File: rsa-keygen.c

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/* rsa-keygen.c

   Generation of RSA keypairs

   Copyright (C) 2002 Niels Möller

   This file is part of GNU Nettle.

   GNU Nettle is free software: you can redistribute it and/or
   modify it under the terms of either:

     * the GNU Lesser General Public License as published by the Free
       Software Foundation; either version 3 of the License, or (at your
       option) any later version.

   or

     * 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.

   or both in parallel, as here.

   GNU Nettle 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 copies of the GNU General Public License and
   the GNU Lesser General Public License along with this program.  If
   not, see http://www.gnu.org/licenses/.
*/

#if HAVE_CONFIG_H
# include "config.h"
#endif

#include <assert.h>
#include <stdlib.h>

#include "rsa.h"
#include "bignum.h"

#ifndef DEBUG
# define DEBUG 0
#endif

#if DEBUG
# include <stdio.h>
#endif


int
rsa_generate_keypair(struct rsa_public_key *pub,
		     struct rsa_private_key *key,
		     void *random_ctx, nettle_random_func *random,
		     void *progress_ctx, nettle_progress_func *progress,
		     unsigned n_size,
		     unsigned e_size)
{
  mpz_t p1;
  mpz_t q1;
  mpz_t phi;
  mpz_t tmp;

  if (e_size)
    {
      /* We should choose e randomly. Is the size reasonable? */
      if ((e_size < 16) || (e_size >= n_size) )
	return 0;
    }
  else
    {
      /* We have a fixed e. Check that it makes sense */

      /* It must be odd */
      if (!mpz_tstbit(pub->e, 0))
	return 0;

      /* And 3 or larger */
      if (mpz_cmp_ui(pub->e, 3) < 0)
	return 0;

      /* And size less than n */
      if (mpz_sizeinbase(pub->e, 2) >= n_size)
	return 0;
    }

  if (n_size < RSA_MINIMUM_N_BITS)
    return 0;
  
  mpz_init(p1); mpz_init(q1); mpz_init(phi); mpz_init(tmp);

  /* Generate primes */
  for (;;)
    {
      /* Generate p, such that gcd(p-1, e) = 1 */
      for (;;)
	{
	  nettle_random_prime(key->p, (n_size+1)/2, 1,
			      random_ctx, random,
			      progress_ctx, progress);

	  mpz_sub_ui(p1, key->p, 1);
      
	  /* If e was given, we must chose p such that p-1 has no factors in
	   * common with e. */
	  if (e_size)
	    break;
	  
	  mpz_gcd(tmp, pub->e, p1);

	  if (mpz_cmp_ui(tmp, 1) == 0)
	    break;
	  else if (progress) progress(progress_ctx, 'c');
	} 

      if (progress)
	progress(progress_ctx, '\n');
      
      /* Generate q, such that gcd(q-1, e) = 1 */
      for (;;)
	{
	  nettle_random_prime(key->q, n_size/2, 1,
			      random_ctx, random,
			      progress_ctx, progress);

	  /* Very unlikely. */
	  if (mpz_cmp (key->q, key->p) == 0)
	    continue;

	  mpz_sub_ui(q1, key->q, 1);
      
	  /* If e was given, we must chose q such that q-1 has no factors in
	   * common with e. */
	  if (e_size)
	    break;
	  
	  mpz_gcd(tmp, pub->e, q1);

	  if (mpz_cmp_ui(tmp, 1) == 0)
	    break;
	  else if (progress) progress(progress_ctx, 'c');
	}

      /* Now we have the primes. Is the product of the right size? */
      mpz_mul(pub->n, key->p, key->q);

      assert (mpz_sizeinbase(pub->n, 2) == n_size);

      if (progress)
	progress(progress_ctx, '\n');

      /* c = q^{-1} (mod p) */
      if (mpz_invert(key->c, key->q, key->p))
	/* This should succeed everytime. But if it doesn't,
	 * we try again. */
	break;
      else if (progress) progress(progress_ctx, '?');
    }

  mpz_mul(phi, p1, q1);
  
  /* If we didn't have a given e, generate one now. */
  if (e_size)
    {
      int retried = 0;
      for (;;)
	{
	  nettle_mpz_random_size(pub->e,
				 random_ctx, random,
				 e_size);
	
	  /* Make sure it's odd and that the most significant bit is
	   * set */
	  mpz_setbit(pub->e, 0);
	  mpz_setbit(pub->e, e_size - 1);

	  /* Needs gmp-3, or inverse might be negative. */
	  if (mpz_invert(key->d, pub->e, phi))
	    break;

	  if (progress) progress(progress_ctx, 'e');
	  retried = 1;
	}
      if (retried && progress)
	progress(progress_ctx, '\n');	
    }
  else
    {
      /* Must always succeed, as we already that e
       * doesn't have any common factor with p-1 or q-1. */
      int res = mpz_invert(key->d, pub->e, phi);
      assert(res);
    }

  /* Done! Almost, we must compute the auxillary private values. */
  /* a = d % (p-1) */
  mpz_fdiv_r(key->a, key->d, p1);

  /* b = d % (q-1) */
  mpz_fdiv_r(key->b, key->d, q1);

  /* c was computed earlier */

  pub->size = key->size = (n_size + 7) / 8;
  assert(pub->size >= RSA_MINIMUM_N_OCTETS);
  
  mpz_clear(p1); mpz_clear(q1); mpz_clear(phi); mpz_clear(tmp);

  return 1;
}