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Diffstat (limited to 'src/pluto/primegen.c')
-rw-r--r-- | src/pluto/primegen.c | 593 |
1 files changed, 0 insertions, 593 deletions
diff --git a/src/pluto/primegen.c b/src/pluto/primegen.c deleted file mode 100644 index 159490345..000000000 --- a/src/pluto/primegen.c +++ /dev/null @@ -1,593 +0,0 @@ -/* 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 - * - * *********************************************************************** - * 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 <stdio.h> -#include <stdlib.h> -#include <string.h> - -#ifdef PLUTO -#include <gmp.h> -#include <freeswan.h> -#include "constants.h" -#include "defs.h" -#include "log.h" -#include "rnd.h" -#include "gcryptfix.h" -#else /*! PLUTO */ -/* #include <assert.h> */ -/* #include <config.h> */ -/* #include "util.h" */ -/* #include "mpi.h" */ -/* #include "cipher.h" */ -#endif /* !PLUTO */ - -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, unsigned steps, int *count ); -static void m_out_of_n( char *array, int m, int n ); - - -static void -progress( int c ) -{ - 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, 1 ); - q_factor = mode==1? gen_prime( req_qbits, 0, 1 ) : NULL; - - /* allocate an array to hold the factors + 2 for later usage */ -#ifdef PLUTO - m_alloc_ptrs_clear(factors, n+2); -#else - factors = m_alloc_clear( (n+2) * sizeof *factors ); -#endif - - /* 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; -#ifdef PLUTO - m_alloc_ptrs_clear(pool, m); -#else - pool = m_alloc_clear( m * sizeof *pool ); -#endif - - /* 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() */ -#ifdef PLUTO - perms = alloc_bytes( m, "perms" ); -#else - perms = m_alloc_clear( m ); -#endif - 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; - 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('>'); - q = gen_prime( qbits, 0, 1 ); - goto next_try; - } - } - else - count1 = 0; - if( nprime > pbits ) { - if( ++count2 > 20 ) { - count2 = 0; - qbits--; - progress('<'); - q = gen_prime( qbits, 0, 1 ); - 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 */ -#ifdef PLUTO - m_alloc_ptrs_clear(*ret_factors, n+2); -#else - *ret_factors = m_alloc_clear( (n+2) * sizeof **ret_factors); -#endif - 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 ) { -#ifdef PLUTO - log_mpidump("checking g: ", g); -#else - log_debug("checking g: "); - mpi_print( stderr, g, 1 ); -#endif - } - 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'); - - m_free( factors ); /* (factors are shallow copies) */ - for(i=0; i < m; i++ ) - mpi_free( pool[i] ); - m_free( pool ); - m_free(perms); - mpi_free(val_2); - return prime; -} - - - -static MPI -gen_prime( unsigned nbits, int secret, int randomlevel ) -{ - unsigned nlimbs; - MPI prime, ptest, pminus1, 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; - 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 ); - m_free(p); - } - - /* 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); - - /* 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); - m_free(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, unsigned 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 );*/ - { char *p = get_random_bits( nbits, 0, 0 ); - mpi_set_buffer( x, p, (nbits+7)/8, 0 ); - m_free(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 ); - - 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]; -} - |