1997-11-18 14:06:00 +00:00
|
|
|
/* primegen.c - prime number generator
|
|
|
|
* Copyright (c) 1997 by Werner Koch (dd9jn)
|
|
|
|
*
|
|
|
|
* This file is part of G10.
|
|
|
|
*
|
|
|
|
* G10 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.
|
|
|
|
*
|
|
|
|
* G10 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;
|
1997-12-19 11:41:47 +00:00
|
|
|
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 );
|
1997-11-18 14:06:00 +00:00
|
|
|
|
|
|
|
|
|
|
|
/****************
|
|
|
|
* Generate a prime number (stored in secure memory)
|
|
|
|
*/
|
|
|
|
MPI
|
1997-11-24 22:24:04 +00:00
|
|
|
generate_secret_prime( unsigned nbits )
|
|
|
|
{
|
1997-12-19 11:41:47 +00:00
|
|
|
MPI prime;
|
|
|
|
|
|
|
|
prime = gen_prime( nbits, 1, 2 );
|
|
|
|
fputc('\n', stderr);
|
|
|
|
return prime;
|
1997-11-24 22:24:04 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
MPI
|
|
|
|
generate_public_prime( unsigned nbits )
|
|
|
|
{
|
1997-12-19 11:41:47 +00:00
|
|
|
MPI prime;
|
|
|
|
|
1997-12-20 17:23:29 +00:00
|
|
|
prime = gen_prime( nbits, 0, 2 );
|
1997-12-19 11:41:47 +00:00
|
|
|
fputc('\n', stderr);
|
|
|
|
return prime;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
MPI
|
|
|
|
generate_elg_prime( unsigned pbits, unsigned qbits, MPI g )
|
|
|
|
{
|
|
|
|
int n; /* number of factors */
|
|
|
|
int m; /* number of primes in pool */
|
|
|
|
unsigned fbits; /* length of prime factors */
|
|
|
|
MPI *factors; /* curent factors */
|
|
|
|
MPI *pool; /* pool of primes */
|
|
|
|
MPI q; /* first prime factor */
|
|
|
|
MPI prime; /* prime test value */
|
|
|
|
byte *perms = NULL;
|
|
|
|
int i, j;
|
1997-12-20 17:23:29 +00:00
|
|
|
int count1, count2;
|
|
|
|
unsigned nprime;
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
/* find number of needed prime factors */
|
|
|
|
for(n=1; (pbits - qbits - 1) / n >= qbits; n++ )
|
|
|
|
;
|
|
|
|
n--;
|
|
|
|
if( !n )
|
|
|
|
log_fatal("can't gen prime with pbits=%u qbits=%u\n", pbits, qbits );
|
|
|
|
fbits = (pbits - qbits -1) / n;
|
|
|
|
while( qbits + n*fbits < pbits )
|
|
|
|
qbits++;
|
1997-12-20 17:23:29 +00:00
|
|
|
if( DBG_CIPHER )
|
|
|
|
log_debug("gen prime: pbits=%u qbits=%u fbits=%u n=%d\n",
|
1997-12-19 11:41:47 +00:00
|
|
|
pbits, qbits, fbits, n );
|
|
|
|
|
|
|
|
prime = mpi_alloc( (pbits + BITS_PER_MPI_LIMB - 1) / BITS_PER_MPI_LIMB );
|
1997-12-20 17:23:29 +00:00
|
|
|
q = gen_prime( qbits, 0, 2 );
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
/* allocate an array to hold the factors + 2 for later usage */
|
|
|
|
factors = m_alloc_clear( (n+2) * sizeof *factors );
|
|
|
|
|
1997-12-20 17:23:29 +00:00
|
|
|
/* make a pool of 3n+5 primes (this is an arbitrary value) */
|
|
|
|
m = n*3+5;
|
|
|
|
if( m < 25 )
|
|
|
|
m = 25;
|
1997-12-19 11:41:47 +00:00
|
|
|
pool = m_alloc_clear( m * sizeof *pool );
|
|
|
|
|
|
|
|
/* permutate over the pool of primes */
|
1997-12-20 17:23:29 +00:00
|
|
|
count1=count2=0;
|
1997-12-19 11:41:47 +00:00
|
|
|
do {
|
|
|
|
next_try:
|
|
|
|
if( !perms ) {
|
|
|
|
/* allocate new primes */
|
|
|
|
for(i=0; i < m; i++ ) {
|
|
|
|
mpi_free(pool[i]);
|
1997-12-31 12:32:54 +00:00
|
|
|
pool[i] = NULL;
|
1997-12-19 11:41:47 +00:00
|
|
|
}
|
|
|
|
/* init m_out_of_n() */
|
|
|
|
perms = m_alloc_clear( m );
|
|
|
|
for(i=0; i < n; i++ ) {
|
|
|
|
perms[i] = 1;
|
1997-12-31 12:32:54 +00:00
|
|
|
pool[i] = gen_prime( fbits, 0, 2 );
|
1997-12-19 11:41:47 +00:00
|
|
|
factors[i] = pool[i];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else {
|
|
|
|
m_out_of_n( perms, n, m );
|
|
|
|
for(i=j=0; i < m && j < n ; i++ )
|
1997-12-31 12:32:54 +00:00
|
|
|
if( perms[i] ) {
|
|
|
|
if( !pool[i] )
|
|
|
|
pool[i] = gen_prime( fbits, 0, 2 );
|
1997-12-19 11:41:47 +00:00
|
|
|
factors[j++] = pool[i];
|
1997-12-31 12:32:54 +00:00
|
|
|
}
|
1997-12-19 11:41:47 +00:00
|
|
|
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 );
|
|
|
|
for(i=0; i < n; i++ )
|
|
|
|
mpi_mul( prime, prime, factors[i] );
|
|
|
|
mpi_add_ui( prime, prime, 1 );
|
1997-12-20 17:23:29 +00:00
|
|
|
nprime = mpi_get_nbits(prime);
|
|
|
|
if( nprime < pbits ) {
|
|
|
|
if( ++count1 > 20 ) {
|
|
|
|
count1 = 0;
|
|
|
|
qbits++;
|
|
|
|
fputc('>', stderr);
|
|
|
|
q = gen_prime( qbits, 0, 2 );
|
|
|
|
goto next_try;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
count1 = 0;
|
|
|
|
if( nprime > pbits ) {
|
|
|
|
if( ++count2 > 20 ) {
|
|
|
|
count2 = 0;
|
|
|
|
qbits--;
|
|
|
|
fputc('<', stderr);
|
|
|
|
q = gen_prime( qbits, 0, 2 );
|
|
|
|
goto next_try;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
count2 = 0;
|
|
|
|
} while( !(nprime == pbits && check_prime( prime )) );
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
|
1997-12-20 17:23:29 +00:00
|
|
|
if( DBG_CIPHER ) {
|
|
|
|
putc('\n', stderr);
|
|
|
|
log_mpidump( "prime : ", prime );
|
|
|
|
log_mpidump( "factor q: ", q );
|
|
|
|
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) );
|
|
|
|
for(i=0; i < n; i++ )
|
|
|
|
fprintf(stderr, ", p%d=%u", i, mpi_get_nbits(factors[i]) );
|
|
|
|
putc('\n', stderr);
|
|
|
|
}
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
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) );
|
|
|
|
|
|
|
|
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);
|
1997-12-20 17:23:29 +00:00
|
|
|
if( DBG_CIPHER ) {
|
|
|
|
log_debug("checking g: ");
|
|
|
|
mpi_print( stderr, g, 1 );
|
|
|
|
}
|
|
|
|
else
|
|
|
|
fputc('^', stderr);
|
1997-12-19 11:41:47 +00:00
|
|
|
for(i=0; i < n+2; i++ ) {
|
1997-12-20 17:23:29 +00:00
|
|
|
fputc('~', stderr);
|
1997-12-19 11:41:47 +00:00
|
|
|
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;
|
|
|
|
}
|
1997-12-20 17:23:29 +00:00
|
|
|
if( DBG_CIPHER )
|
|
|
|
fputc('\n', stderr);
|
|
|
|
} while( i < n+2 );
|
1997-12-19 11:41:47 +00:00
|
|
|
mpi_free(factors[n+1]);
|
|
|
|
mpi_free(tmp);
|
|
|
|
mpi_free(b);
|
|
|
|
mpi_free(pmin1);
|
|
|
|
}
|
1997-12-20 17:23:29 +00:00
|
|
|
if( !DBG_CIPHER )
|
|
|
|
putc('\n', stderr);
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
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;
|
1997-11-24 22:24:04 +00:00
|
|
|
}
|
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
|
1997-11-24 22:24:04 +00:00
|
|
|
static MPI
|
1997-12-19 11:41:47 +00:00
|
|
|
gen_prime( unsigned nbits, int secret, int randomlevel )
|
1997-11-18 14:06:00 +00:00
|
|
|
{
|
|
|
|
unsigned nlimbs;
|
|
|
|
MPI prime, val_2, val_3, result;
|
|
|
|
int i;
|
|
|
|
unsigned x, step;
|
|
|
|
unsigned count1, count2;
|
|
|
|
int *mods;
|
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
if( 0 && DBG_CIPHER )
|
1997-11-18 14:06:00 +00:00
|
|
|
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 );
|
1997-11-24 22:24:04 +00:00
|
|
|
prime = secret? mpi_alloc_secure( nlimbs ): mpi_alloc( nlimbs );
|
1997-11-18 14:06:00 +00:00
|
|
|
count1 = count2 = 0;
|
|
|
|
/* enter (endless) loop */
|
|
|
|
for(;;) {
|
|
|
|
/* generate a random number */
|
1997-12-19 11:41:47 +00:00
|
|
|
mpi_set_bytes( prime, nbits, get_random_byte, randomlevel );
|
1997-11-18 14:06:00 +00:00
|
|
|
/* set high order bit to 1, set low order bit to 1 */
|
1997-12-19 11:41:47 +00:00
|
|
|
mpi_set_highbit( prime, nbits-1 );
|
1997-11-18 14:06:00 +00:00
|
|
|
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 );
|
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
#if 0
|
1997-11-18 14:06:00 +00:00
|
|
|
/* do a Fermat test */
|
|
|
|
count2++;
|
|
|
|
mpi_powm( result, val_2, prime, prime );
|
|
|
|
if( mpi_cmp_ui(result, 2) )
|
|
|
|
continue; /* stepping (fermat test failed) */
|
1997-12-09 12:46:23 +00:00
|
|
|
fputc('+', stderr);
|
1997-12-19 11:41:47 +00:00
|
|
|
#endif
|
1997-11-18 14:06:00 +00:00
|
|
|
|
1997-11-27 11:44:13 +00:00
|
|
|
/* perform stronger tests */
|
1997-12-19 11:41:47 +00:00
|
|
|
if( is_prime(prime, 5, &count2 ) ) {
|
1997-11-18 14:06:00 +00:00
|
|
|
if( !mpi_test_bit( prime, nbits-1 ) ) {
|
1997-12-19 11:41:47 +00:00
|
|
|
if( 0 && DBG_CIPHER ) {
|
1997-11-18 14:06:00 +00:00
|
|
|
fputc('\n', stderr);
|
|
|
|
log_debug("overflow in prime generation\n");
|
|
|
|
break; /* step loop, cont with a new prime */
|
|
|
|
}
|
|
|
|
}
|
1997-12-09 12:46:23 +00:00
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
if( 0 && DBG_CIPHER ) {
|
1997-11-27 11:44:13 +00:00
|
|
|
log_debug("performed %u simple and %u stronger tests\n",
|
1997-11-18 14:06:00 +00:00
|
|
|
count1, count2 );
|
|
|
|
log_mpidump("found prime: ", prime );
|
|
|
|
}
|
|
|
|
|
|
|
|
mpi_free(val_2);
|
|
|
|
mpi_free(val_3);
|
|
|
|
mpi_free(result);
|
|
|
|
m_free(mods);
|
|
|
|
return prime;
|
|
|
|
}
|
1997-12-20 17:23:29 +00:00
|
|
|
fputc('.', stderr);
|
1997-11-18 14:06:00 +00:00
|
|
|
}
|
1997-12-09 12:46:23 +00:00
|
|
|
fputc(':', stderr); /* restart with a new random value */
|
1997-11-18 14:06:00 +00:00
|
|
|
}
|
|
|
|
}
|
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
/****************
|
|
|
|
* Returns: true if this is may me a prime
|
|
|
|
*/
|
|
|
|
static int
|
|
|
|
check_prime( MPI prime )
|
|
|
|
{
|
|
|
|
int i;
|
|
|
|
unsigned x;
|
|
|
|
int count=0;
|
|
|
|
MPI result;
|
|
|
|
MPI val_2;
|
|
|
|
|
|
|
|
/* 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 */
|
1997-12-20 17:23:29 +00:00
|
|
|
fputc('.', stderr);
|
1997-12-19 11:41:47 +00:00
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|
1997-11-18 14:06:00 +00:00
|
|
|
|
|
|
|
/****************
|
1997-12-19 11:41:47 +00:00
|
|
|
* Return true if n is propably a prime
|
1997-11-18 14:06:00 +00:00
|
|
|
*/
|
|
|
|
static int
|
1997-12-19 11:41:47 +00:00
|
|
|
is_prime( MPI n, int steps, int *count )
|
1997-11-18 14:06:00 +00:00
|
|
|
{
|
1997-11-27 11:44:13 +00:00
|
|
|
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;
|
1997-12-19 11:41:47 +00:00
|
|
|
int rc = 0;
|
|
|
|
unsigned nbits = mpi_get_nbits( n );
|
1997-11-27 11:44:13 +00:00
|
|
|
|
|
|
|
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;
|
1997-12-19 11:41:47 +00:00
|
|
|
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 );
|
|
|
|
}
|
1997-11-27 11:44:13 +00:00
|
|
|
mpi_powm( y, x, q, n);
|
|
|
|
if( mpi_cmp_ui(y, 1) && mpi_cmp( y, nminus1 ) ) {
|
1997-12-19 11:41:47 +00:00
|
|
|
for( j=1; j < k && mpi_cmp( y, nminus1 ); j++ ) {
|
1997-11-27 11:44:13 +00:00
|
|
|
mpi_powm(y, y, a2, n);
|
|
|
|
if( !mpi_cmp_ui( y, 1 ) )
|
|
|
|
goto leave; /* not a prime */
|
|
|
|
}
|
1997-12-19 11:41:47 +00:00
|
|
|
if( mpi_cmp( y, nminus1 ) )
|
|
|
|
goto leave; /* not a prime */
|
1997-11-27 11:44:13 +00:00
|
|
|
}
|
1997-12-09 12:46:23 +00:00
|
|
|
fputc('+', stderr);
|
1997-11-27 11:44:13 +00:00
|
|
|
}
|
1997-12-19 11:41:47 +00:00
|
|
|
rc = 1; /* may be a prime */
|
1997-11-27 11:44:13 +00:00
|
|
|
|
|
|
|
leave:
|
|
|
|
mpi_free( x );
|
|
|
|
mpi_free( y );
|
|
|
|
mpi_free( z );
|
|
|
|
mpi_free( nminus1 );
|
|
|
|
mpi_free( q );
|
|
|
|
|
|
|
|
return rc;
|
1997-11-18 14:06:00 +00:00
|
|
|
}
|
|
|
|
|
1997-12-19 11:41:47 +00:00
|
|
|
|
|
|
|
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;
|
|
|
|
}
|
|
|
|
log_bug(NULL);
|
|
|
|
}
|
|
|
|
|
|
|
|
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];
|
|
|
|
}
|
|
|
|
|