/****************
* 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
* 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 ( mpi_nlimb_hint_from_nbits (nbits) );
temp = mpi_alloc ( mpi_nlimb_hint_from_nbits (nbits) );
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 ( mpi_nlimb_hint_from_nbits (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 ... */
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 ( mpi_nlimb_hint_from_nbits (nbits) );
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 );
}
