rsa-keygen.c 7.98 KB
Newer Older
Niels Möller's avatar
Niels Möller committed
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
/* rsa-keygen.c
 *
 * Generation of RSA keypairs
 */

/* nettle, low-level cryptographics library
 *
 * Copyright (C) 2002 Niels Mller
 *  
 * The nettle library 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.
 * 
 * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
 * the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

#if HAVE_CONFIG_H
27
# include "config.h"
Niels Möller's avatar
Niels Möller committed
28
29
30
31
32
33
#endif

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

34
35
#include "rsa.h"
#include "bignum.h"
36
#include "nettle-internal.h"
37

Niels Möller's avatar
Niels Möller committed
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
#ifndef DEBUG
# define DEBUG 0
#endif

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


#define NUMBER_OF_PRIMES 167

static const unsigned long primes[NUMBER_OF_PRIMES] = {
  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
};

/* NOTE: The mpz_nextprime in current GMP is unoptimized. */
static void
bignum_next_prime(mpz_t p, mpz_t n, int count,
		  void *progress_ctx, nettle_progress_func progress)
{
  mpz_t tmp;
71
72
  TMP_DECL(moduli, unsigned long, NUMBER_OF_PRIMES);
  
Niels Möller's avatar
Niels Möller committed
73
  unsigned long difference;
74
75
  unsigned prime_limit = NUMBER_OF_PRIMES;
  
Niels Möller's avatar
Niels Möller committed
76
77
78
79
80
81
82
83
84
85
86
87
88
89
  /* First handle tiny numbers */
  if (mpz_cmp_ui(n, 2) <= 0)
    {
      mpz_set_ui(p, 2);
      return;
    }
  mpz_set(p, n);
  mpz_setbit(p, 0);

  if (mpz_cmp_ui(p, 8) < 0)
    return;

  mpz_init(tmp);

90
91
  if (mpz_cmp_ui(p, primes[prime_limit-1]) <= 0)
    /* Use only 3, 5 and 7 */
Niels Möller's avatar
Niels Möller committed
92
    prime_limit = 3;
93
94
95
96
97
98
99
100
101
  
  /* Compute residues modulo small odd primes */
  TMP_ALLOC(moduli, prime_limit);
  {
    unsigned i;
    for (i = 0; i < prime_limit; i++)
      moduli[i] = mpz_fdiv_ui(p, primes[i]);
  }
  
Niels Möller's avatar
Niels Möller committed
102
103
  for (difference = 0; ; difference += 2)
    {
104
105
106
      int composite = 0;
      unsigned i;

Niels Möller's avatar
Niels Möller committed
107
108
109
110
111
112
113
      if (difference >= ULONG_MAX - 10)
	{ /* Should not happen, at least not very often... */
	  mpz_add_ui(p, p, difference);
	  difference = 0;
	}

      /* First check residues */
114
      for (i = 0; i < prime_limit; i++)
Niels Möller's avatar
Niels Möller committed
115
	{
116
117
118
	  if (moduli[i] == 0)
	    composite = 1;
	  moduli[i] = (moduli[i] + 2) % primes[i];
Niels Möller's avatar
Niels Möller committed
119
	}
120
121
      if (composite)
	continue;
Niels Möller's avatar
Niels Möller committed
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
      
      mpz_add_ui(p, p, difference);
      difference = 0;

      if (progress)
	progress(progress_ctx, '.');
      
      /* Fermat test, with respect to 2 */
      mpz_set_ui(tmp, 2);
      mpz_powm(tmp, tmp, p, p);
      if (mpz_cmp_ui(tmp, 2) != 0)
	continue;

      if (progress)
	progress(progress_ctx, '+');

      /* Miller-Rabin test */
      if (mpz_probab_prime_p(p, count))
	break;
    }
  mpz_clear(tmp);
}

/* Returns a random prime of size BITS */
static void
bignum_random_prime(mpz_t x, unsigned bits,
		    void *random_ctx, nettle_random_func random,
		    void *progress_ctx, nettle_progress_func progress)
{
  assert(bits);
  
  for (;;)
    {
Niels Möller's avatar
Niels Möller committed
155
      nettle_mpz_random_size(x, random_ctx, random, bits);
Niels Möller's avatar
Niels Möller committed
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
      mpz_setbit(x, bits - 1);

      /* Miller-rabin count of 25 is probably much overkill. */
      bignum_next_prime(x, x, 25, progress_ctx, progress);

      if (mpz_sizeinbase(x, 2) == bits)
	break;
    }
}

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;
    }
  
  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 (;;)
	{
	  bignum_random_prime(key->p, (n_size+1)/2,
			      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 (;;)
	{
	  bignum_random_prime(key->q, n_size/2,
			      random_ctx, random,
			      progress_ctx, progress);
	  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);
      
      if (mpz_sizeinbase(pub->n, 2) != n_size)
	/* We might get an n of size n_size-1. Then just try again. */
	{
#if DEBUG
	  fprintf(stderr,
		  "\nWanted size: %d, p-size: %d, q-size: %d, n-size: %d\n",
		  n_size,
		  mpz_sizeinbase(key->p,2),
		  mpz_sizeinbase(key->q,2),
		  mpz_sizeinbase(pub->n,2));
#endif
	  if (progress)
	    {
	      progress(progress_ctx, 'b');
	      progress(progress_ctx, '\n');
	    }
	  continue;
	}
      
      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)
286
287
288
289
    {
      int retried = 0;
      for (;;)
	{
Niels Möller's avatar
Niels Möller committed
290
291
292
	  nettle_mpz_random_size(pub->e,
				 random_ctx, random,
				 e_size);
Niels Möller's avatar
Niels Möller committed
293
	
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
	  /* 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');	
    }
Niels Möller's avatar
Niels Möller committed
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
  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 = (mpz_sizeinbase(pub->n, 2) + 7) / 8;
  assert(pub->size >= RSA_MINIMUM_N_OCTETS);
  
  mpz_clear(p1); mpz_clear(q1); mpz_clear(phi); mpz_clear(tmp);

  return 1;
}