From f5660c6460a863b19f9ef745575780e37cc192a9 Mon Sep 17 00:00:00 2001 From: Kibum Kim Date: Sat, 7 Jan 2012 00:46:38 +0900 Subject: Git init --- cipher/elgamal.c | 510 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 510 insertions(+) create mode 100644 cipher/elgamal.c (limited to 'cipher/elgamal.c') diff --git a/cipher/elgamal.c b/cipher/elgamal.c new file mode 100644 index 0000000..3c37a28 --- /dev/null +++ b/cipher/elgamal.c @@ -0,0 +1,510 @@ +/* elgamal.c - elgamal Public Key encryption + * Copyright (C) 1998, 2000, 2001, 2003, + * 2004 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, + * 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, int small_k ); +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 (*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 ); + xfree(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"); + + 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. With SMALL_K set, k will be selected for + * better encryption performance - this must never bee used signing! + */ +static MPI +gen_k( MPI p, int small_k ) +{ + 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; + + 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 of %u bits", nbits); + mpi_sub_ui( p_1, p, 1); + for(;;) { + if( !rndbuf || nbits < 32 ) { + xfree(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 ); + xfree(pp); + } + 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( 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: + xfree(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. Note that this is not optimal for + * signing keys becuase it makes an attack using accidential small + * K values even easier. Well, one should not use ElGamal signing + * anyway. + */ + 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 ... */ + xfree(rndbuf); + rndbuf = get_random_bits( xbits, 2, 1 ); + } + else { + char *r = get_random_bits( 16, 2, 1 ); + memcpy(rndbuf, r, 16/8 ); + xfree(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 ) ); + xfree(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, 1 ); + 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); +} + + +/********************************************* + ************** 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; +} + + +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 + */ +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_E: + *use = PUBKEY_USAGE_ENC; + return "ELG-E"; + default: *use = 0; return NULL; + } +} -- cgit v1.2.3