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/* primegen.c - prime number generator
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* Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
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* This file is part of GnuPG.
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* GnuPG is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2 of the License, or
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* (at your option) any later version.
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* GnuPG is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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* ***********************************************************************
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* The algorithm used to generate practically save primes is due to
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* Lim and Lee as described in the CRYPTO '97 proceedings (ISBN3540633847)
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static int no_of_small_prime_numbers;
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static MPI gen_prime( unsigned nbits, int mode, int randomlevel );
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static int check_prime( MPI prime, MPI val_2 );
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static int is_prime( MPI n, int steps, int *count );
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static void m_out_of_n( char *array, int m, int n );
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static void (*progress_cb) ( void *, int );
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static void *progress_cb_data;
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register_primegen_progress ( void (*cb)( void *, int), void *cb_data )
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progress_cb_data = cb_data;
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progress_cb ( progress_cb_data, c );
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* Generate a prime number (stored in secure memory)
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generate_secret_prime( unsigned nbits )
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prime = gen_prime( nbits, 1, 2 );
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generate_public_prime( unsigned nbits )
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prime = gen_prime( nbits, 0, 2 );
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* We do not need to use the strongest RNG because we gain no extra
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* security from it - The prime number is public and we could also
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* offer the factors for those who are willing to check that it is
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* indeed a strong prime.
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* 1: Make sure that at least one factor is of size qbits.
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generate_elg_prime( int mode, unsigned pbits, unsigned qbits,
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MPI g, MPI **ret_factors )
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int n; /* number of factors */
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int m; /* number of primes in pool */
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unsigned fbits; /* length of prime factors */
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MPI *factors; /* current factors */
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MPI *pool; /* pool of primes */
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MPI q; /* first prime factor (variable)*/
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MPI prime; /* prime test value */
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MPI q_factor; /* used for mode 1 */
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unsigned req_qbits = qbits; /* the requested q bits size */
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MPI val_2 = mpi_alloc_set_ui( 2 );
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/* find number of needed prime factors */
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for(n=1; (pbits - qbits - 1) / n >= qbits; n++ )
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if( !n || (mode==1 && n < 2) )
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log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits );
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fbits = (pbits - 2*req_qbits -1) / n;
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qbits = pbits - req_qbits - n*fbits;
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fbits = (pbits - req_qbits -1) / n;
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qbits = pbits - n*fbits;
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log_debug("gen prime: pbits=%u qbits=%u fbits=%u/%u n=%d\n",
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pbits, req_qbits, qbits, fbits, n );
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prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB );
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q = gen_prime( qbits, 0, 0 );
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q_factor = mode==1? gen_prime( req_qbits, 0, 0 ) : NULL;
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/* allocate an array to hold the factors + 2 for later usage */
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factors = m_alloc_clear( (n+2) * sizeof *factors );
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/* make a pool of 3n+5 primes (this is an arbitrary value) */
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m += 5; /* need some more for DSA */
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pool = m_alloc_clear( m * sizeof *pool );
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/* permutate over the pool of primes */
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/* allocate new primes */
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for(i=0; i < m; i++ ) {
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/* init m_out_of_n() */
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perms = m_alloc_clear( m );
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for(i=0; i < n; i++ ) {
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pool[i] = gen_prime( fbits, 0, 0 );
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factors[i] = pool[i];
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m_out_of_n( perms, n, m );
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for(i=j=0; i < m && j < n ; i++ )
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pool[i] = gen_prime( fbits, 0, 0 );
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factors[j++] = pool[i];
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m_free(perms); perms = NULL;
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goto next_try; /* allocate new primes */
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mpi_mul_ui( prime, prime, 2 );
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mpi_mul( prime, prime, q_factor );
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for(i=0; i < n; i++ )
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mpi_mul( prime, prime, factors[i] );
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mpi_add_ui( prime, prime, 1 );
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nprime = mpi_get_nbits(prime);
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if( nprime < pbits ) {
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if( ++count1 > 20 ) {
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q = gen_prime( qbits, 0, 0 );
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if( nprime > pbits ) {
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if( ++count2 > 20 ) {
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q = gen_prime( qbits, 0, 0 );
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} while( !(nprime == pbits && check_prime( prime, val_2 )) );
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log_mpidump( "prime : ", prime );
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log_mpidump( "factor q: ", q );
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log_mpidump( "factor q0: ", q_factor );
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for(i=0; i < n; i++ )
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log_mpidump( "factor pi: ", factors[i] );
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log_debug("bit sizes: prime=%u, q=%u", mpi_get_nbits(prime), mpi_get_nbits(q) );
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fprintf(stderr, ", q0=%u", mpi_get_nbits(q_factor) );
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for(i=0; i < n; i++ )
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fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) );
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if( ret_factors ) { /* caller wants the factors */
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*ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors);
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(*ret_factors)[i++] = mpi_copy( q_factor );
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(*ret_factors)[i] = mpi_copy( factors[i-1] );
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(*ret_factors)[i] = mpi_copy( factors[i] );
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if( g ) { /* create a generator (start with 3)*/
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MPI tmp = mpi_alloc( mpi_get_nlimbs(prime) );
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MPI b = mpi_alloc( mpi_get_nlimbs(prime) );
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MPI pmin1 = mpi_alloc( mpi_get_nlimbs(prime) );
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BUG(); /* not yet implemented */
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factors[n+1] = mpi_alloc_set_ui(2);
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mpi_sub_ui( pmin1, prime, 1 );
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log_debug("checking g: ");
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mpi_print( stderr, g, 1 );
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for(i=0; i < n+2; i++ ) {
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/*fputc('~', stderr);*/
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mpi_fdiv_q(tmp, pmin1, factors[i] );
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/* (no mpi_pow(), but it is okay to use this with mod prime) */
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mpi_powm(b, g, tmp, prime );
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if( !mpi_cmp_ui(b, 1) )
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mpi_free(factors[n+1]);
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m_free( factors ); /* (factors are shallow copies) */
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for(i=0; i < m; i++ )
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gen_prime( unsigned nbits, int secret, int randomlevel )
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MPI prime, ptest, pminus1, val_2, val_3, result;
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if( 0 && DBG_CIPHER )
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log_debug("generate a prime of %u bits ", nbits );
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if( !no_of_small_prime_numbers ) {
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for(i=0; small_prime_numbers[i]; i++ )
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no_of_small_prime_numbers++;
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mods = m_alloc( no_of_small_prime_numbers * sizeof *mods );
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/* make nbits fit into MPI implementation */
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nlimbs = (nbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB;
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val_2 = mpi_alloc_set_ui( 2 );
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val_3 = mpi_alloc_set_ui( 3);
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prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
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result = mpi_alloc_like( prime );
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pminus1= mpi_alloc_like( prime );
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ptest = mpi_alloc_like( prime );
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for(;;) { /* try forvever */
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/* generate a random number */
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{ char *p = get_random_bits( nbits, randomlevel, secret );
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mpi_set_buffer( prime, p, (nbits+7)/8, 0 );
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/* Set high order bit to 1, set low order bit to 0.
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If we are generating a secret prime we are most probably
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doing that for RSA, to make sure that the modulus does have
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the requested keysize we set the 2 high order bits */
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mpi_set_highbit( prime, nbits-1 );
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mpi_set_bit (prime, nbits-2);
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mpi_set_bit( prime, 0 );
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/* calculate all remainders */
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for(i=0; (x = small_prime_numbers[i]); i++ )
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mods[i] = mpi_fdiv_r_ui(NULL, prime, x);
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/* now try some primes starting with prime */
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for(step=0; step < 20000; step += 2 ) {
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/* check against all the small primes we have in mods */
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for(i=0; (x = small_prime_numbers[i]); i++ ) {
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while( mods[i] + step >= x )
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if( !(mods[i] + step) )
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continue; /* found a multiple of an already known prime */
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mpi_add_ui( ptest, prime, step );
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/* do a faster Fermat test */
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mpi_sub_ui( pminus1, ptest, 1);
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mpi_powm( result, val_2, pminus1, ptest );
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if( !mpi_cmp_ui( result, 1 ) ) { /* not composite */
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/* perform stronger tests */
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if( is_prime(ptest, 5, &count2 ) ) {
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if( !mpi_test_bit( ptest, nbits-1 ) ) {
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log_debug("overflow in prime generation\n");
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break; /* step loop, continue with a new prime */
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if( ++dotcount == 10 ) {
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progress(':'); /* restart with a new random value */
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* Returns: true if this may be a prime
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check_prime( MPI prime, MPI val_2 )
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/* check against small primes */
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for(i=0; (x = small_prime_numbers[i]); i++ ) {
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if( mpi_divisible_ui( prime, x ) )
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/* a quick fermat test */
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MPI result = mpi_alloc_like( prime );
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MPI pminus1 = mpi_alloc_like( prime );
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mpi_sub_ui( pminus1, prime, 1);
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mpi_powm( result, val_2, pminus1, prime );
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if( mpi_cmp_ui( result, 1 ) ) { /* if composite */
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/* perform stronger tests */
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if( is_prime(prime, 5, &count ) )
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return 1; /* is probably a prime */
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* Return true if n is probably a prime
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is_prime( MPI n, int steps, int *count )
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MPI x = mpi_alloc( mpi_get_nlimbs( n ) );
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MPI y = mpi_alloc( mpi_get_nlimbs( n ) );
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MPI z = mpi_alloc( mpi_get_nlimbs( n ) );
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MPI nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
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MPI a2 = mpi_alloc_set_ui( 2 );
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unsigned nbits = mpi_get_nbits( n );
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mpi_sub_ui( nminus1, n, 1 );
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/* find q and k, so that n = 1 + 2^k * q */
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q = mpi_copy( nminus1 );
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k = mpi_trailing_zeros( q );
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mpi_tdiv_q_2exp(q, q, k);
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for(i=0 ; i < steps; i++ ) {
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/*mpi_set_bytes( x, nbits-1, get_random_byte, 0 );*/
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{ char *p = get_random_bits( nbits, 0, 0 );
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mpi_set_buffer( x, p, (nbits+7)/8, 0 );
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/* make sure that the number is smaller than the prime
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* and keep the randomness of the high bit */
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if( mpi_test_bit( x, nbits-2 ) ) {
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mpi_set_highbit( x, nbits-2 ); /* clear all higher bits */
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mpi_set_highbit( x, nbits-2 );
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mpi_clear_bit( x, nbits-2 );
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assert( mpi_cmp( x, nminus1 ) < 0 && mpi_cmp_ui( x, 1 ) > 0 );
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mpi_powm( y, x, q, n);
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if( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) {
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for( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) {
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mpi_powm(y, y, a2, n);
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if( !mpi_cmp_ui( y, 1 ) )
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goto leave; /* not a prime */
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if( mpi_cmp( y, nminus1 ) )
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goto leave; /* not a prime */
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rc = 1; /* may be a prime */
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m_out_of_n( char *array, int m, int n )
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int i=0, i1=0, j=0, jp=0, j1=0, k1=0, k2=0;
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if( m == 1 ) { /* special case */
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for(i=0; i < n; i++ )
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for(j=1; j < n; j++ ) {
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if( array[n-1] == array[n-j-1] )
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if( m & 1 ) { /* m is odd */
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else if( array[k2] && array[k2-1] )
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else { /* m is even */
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for(i=1; i <= jp; i++ ) {
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array[k1-1] = !array[k1-1];
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array[k2-1] = !array[k2-1];
added
removed
cipher/primegen.c
