t y; /* g^x mod p */ gcry_mpi_t x; /* secret exponent */ } ELG_secret_key; static int test_keys (ELG_secret_key *sk, unsigned int nbits, int nodie); static gcry_mpi_t gen_k (gcry_mpi_t p, int small_k); static void generate (ELG_secret_key *sk, unsigned nbits, gcry_mpi_t **factors); static int check_secret_key (ELG_secret_key *sk); static void do_encrypt (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey); static void decrypt (gcry_mpi_t output, gcry_mpi_t a, gcry_mpi_t b, ELG_secret_key *skey); static void sign (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_secret_key *skey); static int verify (gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey); static void (*progress_cb) (void *, const char *, int, int, 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 an arbitrary high number. */ return n / 8 + 200; } static int test_keys ( ELG_secret_key *sk, unsigned int nbits, int nodie ) { ELG_public_key pk; gcry_mpi_t test = gcry_mpi_new ( 0 ); gcry_mpi_t out1_a = gcry_mpi_new ( nbits ); gcry_mpi_t out1_b = gcry_mpi_new ( nbits ); gcry_mpi_t out2 = gcry_mpi_new ( nbits ); int failed = 0; 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 ) ) failed |= 1; sign ( out1_a, out1_b, test, sk ); if ( !verify( out1_a, out1_b, test, &pk ) ) failed |= 2; gcry_mpi_release ( test ); gcry_mpi_release ( out1_a ); gcry_mpi_release ( out1_b ); gcry_mpi_release ( out2 ); if (failed && !nodie) log_fatal ("Elgamal test key for %s %s failed\n", (failed & 1)? "encrypt+decrypt":"", (failed & 2)? "sign+verify":""); if (failed && DBG_CIPHER) log_debug ("Elgamal test key for %s %s failed\n", (failed & 1)? "encrypt+decrypt":"", (failed & 2)? "sign+verify":""); return failed; } /**************** * Generate a random secret exponent k from prime p, so that k is * relatively prime to p-1. With SMALL_K set, k will be selected for * better encryption performance - this must never be used signing! */ static gcry_mpi_t gen_k( gcry_mpi_t p, int small_k ) { gcry_mpi_t k = mpi_alloc_secure( 0 ); gcry_mpi_t temp = mpi_alloc( mpi_get_nlimbs(p) ); gcry_mpi_t p_1 = mpi_copy(p); unsigned int orig_nbits = mpi_get_nbits(p); unsigned int nbits, nbytes; char *rndbuf = NULL; if (small_k) { /* Using a k much lesser than p is sufficient for encryption 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(); } else nbits = orig_nbits; 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); } _gcry_mpi_set_buffer( k, rndbuf, nbytes, 0 ); for(;;) { 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 relative 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 filled with all needed values * and an array with n-1 factors of (p-1) */ static void generate ( ELG_secret_key *sk, unsigned int nbits, gcry_mpi_t **ret_factors ) { gcry_mpi_t p; /* the prime */ gcry_mpi_t p_min1; gcry_mpi_t g; gcry_mpi_t x; /* the secret exponent */ gcry_mpi_t y; unsigned int qbits; unsigned int xbits; byte *rndbuf; p_min1 = 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; gcry_mpi_release ( p_min1 ); /* Now we can test our keys (this should never fail!) */ test_keys ( sk, nbits - 64, 0 ); } /* Generate a key pair with a key of size NBITS not using a random value for the secret key but the one given as X. This is useful to implement a passphrase based decryption for a public key based encryption. It has appliactions in backup systems. Returns: A structure filled with all needed values and an array with n-1 factors of (p-1). */ static gcry_err_code_t generate_using_x (ELG_secret_key *sk, unsigned int nbits, gcry_mpi_t x, gcry_mpi_t **ret_factors ) { gcry_mpi_t p; /* The prime. */ gcry_mpi_t p_min1; /* The prime minus 1. */ gcry_mpi_t g; /* The generator. */ gcry_mpi_t y; /* g^x mod p. */ unsigned int qbits; unsigned int xbits; sk->p = NULL; sk->g = NULL; sk->y = NULL; sk->x = NULL; /* Do a quick check to see whether X is suitable. */ xbits = mpi_get_nbits (x); if ( xbits < 64 || xbits >= nbits ) return GPG_ERR_INV_VALUE; p_min1 = gcry_mpi_new ( nbits ); qbits = wiener_map ( nbits ); if ( (qbits & 1) ) /* Better have an 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); if (DBG_CIPHER) log_debug ("using a supplied x of size %u", xbits ); if ( !(mpi_cmp_ui ( x, 0 ) > 0 && mpi_cmp ( x, p_min1 ) <0 ) ) { gcry_mpi_release ( p_min1 ); gcry_mpi_release ( p ); gcry_mpi_release ( g ); return GPG_ERR_INV_VALUE; } 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 = gcry_mpi_copy (x); gcry_mpi_release ( p_min1 ); /* Now we can test our keys. */ if ( test_keys ( sk, nbits - 64, 1 ) ) { gcry_mpi_release ( sk->p ); sk->p = NULL; gcry_mpi_release ( sk->g ); sk->g = NULL; gcry_mpi_release ( sk->y ); sk->y = NULL; gcry_mpi_release ( sk->x ); sk->x = NULL; return GPG_ERR_BAD_SECKEY; } return 0; } /**************** * 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; gcry_mpi_t 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(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey ) { gcry_mpi_t 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, 1 ); 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(gcry_mpi_t output, gcry_mpi_t a, gcry_mpi_t b, ELG_secret_key *skey ) { gcry_mpi_t 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(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_secret_key *skey ) { gcry_mpi_t k; gcry_mpi_t t = mpi_alloc( mpi_get_nlimbs(a) ); gcry_mpi_t inv = mpi_alloc( mpi_get_nlimbs(a) ); gcry_mpi_t 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, 0 /* no small K ! */ ); 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(gcry_mpi_t a, gcry_mpi_t b, gcry_mpi_t input, ELG_public_key *pkey ) { int rc; gcry_mpi_t t1; gcry_mpi_t t2; gcry_mpi_t base[4]; gcry_mpi_t ex[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; ex[0] = a; base[1] = a; ex[1] = b; base[2] = NULL; ex[2] = NULL; mpi_mulpowm( t1, base, ex, 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 ; ex[0] = input; base[1] = pkey->y; ex[1] = a; base[2] = a; ex[2] = b; base[3] = NULL; ex[3] = NULL; mpi_mulpowm( t1, base, ex, pkey->p ); rc = !mpi_cmp_ui( t1, 1 ); #endif mpi_free(t1); mpi_free(t2); return rc; } /********************************************* ************** interface ****************** *********************************************/ gcry_err_code_t _gcry_elg_generate (int algo, unsigned int nbits, unsigned long dummy, gcry_mpi_t *skey, gcry_mpi_t **retfactors) { ELG_secret_key sk; (void)algo; (void)dummy; generate (&sk, nbits, retfactors); skey[0] = sk.p; skey[1] = sk.g; skey[2] = sk.y; skey[3] = sk.x; return GPG_ERR_NO_ERROR; } /* This is a specila generate function which is not called via the module interface. */ gcry_err_code_t _gcry_elg_generate_using_x (int algo, unsigned int nbits, gcry_mpi_t x, gcry_mpi_t *skey, gcry_mpi_t **retfactors) { gcry_err_code_t ec; ELG_secret_key sk; (void)algo; ec = generate_using_x (&sk, nbits, x, retfactors); if (!ec) { skey[0] = sk.p; skey[1] = sk.g; skey[2] = sk.y; skey[3] = sk.x; } return ec; } gcry_err_code_t _gcry_elg_check_secret_key (int algo, gcry_mpi_t *skey) { gcry_err_code_t err = GPG_ERR_NO_ERROR; ELG_secret_key sk; (void)algo; if ((! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3])) err = GPG_ERR_BAD_MPI; else { sk.p = skey[0]; sk.g = skey[1]; sk.y = skey[2]; sk.x = skey[3]; if (! check_secret_key (&sk)) err = GPG_ERR_BAD_SECKEY; } return err; } gcry_err_code_t _gcry_elg_encrypt (int algo, gcry_mpi_t *resarr, gcry_mpi_t data, gcry_mpi_t *pkey, int flags) { gcry_err_code_t err = GPG_ERR_NO_ERROR; ELG_public_key pk; (void)algo; (void)flags; if ((! data) || (! pkey[0]) || (! pkey[1]) || (! pkey[2])) err = GPG_ERR_BAD_MPI; else { 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 err; } gcry_err_code_t _gcry_elg_decrypt (int algo, gcry_mpi_t *result, gcry_mpi_t *data, gcry_mpi_t *skey, int flags) { gcry_err_code_t err = GPG_ERR_NO_ERROR; ELG_secret_key sk; (void)algo; (void)flags; if ((! data[0]) || (! data[1]) || (! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3])) err = GPG_ERR_BAD_MPI; else { 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 err; } gcry_err_code_t _gcry_elg_sign (int algo, gcry_mpi_t *resarr, gcry_mpi_t data, gcry_mpi_t *skey) { gcry_err_code_t err = GPG_ERR_NO_ERROR; ELG_secret_key sk; (void)algo; if ((! data) || (! skey[0]) || (! skey[1]) || (! skey[2]) || (! skey[3])) err = GPG_ERR_BAD_MPI; else { 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 err; } gcry_err_code_t _gcry_elg_verify (int algo, gcry_mpi_t hash, gcry_mpi_t *data, gcry_mpi_t *pkey, int (*cmp) (void *, gcry_mpi_t), void *opaquev) { gcry_err_code_t err = GPG_ERR_NO_ERROR; ELG_public_key pk; (void)algo; (void)cmp; (void)opaquev; if ((! data[0]) || (! data[1]) || (! hash) || (! pkey[0]) || (! pkey[1]) || (! pkey[2])) err = GPG_ERR_BAD_MPI; else { pk.p = pkey[0]; pk.g = pkey[1]; pk.y = pkey[2]; if (! verify (data[0], data[1], hash, &pk)) err = GPG_ERR_BAD_SIGNATURE; } return err; } unsigned int _gcry_elg_get_nbits (int algo, gcry_mpi_t *pkey) { (void)algo; return mpi_get_nbits (pkey[0]); } static const char *elg_names[] = { "elg", "openpgp-elg", "openpgp-elg-sig", NULL, }; gcry_pk_spec_t _gcry_pubkey_spec_elg = { "ELG", elg_names, "pgy", "pgyx", "ab", "rs", "pgy", GCRY_PK_USAGE_SIGN | GCRY_PK_USAGE_ENCR, _gcry_elg_generate, _gcry_elg_check_secret_key, _gcry_elg_encrypt, _gcry_elg_decrypt, _gcry_elg_sign, _gcry_elg_verify, _gcry_elg_get_nbits, };