path: root/cipher/elgamal.c

/* 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 <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#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 void test_keys (ELG_secret_key *sk, unsigned nbits);
static gcry_mpi_t gen_k (gcry_mpi_t p);
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 some arbitrary high number ;-) */
    return  n / 8 + 200;
}

static void
test_keys( ELG_secret_key *sk, unsigned nbits )
{
    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 );

    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 gcry_mpi_t
gen_k( gcry_mpi_t p )
{
    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;

    /* 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, 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;
    gcry_mpi_t 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;
    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 );
    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 );
    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 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  ******************
 *********************************************/

gcry_err_code_t
_gcry_elg_generate (int algo, unsigned nbits, unsigned long dummy,
                    gcry_mpi_t *skey, gcry_mpi_t **retfactors)
{
  ELG_secret_key sk;

  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;
}


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;

  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;

  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;

  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;

  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;

  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)
{
  return mpi_get_nbits (pkey[0]);
}

static char *elg_names[] =
  {
    "elg",
    "openpgp-elg",
    "openpgp-elg-sig",
    NULL,
  };


gcry_pk_spec_t 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,
  };