path: root/pwmanager/libcrypt/cipher/primegen.c

/* primegen.c - prime number generator
 * Copyright (C) 1998, 2000, 2001, 2002, 2003
 *               2004 Free Software Foundation, Inc.
 *
 * This file is part of Libgcrypt.
 *
 * Libgcrypt is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser general Public License as
 * published by the Free Software Foundation; either version 2.1 of
 * the License, or (at your option) any later version.
 *
 * Libgcrypt 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 Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser 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 <config.h>

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <errno.h>

#include "g10lib.h"
#include "mpi.h"
#include "cipher.h"

static gcry_mpi_t gen_prime (unsigned int nbits, int secret, int randomlevel, 
                             int (*extra_check)(void *, gcry_mpi_t),
                             void *extra_check_arg);
static int check_prime( gcry_mpi_t prime, gcry_mpi_t val_2,
                        gcry_prime_check_func_t cb_func, void *cb_arg );
static int is_prime( gcry_mpi_t n, int steps, int *count );
static void m_out_of_n( char *array, int m, int n );

static void (*progress_cb) (void *,const char*,int,int, int );
static void *progress_cb_data;

/* Note: 2 is not included because it can be tested more easily by
   looking at bit 0. The last entry in this list is marked by a zero */
static ushort small_prime_numbers[] = {
    3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
    47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
    103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
    157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
    211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
    269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
    331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
    389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
    449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
    509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
    587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
    643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
    709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
    773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
    853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
    919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
    991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
    1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
    1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
    1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
    1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
    1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
    1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
    1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
    1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
    1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
    1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
    1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
    1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
    1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
    1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
    1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
    1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
    1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
    2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
    2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
    2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
    2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
    2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
    2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
    2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
    2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
    2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
    2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
    2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
    2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
    2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
    2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
    2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
    3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
    3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
    3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
    3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
    3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
    3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
    3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
    3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
    3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
    3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
    3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
    3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
    3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
    3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
    3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
    4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
    4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
    4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
    4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
    4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
    4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
    4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
    4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
    4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
    4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
    4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
    4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
    4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
    4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
    4957, 4967, 4969, 4973, 4987, 4993, 4999,
    0
};
static int no_of_small_prime_numbers = DIM (small_prime_numbers) - 1;

void
_gcry_register_primegen_progress ( void (*cb)(void *,const char*,int,int,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, "primegen", c, 0, 0 );
}


/****************
 * Generate a prime number (stored in secure memory)
 */
gcry_mpi_t
_gcry_generate_secret_prime (unsigned int nbits,
                             int (*extra_check)(void*, gcry_mpi_t),
                             void *extra_check_arg)
{
  gcry_mpi_t prime;

  prime = gen_prime( nbits, 1, 2, extra_check, extra_check_arg);
  progress('\n');
  return prime;
}

gcry_mpi_t
_gcry_generate_public_prime( unsigned int nbits,
                             int (*extra_check)(void*, gcry_mpi_t),
                             void *extra_check_arg)
{
  gcry_mpi_t prime;

  prime = gen_prime( nbits, 0, 2, extra_check, extra_check_arg );
  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.  With ALL_FACTORS set to true all afcors of
 * prime-1 are returned in FACTORS.
 *
 * mode 0: Standard
 *	1: Make sure that at least one factor is of size qbits.
 */
static gcry_err_code_t
prime_generate_internal (int mode,
			 gcry_mpi_t *prime_generated, unsigned int pbits,
			 unsigned int qbits, gcry_mpi_t g,
			 gcry_mpi_t **ret_factors,
			 gcry_random_level_t randomlevel, unsigned int flags,
                         int all_factors,
                         gcry_prime_check_func_t cb_func, void *cb_arg)
{
  gcry_err_code_t err = 0;
  gcry_mpi_t *factors_new = NULL; /* Factors to return to the
				     caller.  */
  gcry_mpi_t *factors = NULL;	/* Current factors.  */
  gcry_mpi_t *pool = NULL;	/* Pool of primes.  */
  unsigned char *perms = NULL;	/* Permutations of POOL.  */
  gcry_mpi_t q_factor = NULL;	/* Used if QBITS is non-zero.  */
  unsigned int fbits = 0;	/* Length of prime factors.  */
  unsigned int n = 0;		/* Number of factors.  */
  unsigned int m = 0;		/* Number of primes in pool.  */
  gcry_mpi_t q = NULL;		/* First prime factor.  */
  gcry_mpi_t prime = NULL;	/* Prime candidate.  */
  unsigned int nprime = 0;	/* Bits of PRIME.  */
  unsigned int req_qbits;       /* The original QBITS value.  */
  gcry_mpi_t val_2;             /* For check_prime().  */
  unsigned int is_secret = (flags & GCRY_PRIME_FLAG_SECRET);
  unsigned int count1 = 0, count2 = 0;
  unsigned int i = 0, j = 0;

  if (pbits < 48)
    return GPG_ERR_INV_ARG;

  /* If QBITS is not given, assume a reasonable value. */
  if (!qbits)
    qbits = pbits / 3;

  req_qbits = qbits;

  /* Find number of needed prime factors.  */
  for (n = 1; (pbits - qbits - 1) / n  >= qbits; n++)
    ;
  n--;

  val_2 = mpi_alloc_set_ui (2);

  if ((! n) || ((mode == 1) && (n < 2)))
    {
      err = GPG_ERR_INV_ARG;
      goto leave;
    }

  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 = gcry_mpi_new (pbits);

  /* Generate first prime factor.  */
  q = gen_prime (qbits, is_secret, randomlevel, NULL, NULL);
  
  if (mode == 1)
    q_factor = gen_prime (req_qbits, is_secret, randomlevel, NULL, NULL);
  
  /* Allocate an array to hold the factors + 2 for later usage.  */
  factors = gcry_calloc (n + 2, sizeof (*factors));
  if (!factors)
    {
      err = gpg_err_code_from_errno (errno);
      goto leave;
    }
      
  /* Make a pool of 3n+5 primes (this is an arbitrary value).  */
  m = n * 3 + 5;
  if (mode == 1) /* Need some more (for e.g. DSA).  */
    m += 5;
  if (m < 25)
    m = 25;
  pool = gcry_calloc (m , sizeof (*pool));
  if (! pool)
    {
      err = gpg_err_code_from_errno (errno);
      goto leave;
    }

  /* Permutate over the pool of primes.  */
  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 = gcry_calloc (1, m);
          if (! perms)
            {
              err = gpg_err_code_from_errno (errno);
              goto leave;
            }
          for(i = 0; i < n; i++)
            {
              perms[i] = 1;
              pool[i] = gen_prime (fbits, is_secret,
                                   randomlevel, NULL, NULL);
              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, NULL, NULL);
                factors[j++] = pool[i];
              }
          if (i == n)
            {
              gcry_free (perms);
              perms = NULL;
              progress ('!');
              goto next_try;	/* Allocate new primes.  */
            }
        }

	/* Generate next prime candidate:
	   p = 2 * q [ * q_factor] * factor_0 * factor_1 * ... * factor_n + 1. 
        */
	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, NULL, NULL);
		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, NULL, NULL);
		goto next_try;
	      }
	  }
	else
	  count2 = 0;
    }
  while (! ((nprime == pbits) && check_prime (prime, val_2, cb_func, cb_arg)));

  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)
        log_debug (", q0=%u", mpi_get_nbits (q_factor));
      for (i = 0; i < n; i++)
        log_debug (", p%d=%u", i, mpi_get_nbits (factors[i]));
      progress('\n');
    }

  if (ret_factors)
    {
      /* Caller wants the factors.  */
      factors_new = gcry_calloc (n + 4, sizeof (*factors_new));
      if (! factors_new)
        {
          err = gpg_err_code_from_errno (errno);
          goto leave;
        }

      if (all_factors)
        {
          i = 0;
          factors_new[i++] = gcry_mpi_set_ui (NULL, 2);
          factors_new[i++] = mpi_copy (q);
          if (mode == 1)
            factors_new[i++] = mpi_copy (q_factor);
          for(j=0; j < n; j++)
            factors_new[i++] = mpi_copy (factors[j]);
        }
      else
        {
          i = 0;
          if (mode == 1)
            {
              factors_new[i++] = mpi_copy (q_factor);
              for (; i <= n; i++)
                factors_new[i] = mpi_copy (factors[i]);
            }
          else
            for (; i < n; i++ )
              factors_new[i] = mpi_copy (factors[i]);
        }
    }
  
  if (g)
    {
      /* Create a generator (start with 3).  */
      gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs (prime));
      gcry_mpi_t b = mpi_alloc (mpi_get_nlimbs (prime));
      gcry_mpi_t pmin1 = mpi_alloc (mpi_get_nlimbs (prime));
      
      if (mode == 1)
        err = GPG_ERR_NOT_IMPLEMENTED;
      else
        {
          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:");
                  gcry_mpi_dump (g);
                  log_printf ("\n");
                }
              else
                progress('^');
              for (i = 0; i < n + 2; i++)
                {
                  mpi_fdiv_q (tmp, pmin1, factors[i]);
                  /* No mpi_pow(), but it is okay to use this with mod
                     prime.  */
                  gcry_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');


 leave:
  if (pool)
    {
      for(i = 0; i < m; i++)
	mpi_free (pool[i]);
      gcry_free (pool);
    }
  if (factors)
    gcry_free (factors);  /* Factors are shallow copies.  */
  if (perms)
    gcry_free (perms);

  mpi_free (val_2);
  mpi_free (q);
  mpi_free (q_factor);

  if (! err)
    {
      *prime_generated = prime;
      if (ret_factors)
	*ret_factors = factors_new;
    }
  else
    {
      if (factors_new)
	{
	  for (i = 0; factors_new[i]; i++)
	    mpi_free (factors_new[i]);
	  gcry_free (factors_new);
	}
      mpi_free (prime);
    }

  return err;
}

gcry_mpi_t
_gcry_generate_elg_prime (int mode, unsigned pbits, unsigned qbits,
			  gcry_mpi_t g, gcry_mpi_t **ret_factors)
{
  gcry_err_code_t err = GPG_ERR_NO_ERROR;
  gcry_mpi_t prime = NULL;
  
  err = prime_generate_internal (mode, &prime, pbits, qbits, g,
				 ret_factors, GCRY_WEAK_RANDOM, 0, 0,
                                 NULL, NULL);

  return prime;
}

static gcry_mpi_t
gen_prime (unsigned int nbits, int secret, int randomlevel, 
           int (*extra_check)(void *, gcry_mpi_t), void *extra_check_arg)
{
  gcry_mpi_t prime, ptest, pminus1, val_2, val_3, result;
  int i;
  unsigned x, step;
  unsigned count1, count2;
  int *mods;
  
/*   if (  DBG_CIPHER ) */
/*     log_debug ("generate a prime of %u bits ", nbits ); */

  if (nbits < 16)
    log_fatal ("can't generate a prime with less than %d bits\n", 16);

  mods = gcry_xmalloc( no_of_small_prime_numbers * sizeof *mods );
  /* Make nbits fit into gcry_mpi_t implementation. */
  val_2  = mpi_alloc_set_ui( 2 );
  val_3 = mpi_alloc_set_ui( 3);
  prime  = secret? gcry_mpi_snew ( nbits ): gcry_mpi_new ( nbits );
  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 */
      gcry_mpi_randomize( prime, nbits, randomlevel );
      
      /* Set high order bit to 1, set low order bit to 1.  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 key size 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 fast Fermat test now. */
          count2++;
          mpi_sub_ui( pminus1, ptest, 1);
          gcry_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-secret ))
                    {
                      progress('\n');
                      log_debug ("overflow in prime generation\n");
                      break; /* Stop loop, continue with a new prime. */
                    }

                  if (extra_check && extra_check (extra_check_arg, ptest))
                    { 
                      /* The extra check told us that this prime is
                         not of the caller's taste. */
                      progress ('/');
                    }
                  else
                    { 
                      /* Got it. */
                      mpi_free(val_2);
                      mpi_free(val_3);
                      mpi_free(result);
                      mpi_free(pminus1);
                      mpi_free(prime);
                      gcry_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( gcry_mpi_t prime, gcry_mpi_t val_2,
             gcry_prime_check_func_t cb_func, void *cb_arg)
{
  int i;
  unsigned int 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. */
  {
    gcry_mpi_t result = mpi_alloc_like( prime );
    gcry_mpi_t pminus1 = mpi_alloc_like( prime );
    mpi_sub_ui( pminus1, prime, 1);
    gcry_mpi_powm( result, val_2, pminus1, prime );
    mpi_free( pminus1 );
    if ( mpi_cmp_ui( result, 1 ) )
      { 
        /* Is composite. */
        mpi_free( result );
        progress('.');
        return 0;
      }
    mpi_free( result );
  }

  if (!cb_func || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_MAYBE_PRIME, prime))
    {
      /* Perform stronger tests. */
      if ( is_prime( prime, 5, &count ) )
        {
          if (!cb_func
              || cb_func (cb_arg, GCRY_PRIME_CHECK_AT_GOT_PRIME, prime))
            return 1; /* Probably a prime. */
        }
    }
  progress('.');
  return 0;
}


/*
 * Return true if n is probably a prime
 */
static int
is_prime (gcry_mpi_t n, int steps, int *count)
{
  gcry_mpi_t x = mpi_alloc( mpi_get_nlimbs( n ) );
  gcry_mpi_t y = mpi_alloc( mpi_get_nlimbs( n ) );
  gcry_mpi_t z = mpi_alloc( mpi_get_nlimbs( n ) );
  gcry_mpi_t nminus1 = mpi_alloc( mpi_get_nlimbs( n ) );
  gcry_mpi_t a2 = mpi_alloc_set_ui( 2 );
  gcry_mpi_t 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
        {
          gcry_mpi_randomize( x, nbits, GCRY_WEAK_RANDOM );

          /* 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 );
	}
      gcry_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++ )
            {
              gcry_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];
}


/* Generate a new prime number of PRIME_BITS bits and store it in
   PRIME.  If FACTOR_BITS is non-zero, one of the prime factors of
   (prime - 1) / 2 must be FACTOR_BITS bits long.  If FACTORS is
   non-zero, allocate a new, NULL-terminated array holding the prime
   factors and store it in FACTORS.  FLAGS might be used to influence
   the prime number generation process.  */
gcry_error_t
gcry_prime_generate (gcry_mpi_t *prime, unsigned int prime_bits,
		     unsigned int factor_bits, gcry_mpi_t **factors,
		     gcry_prime_check_func_t cb_func, void *cb_arg,
		     gcry_random_level_t random_level,
		     unsigned int flags)
{
  gcry_err_code_t err = GPG_ERR_NO_ERROR;
  gcry_mpi_t *factors_generated = NULL;
  gcry_mpi_t prime_generated = NULL;
  unsigned int mode = 0;

  if (!prime)
    return gpg_error (GPG_ERR_INV_ARG);
  *prime = NULL; 

  if (flags & GCRY_PRIME_FLAG_SPECIAL_FACTOR)
    mode = 1;

  /* Generate.  */
  err = prime_generate_internal (mode, &prime_generated, prime_bits,
				 factor_bits, NULL,
                                 factors? &factors_generated : NULL,
				 random_level, flags, 1,
                                 cb_func, cb_arg);

  if (! err)
    if (cb_func)
      {
	/* Additional check. */
	if ( !cb_func (cb_arg, GCRY_PRIME_CHECK_AT_FINISH, prime_generated))
	  {
	    /* Failed, deallocate resources.  */
	    unsigned int i;

	    mpi_free (prime_generated);
            if (factors)
              {
                for (i = 0; factors_generated[i]; i++)
                  mpi_free (factors_generated[i]);
                gcry_free (factors_generated);
              }
	    err = GPG_ERR_GENERAL; 
	  }
      }

  if (! err)
    {
      if (factors)
        *factors = factors_generated;
      *prime = prime_generated;
    }

  return gcry_error (err);
}

/* Check wether the number X is prime.  */
gcry_error_t
gcry_prime_check (gcry_mpi_t x, unsigned int flags)
{
  gcry_err_code_t err = GPG_ERR_NO_ERROR;
  gcry_mpi_t val_2 = mpi_alloc_set_ui (2); /* Used by the Fermat test. */

  if (! check_prime (x, val_2, NULL, NULL))
    err = GPG_ERR_NO_PRIME;

  mpi_free (val_2);

  return gcry_error (err);
}

/* Find a generator for PRIME where the factorization of (prime-1) is
   in the NULL terminated array FACTORS. Return the generator as a
   newly allocated MPI in R_G.  If START_G is not NULL, use this as s
   atart for the search. Returns 0 on success.*/
gcry_error_t
gcry_prime_group_generator (gcry_mpi_t *r_g,
                            gcry_mpi_t prime, gcry_mpi_t *factors,
                            gcry_mpi_t start_g)
{
  gcry_mpi_t tmp = gcry_mpi_new (0);
  gcry_mpi_t b = gcry_mpi_new (0);
  gcry_mpi_t pmin1 = gcry_mpi_new (0);
  gcry_mpi_t g = start_g? gcry_mpi_copy (start_g) : gcry_mpi_set_ui (NULL, 3);
  int first = 1;
  int i, n;

  if (!factors || !r_g || !prime)
    return gpg_error (GPG_ERR_INV_ARG);
  *r_g = NULL; 

  for (n=0; factors[n]; n++)
    ;
  if (n < 2)
    return gpg_error (GPG_ERR_INV_ARG);

  /* Extra sanity check - usually disabled. */  
/*   mpi_set (tmp, factors[0]); */
/*   for(i = 1; i < n; i++) */
/*     mpi_mul (tmp, tmp, factors[i]); */
/*   mpi_add_ui (tmp, tmp, 1); */
/*   if (mpi_cmp (prime, tmp)) */
/*     return gpg_error (GPG_ERR_INV_ARG); */
  
  gcry_mpi_sub_ui (pmin1, prime, 1);      
  do         
    {
      if (first)
        first = 0;
      else
        gcry_mpi_add_ui (g, g, 1);
      
      if (DBG_CIPHER)
        {
          log_debug ("checking g:");
          gcry_mpi_dump (g);
          log_debug ("\n");
        }
      else
        progress('^');
      
      for (i = 0; i < n; i++)
        {
          mpi_fdiv_q (tmp, pmin1, factors[i]);
          gcry_mpi_powm (b, g, tmp, prime);
          if (! mpi_cmp_ui (b, 1))
            break;
        }
      if (DBG_CIPHER)
        progress('\n');
    }
  while (i < n);
  
  gcry_mpi_release (tmp);
  gcry_mpi_release (b); 
  gcry_mpi_release (pmin1); 
  *r_g = g; 

  return 0; 
}

/* Convenience function to release the factors array. */
void
gcry_prime_release_factors (gcry_mpi_t *factors)
{
  if (factors)
    {
      int i;
      
      for (i=0; factors[i]; i++)
        mpi_free (factors[i]);
      gcry_free (factors);
    }
}