summaryrefslogtreecommitdiff
path: root/cipher/primegen.c
diff options
context:
space:
mode:
Diffstat (limited to 'cipher/primegen.c')
-rw-r--r--cipher/primegen.c594
1 files changed, 594 insertions, 0 deletions
diff --git a/cipher/primegen.c b/cipher/primegen.c
new file mode 100644
index 0000000..0662d39
--- /dev/null
+++ b/cipher/primegen.c
@@ -0,0 +1,594 @@
+/* primegen.c - prime number generator
+ * Copyright (C) 1998, 1999, 2000, 2001 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
+ * USA.
+ *
+ * ***********************************************************************
+ * The algorithm used to generate practically save primes is due to
+ * Lim and Lee as described in the CRYPTO '97 proceedings (ISBN3540633847)
+ * page 260.
+ */
+
+#include <config.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#include "util.h"
+#include "mpi.h"
+#include "cipher.h"
+#include "i18n.h"
+
+static int no_of_small_prime_numbers;
+static MPI gen_prime( unsigned nbits, int mode, int randomlevel );
+static int check_prime( MPI prime, MPI val_2 );
+static int is_prime( MPI n, int steps, int *count );
+static void m_out_of_n( char *array, int m, int n );
+
+static void (*progress_cb) ( void *, int );
+static void *progress_cb_data;
+
+void
+register_primegen_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 );
+}
+
+
+/****************
+ * Generate a prime number (stored in secure memory)
+ */
+MPI
+generate_secret_prime( unsigned nbits )
+{
+ MPI prime;
+
+ prime = gen_prime( nbits, 1, 2 );
+ progress('\n');
+ return prime;
+}
+
+MPI
+generate_public_prime( unsigned nbits )
+{
+ MPI prime;
+
+ prime = gen_prime( nbits, 0, 2 );
+ progress('\n');
+ 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 */
+ MPI val_2 = mpi_alloc_set_ui( 2 );
+
+ /* 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, 0 );
+ q_factor = mode==1? gen_prime( req_qbits, 0, 0 ) : NULL;
+
+ /* allocate an array to hold the factors + 2 for later usage */
+ factors = xmalloc_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 = xmalloc_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 = xmalloc_clear( m );
+ for(i=0; i < n; i++ ) {
+ perms[i] = 1;
+ pool[i] = gen_prime( fbits, 0, 0 );
+ 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, 0 );
+ factors[j++] = pool[i];
+ }
+ if( i == n ) {
+ xfree(perms); perms = NULL;
+ progress('!');
+ 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++;
+ progress('>');
+ mpi_free (q);
+ q = gen_prime( qbits, 0, 0 );
+ goto next_try;
+ }
+ }
+ else
+ count1 = 0;
+ if( nprime > pbits ) {
+ if( ++count2 > 20 ) {
+ count2 = 0;
+ qbits--;
+ progress('<');
+ mpi_free (q);
+ q = gen_prime( qbits, 0, 0 );
+ goto next_try;
+ }
+ }
+ else
+ count2 = 0;
+ } while( !(nprime == pbits && check_prime( prime, val_2 )) );
+
+ if( DBG_CIPHER ) {
+ progress('\n');
+ 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]) );
+ progress('\n');
+ }
+
+ if( ret_factors ) { /* caller wants the factors */
+ *ret_factors = xmalloc_clear( (n+2) * sizeof **ret_factors);
+ i = 0;
+ if( mode == 1 ) {
+ (*ret_factors)[i++] = mpi_copy( q_factor );
+ for(; i <= n; i++ )
+ (*ret_factors)[i] = mpi_copy( factors[i-1] );
+ }
+ 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
+ progress('^');
+ 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 )
+ progress('\n');
+ } while( i < n+2 );
+ mpi_free(factors[n+1]);
+ mpi_free(tmp);
+ mpi_free(b);
+ mpi_free(pmin1);
+ }
+ if( !DBG_CIPHER )
+ progress('\n');
+
+ xfree( factors ); /* (factors are shallow copies) */
+ for(i=0; i < m; i++ )
+ mpi_free( pool[i] );
+ xfree( pool );
+ xfree(perms);
+ mpi_free(val_2);
+ mpi_free(q);
+ return prime;
+}
+
+
+
+static MPI
+gen_prime( unsigned int nbits, int secret, int randomlevel )
+{
+ unsigned nlimbs;
+ MPI prime, ptest, pminus1, val_2, val_3, result;
+ int i;
+ unsigned x, step;
+ int count1, count2;
+ int *mods;
+
+ if( 0 && DBG_CIPHER )
+ log_debug("generate a prime of %u bits ", nbits );
+
+ if (nbits < 16)
+ {
+ log_error (_("can't generate a prime with less than %d bits\n"), 16);
+ exit (2);
+ }
+
+ if( !no_of_small_prime_numbers ) {
+ for(i=0; small_prime_numbers[i]; i++ )
+ no_of_small_prime_numbers++;
+ }
+ mods = xmalloc( no_of_small_prime_numbers * sizeof *mods );
+ /* make nbits fit into MPI implementation */
+ nlimbs = (nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB;
+ val_2 = mpi_alloc_set_ui( 2 );
+ val_3 = mpi_alloc_set_ui( 3);
+ prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
+ result = mpi_alloc_like( prime );
+ pminus1= mpi_alloc_like( prime );
+ ptest = mpi_alloc_like( prime );
+ count1 = count2 = 0;
+ for(;;) { /* try forvever */
+ int dotcount=0;
+
+ /* generate a random number */
+ { char *p = get_random_bits( nbits, randomlevel, secret );
+ mpi_set_buffer( prime, p, (nbits+7)/8, 0 );
+ xfree(p);
+ }
+
+ /* Set high order bit to 1, set low order bit to 0.
+ If we are generating a secret prime we are most probably
+ doing that for RSA, to make sure that the modulus does have
+ the requested keysize we set the 2 high order bits */
+ mpi_set_highbit( prime, nbits-1 );
+ if (secret)
+ mpi_set_bit (prime, nbits-2);
+ 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);
+
+ /* now try some primes starting with prime */
+ 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 an already known prime */
+
+ mpi_add_ui( ptest, prime, step );
+
+ /* do a faster Fermat test */
+ count2++;
+ mpi_sub_ui( pminus1, ptest, 1);
+ mpi_powm( result, val_2, pminus1, ptest );
+ if( !mpi_cmp_ui( result, 1 ) ) { /* not composite */
+ /* perform stronger tests */
+ if( is_prime(ptest, 5, &count2 ) ) {
+ if( !mpi_test_bit( ptest, nbits-1 ) ) {
+ progress('\n');
+ log_debug("overflow in prime generation\n");
+ break; /* step loop, continue with a new prime */
+ }
+
+ mpi_free(val_2);
+ mpi_free(val_3);
+ mpi_free(result);
+ mpi_free(pminus1);
+ mpi_free(prime);
+ xfree(mods);
+ return ptest;
+ }
+ }
+ if( ++dotcount == 10 ) {
+ progress('.');
+ dotcount = 0;
+ }
+ }
+ progress(':'); /* restart with a new random value */
+ }
+}
+
+/****************
+ * Returns: true if this may be a prime
+ */
+static int
+check_prime( MPI prime, MPI val_2 )
+{
+ 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;
+ }
+
+ /* a quick fermat test */
+ {
+ MPI result = mpi_alloc_like( prime );
+ MPI pminus1 = mpi_alloc_like( prime );
+ mpi_sub_ui( pminus1, prime, 1);
+ mpi_powm( result, val_2, pminus1, prime );
+ mpi_free( pminus1 );
+ if( mpi_cmp_ui( result, 1 ) ) { /* if composite */
+ mpi_free( result );
+ progress('.');
+ return 0;
+ }
+ mpi_free( result );
+ }
+
+ /* perform stronger tests */
+ if( is_prime(prime, 5, &count ) )
+ return 1; /* is probably a prime */
+ progress('.');
+ 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 {
+ char *p;
+
+ p = get_random_bits( nbits, 0, 0 );
+ mpi_set_buffer( x, p, (nbits+7)/8, 0 );
+ xfree(p);
+
+ /* Make sure that the number is smaller than the prime
+ * and keep the randomness of the high bit. */
+ 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 */
+ }
+ progress('+');
+ }
+ rc = 1; /* may be a prime */
+
+ leave:
+ mpi_free( x );
+ mpi_free( y );
+ mpi_free( z );
+ mpi_free( nminus1 );
+ mpi_free( q );
+ mpi_free (a2);
+
+ 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];
+}
+
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-21 15:03:59 +0000