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primegen.c
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/* primegen.c - prime number generator
* Copyright (C) 1998 Free Software Foundation, Inc.
*
* 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 <config.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "util.h"
#include "mpi.h"
#include "cipher.h"
static int no_of_small_prime_numbers;
static MPI gen_prime( unsigned nbits, int mode, int randomlevel );
static int check_prime( MPI prime );
static int is_prime( MPI n, int steps, int *count );
static void m_out_of_n( char *array, int m, int n );
/****************
* Generate a prime number (stored in secure memory)
*/
MPI
generate_secret_prime( unsigned nbits )
{
MPI prime;
prime = gen_prime( nbits, 1, 2 );
fputc('\n', stderr);
return prime;
}
MPI
generate_public_prime( unsigned nbits )
{
MPI prime;
prime = gen_prime( nbits, 0, 2 );
fputc('\n', stderr);
return prime;
}
/****************
* We do not need to use the strongest RNG because we gain no extra
* security from it - The prime number is public and we could also
* offer the factors for those who are willing to check that it is
* indeed a strong prime.
*
* mode 0: Standard
* 1: Make sure that at least one factor is of size qbits.
*/
MPI
generate_elg_prime( int mode, unsigned pbits, unsigned qbits,
MPI g, MPI **ret_factors )
{
int n; /* number of factors */
int m; /* number of primes in pool */
unsigned fbits; /* length of prime factors */
MPI *factors; /* current factors */
MPI *pool; /* pool of primes */
MPI q; /* first prime factor (variable)*/
MPI prime; /* prime test value */
MPI q_factor; /* used for mode 1 */
byte *perms = NULL;
int i, j;
int count1, count2;
unsigned nprime;
unsigned req_qbits = qbits; /* the requested q bits size */
/* find number of needed prime factors */
for(n=1; (pbits - qbits - 1) / n >= qbits; n++ )
;
n--;
if( !n || (mode==1 && n < 2) )
log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits );
if( mode == 1 ) {
n--;
fbits = (pbits - 2*req_qbits -1) / n;
qbits = pbits - req_qbits - n*fbits;
}
else {
fbits = (pbits - req_qbits -1) / n;
qbits = pbits - n*fbits;
}
if( DBG_CIPHER )
log_debug("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
pbits, req_qbits, qbits, fbits, n );
prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB );
q = gen_prime( qbits, 0, 1 );
q_factor = mode==1? gen_prime( req_qbits, 0, 1 ) : NULL;
/* allocate an array to hold the factors + 2 for later usage */
factors = m_alloc_clear( (n+2) * sizeof *factors );
/* make a pool of 3n+5 primes (this is an arbitrary value) */
m = n*3+5;
if( mode == 1 )
m += 5; /* need some more for DSA */
if( m < 25 )
m = 25;
pool = m_alloc_clear( m * sizeof *pool );
/* permutate over the pool of primes */
count1=count2=0;
do {
next_try:
if( !perms ) {
/* allocate new primes */
for(i=0; i < m; i++ ) {
mpi_free(pool[i]);
pool[i] = NULL;
}
/* init m_out_of_n() */
perms = m_alloc_clear( m );
for(i=0; i < n; i++ ) {
perms[i] = 1;
pool[i] = gen_prime( fbits, 0, 1 );
factors[i] = pool[i];
}
}
else {
m_out_of_n( perms, n, m );
for(i=j=0; i < m && j < n ; i++ )
if( perms[i] ) {
if( !pool[i] )
pool[i] = gen_prime( fbits, 0, 1 );
factors[j++] = pool[i];
}
if( i == n ) {
m_free(perms); perms = NULL;
fputc('!', stderr);
goto next_try; /* allocate new primes */
}
}
mpi_set( prime, q );
mpi_mul_ui( prime, prime, 2 );
if( mode == 1 )
mpi_mul( prime, prime, q_factor );
for(i=0; i < n; i++ )
mpi_mul( prime, prime, factors[i] );
mpi_add_ui( prime, prime, 1 );
nprime = mpi_get_nbits(prime);
if( nprime < pbits ) {
if( ++count1 > 20 ) {
count1 = 0;
qbits++;
fputc('>', stderr);
q = gen_prime( qbits, 0, 1 );
goto next_try;
}
}
else
count1 = 0;
if( nprime > pbits ) {
if( ++count2 > 20 ) {
count2 = 0;
qbits--;
fputc('<', stderr);
q = gen_prime( qbits, 0, 1 );
goto next_try;
}
}
else
count2 = 0;
} while( !(nprime == pbits && check_prime( prime )) );
if( DBG_CIPHER ) {
putc('\n', stderr);
log_mpidump( "prime : ", prime );
log_mpidump( "factor q: ", q );
if( mode == 1 )
log_mpidump( "factor q0: ", q_factor );
for(i=0; i < n; i++ )
log_mpidump( "factor pi: ", factors[i] );
log_debug("bit sizes: prime=%u, q=%u", mpi_get_nbits(prime), mpi_get_nbits(q) );
if( mode == 1 )
fprintf(stderr, ", q0=%u", mpi_get_nbits(q_factor) );
for(i=0; i < n; i++ )
fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) );
putc('\n', stderr);
}
if( ret_factors ) { /* caller wants the factors */
*ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors);
if( mode == 1 ) {
i = 0;
(*ret_factors)[i++] = mpi_copy( q_factor );
for(; i <= n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
else {
for(; i < n; i++ )
(*ret_factors)[i] = mpi_copy( factors[i] );
}
}
if( g ) { /* create a generator (start with 3)*/
MPI tmp = mpi_alloc( mpi_get_nlimbs(prime) );
MPI b = mpi_alloc( mpi_get_nlimbs(prime) );
MPI pmin1 = mpi_alloc( mpi_get_nlimbs(prime) );
if( mode == 1 )
BUG(); /* not yet implemented */
factors[n] = q;
factors[n+1] = mpi_alloc_set_ui(2);
mpi_sub_ui( pmin1, prime, 1 );
mpi_set_ui(g,2);
do {
mpi_add_ui(g, g, 1);
if( DBG_CIPHER ) {
log_debug("checking g: ");
mpi_print( stderr, g, 1 );
}
else
fputc('^', stderr);
for(i=0; i < n+2; i++ ) {
/*fputc('~', stderr);*/
mpi_fdiv_q(tmp, pmin1, factors[i] );
/* (no mpi_pow(), but it is okay to use this with mod prime) */
mpi_powm(b, g, tmp, prime );
if( !mpi_cmp_ui(b, 1) )
break;
}
if( DBG_CIPHER )
fputc('\n', stderr);
} while( i < n+2 );
mpi_free(factors[n+1]);
mpi_free(tmp);
mpi_free(b);
mpi_free(pmin1);
}
if( !DBG_CIPHER )
putc('\n', stderr);
m_free( factors ); /* (factors are shallow copies) */
for(i=0; i < m; i++ )
mpi_free( pool[i] );
m_free( pool );
m_free(perms);
return prime;
}
static MPI
gen_prime( unsigned nbits, int secret, int randomlevel )
{
unsigned nlimbs;
MPI prime, val_2, val_3, result;
int i;
unsigned x, step;
unsigned count1, count2;
int *mods;
if( 0 && DBG_CIPHER )
log_debug("generate a prime of %u bits ", nbits );
if( !no_of_small_prime_numbers ) {
for(i=0; small_prime_numbers[i]; i++ )
no_of_small_prime_numbers++;
}
mods = m_alloc( no_of_small_prime_numbers * sizeof *mods );
/* make nbits fit into MPI implementation */
nlimbs = (nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB;
assert( nlimbs );
val_2 = mpi_alloc( nlimbs );
mpi_set_ui(val_2, 2);
val_3 = mpi_alloc( nlimbs );
mpi_set_ui(val_3, 3);
result = mpi_alloc( nlimbs );
prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
count1 = count2 = 0;
/* enter (endless) loop */
for(;;) {
int dotcount=0;
/* generate a random number */
mpi_set_bytes( prime, nbits, get_random_byte, randomlevel );
/* set high order bit to 1, set low order bit to 1 */
mpi_set_highbit( prime, nbits-1 );
mpi_set_bit( prime, 0 );
/* calculate all remainders */
for(i=0; (x = small_prime_numbers[i]); i++ )
mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
for(step=0; step < 20000; step += 2 ) {
/* check against all the small primes we have in mods */
count1++;
for(i=0; (x = small_prime_numbers[i]); i++ ) {
while( mods[i] + step >= x )
mods[i] -= x;
if( !(mods[i] + step) )
break;
}
if( x )
continue; /* found a multiple of a already known prime */
mpi_add_ui( prime, prime, step );
#if 0
/* do a Fermat test */
count2++;
mpi_powm( result, val_2, prime, prime );
if( mpi_cmp_ui(result, 2) )
continue; /* stepping (fermat test failed) */
fputc('+', stderr);
#endif
/* perform stronger tests */
if( is_prime(prime, 5, &count2 ) ) {
if( !mpi_test_bit( prime, nbits-1 ) ) {
if( 0 && DBG_CIPHER ) {
fputc('\n', stderr);
log_debug("overflow in prime generation\n");
break; /* step loop, cont with a new prime */
}
}
if( 0 && DBG_CIPHER ) {
log_debug("performed %u simple and %u stronger tests\n",
count1, count2 );
log_mpidump("found prime: ", prime );
}
mpi_free(val_2);
mpi_free(val_3);
mpi_free(result);
m_free(mods);
return prime;
}
if( ++dotcount == 10 ) {
fputc('.', stderr);
dotcount = 0;
}
}
fputc(':', stderr); /* restart with a new random value */
}
}
/****************
* Returns: true if this may be a prime
*/
static int
check_prime( MPI prime )
{
int i;
unsigned x;
int count=0;
/* check against small primes */
for(i=0; (x = small_prime_numbers[i]); i++ ) {
if( mpi_divisible_ui( prime, x ) )
return 0;
}
#if 0
result = mpi_alloc( mpi_get_nlimbs(prime) );
val_2 = mpi_alloc_set_ui( 2 );
mpi_powm( result, val_2, prime, prime );
if( mpi_cmp_ui(result, 2) ) {
mpi_free(result);
mpi_free(val_2);
return 0;
}
mpi_free(result);
mpi_free(val_2);
fputc('+', stderr);
#endif
/* perform stronger tests */
if( is_prime(prime, 5, &count ) )
return 1; /* is probably a prime */
fputc('.', stderr);
return 0;
}
/****************
* Return true if n is probably a prime
*/
static int
is_prime( MPI n, int steps, int *count )
{
MPI x = mpi_alloc( mpi_get_nlimbs( n ) );
MPI y = mpi_alloc( mpi_get_nlimbs( n ) );
MPI z = mpi_alloc( mpi_get_nlimbs( n ) );
MPI nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
MPI a2 = mpi_alloc_set_ui( 2 );
MPI q;
unsigned i, j, k;
int rc = 0;
unsigned nbits = mpi_get_nbits( n );
mpi_sub_ui( nminus1, n, 1 );
/* find q and k, so that n = 1 + 2^k * q */
q = mpi_copy( nminus1 );
k = mpi_trailing_zeros( q );
mpi_tdiv_q_2exp(q, q, k);
for(i=0 ; i < steps; i++ ) {
++*count;
if( !i ) {
mpi_set_ui( x, 2 );
}
else {
mpi_set_bytes( x, nbits-1, get_random_byte, 0 );
/* work around a bug in mpi_set_bytes */
if( mpi_test_bit( x, nbits-2 ) ) {
mpi_set_highbit( x, nbits-2 ); /* clear all higher bits */
}
else {
mpi_set_highbit( x, nbits-2 );
mpi_clear_bit( x, nbits-2 );
}
assert( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
}
mpi_powm( y, x, q, n);
if( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) {
for( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) {
mpi_powm(y, y, a2, n);
if( !mpi_cmp_ui( y, 1 ) )
goto leave; /* not a prime */
}
if( mpi_cmp( y, nminus1 ) )
goto leave; /* not a prime */
}
fputc('+', stderr);
}
rc = 1; /* may be a prime */
leave:
mpi_free( x );
mpi_free( y );
mpi_free( z );
mpi_free( nminus1 );
mpi_free( q );
return rc;
}
static void
m_out_of_n( char *array, int m, int n )
{
int i=0, i1=0, j=0, jp=0, j1=0, k1=0, k2=0;
if( !m || m >= n )
return;
if( m == 1 ) { /* special case */
for(i=0; i < n; i++ )
if( array[i] ) {
array[i++] = 0;
if( i >= n )
i = 0;
array[i] = 1;
return;
}
BUG();
}
for(j=1; j < n; j++ ) {
if( array[n-1] == array[n-j-1] )
continue;
j1 = j;
break;
}
if( m & 1 ) { /* m is odd */
if( array[n-1] ) {
if( j1 & 1 ) {
k1 = n - j1;
k2 = k1+2;
if( k2 > n )
k2 = n;
goto leave;
}
goto scan;
}
k2 = n - j1 - 1;
if( k2 == 0 ) {
k1 = i;
k2 = n - j1;
}
else if( array[k2] && array[k2-1] )
k1 = n;
else
k1 = k2 + 1;
}
else { /* m is even */
if( !array[n-1] ) {
k1 = n - j1;
k2 = k1 + 1;
goto leave;
}
if( !(j1 & 1) ) {
k1 = n - j1;
k2 = k1+2;
if( k2 > n )
k2 = n;
goto leave;
}
scan:
jp = n - j1 - 1;
for(i=1; i <= jp; i++ ) {
i1 = jp + 2 - i;
if( array[i1-1] ) {
if( array[i1-2] ) {
k1 = i1 - 1;
k2 = n - j1;
}
else {
k1 = i1 - 1;
k2 = n + 1 - j1;
}
goto leave;
}
}
k1 = 1;
k2 = n + 1 - m;
}
leave:
array[k1-1] = !array[k1-1];
array[k2-1] = !array[k2-1];
}

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