1 /* crypto/bn/bn_prime.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58 /* ====================================================================
59 * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112 #include <stdio.h>
113 #include <time.h>
114 #include "cryptlib.h"
115 #include "bn_lcl.h"
116 #include <openssl/rand.h>
117
118 /* NB: these functions have been "upgraded", the deprecated versions (which are
119 * compatibility wrappers using these functions) are in bn_depr.c.
120 * - Geoff
121 */
122
123 /* The quick sieve algorithm approach to weeding out primes is
124 * Philip Zimmermann's, as implemented in PGP. I have had a read of
125 * his comments and implemented my own version.
126 */
127 #include "bn_prime.h"
128
129 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
130 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
131 static int probable_prime(BIGNUM *rnd, int bits);
132 static int probable_prime_dh(BIGNUM *rnd, int bits,
133 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
134 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
135 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
136
137 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
138 {
139 /* No callback means continue */
140 if(!cb) return 1;
141 switch(cb->ver)
142 {
143 case 1:
144 /* Deprecated-style callbacks */
145 if(!cb->cb.cb_1)
146 return 1;
147 cb->cb.cb_1(a, b, cb->arg);
148 return 1;
149 case 2:
150 /* New-style callbacks */
151 return cb->cb.cb_2(a, b, cb);
152 default:
153 break;
154 }
155 /* Unrecognised callback type */
156 return 0;
157 }
158
159 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
160 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
161 {
162 BIGNUM *t;
163 int found=0;
164 int i,j,c1=0;
165 BN_CTX *ctx;
166 int checks = BN_prime_checks_for_size(bits);
167
168 ctx=BN_CTX_new();
169 if (ctx == NULL) goto err;
170 BN_CTX_start(ctx);
171 t = BN_CTX_get(ctx);
172 if(!t) goto err;
173 loop:
174 /* make a random number and set the top and bottom bits */
175 if (add == NULL)
176 {
177 if (!probable_prime(ret,bits)) goto err;
178 }
179 else
180 {
181 if (safe)
182 {
183 if (!probable_prime_dh_safe(ret,bits,add,rem,ctx))
184 goto err;
185 }
186 else
187 {
188 if (!probable_prime_dh(ret,bits,add,rem,ctx))
189 goto err;
190 }
191 }
192 /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
193 if(!BN_GENCB_call(cb, 0, c1++))
194 /* aborted */
195 goto err;
196
197 if (!safe)
198 {
199 i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb);
200 if (i == -1) goto err;
201 if (i == 0) goto loop;
202 }
203 else
204 {
205 /* for "safe prime" generation,
206 * check that (p-1)/2 is prime.
207 * Since a prime is odd, We just
208 * need to divide by 2 */
209 if (!BN_rshift1(t,ret)) goto err;
210
211 for (i=0; i<checks; i++)
212 {
213 j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb);
214 if (j == -1) goto err;
215 if (j == 0) goto loop;
216
217 j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb);
218 if (j == -1) goto err;
219 if (j == 0) goto loop;
220
221 if(!BN_GENCB_call(cb, 2, c1-1))
222 goto err;
223 /* We have a safe prime test pass */
224 }
225 }
226 /* we have a prime :-) */
227 found = 1;
228 err:
229 if (ctx != NULL)
230 {
231 BN_CTX_end(ctx);
232 BN_CTX_free(ctx);
233 }
234 bn_check_top(ret);
235 return found;
236 }
237
238 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb)
239 {
240 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
241 }
242
243 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
244 int do_trial_division, BN_GENCB *cb)
245 {
246 int i, j, ret = -1;
247 int k;
248 BN_CTX *ctx = NULL;
249 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
250 BN_MONT_CTX *mont = NULL;
251 const BIGNUM *A = NULL;
252
253 if (BN_cmp(a, BN_value_one()) <= 0)
254 return 0;
255
256 if (checks == BN_prime_checks)
257 checks = BN_prime_checks_for_size(BN_num_bits(a));
258
259 /* first look for small factors */
260 if (!BN_is_odd(a))
261 /* a is even => a is prime if and only if a == 2 */
262 return BN_is_word(a, 2);
263 if (do_trial_division)
264 {
265 for (i = 1; i < NUMPRIMES; i++)
266 if (BN_mod_word(a, primes[i]) == 0)
267 return 0;
268 if(!BN_GENCB_call(cb, 1, -1))
269 goto err;
270 }
271
272 if (ctx_passed != NULL)
273 ctx = ctx_passed;
274 else
275 if ((ctx=BN_CTX_new()) == NULL)
276 goto err;
277 BN_CTX_start(ctx);
278
279 /* A := abs(a) */
280 if (a->neg)
281 {
282 BIGNUM *t;
283 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
284 BN_copy(t, a);
285 t->neg = 0;
286 A = t;
287 }
288 else
289 A = a;
290 A1 = BN_CTX_get(ctx);
291 A1_odd = BN_CTX_get(ctx);
292 check = BN_CTX_get(ctx);
293 if (check == NULL) goto err;
294
295 /* compute A1 := A - 1 */
296 if (!BN_copy(A1, A))
297 goto err;
298 if (!BN_sub_word(A1, 1))
299 goto err;
300 if (BN_is_zero(A1))
301 {
302 ret = 0;
303 goto err;
304 }
305
306 /* write A1 as A1_odd * 2^k */
307 k = 1;
308 while (!BN_is_bit_set(A1, k))
309 k++;
310 if (!BN_rshift(A1_odd, A1, k))
311 goto err;
312
313 /* Montgomery setup for computations mod A */
314 mont = BN_MONT_CTX_new();
315 if (mont == NULL)
316 goto err;
317 if (!BN_MONT_CTX_set(mont, A, ctx))
318 goto err;
319
320 for (i = 0; i < checks; i++)
321 {
322 if (!BN_pseudo_rand_range(check, A1))
323 goto err;
324 if (!BN_add_word(check, 1))
325 goto err;
326 /* now 1 <= check < A */
327
328 j = witness(check, A, A1, A1_odd, k, ctx, mont);
329 if (j == -1) goto err;
330 if (j)
331 {
332 ret=0;
333 goto err;
334 }
335 if(!BN_GENCB_call(cb, 1, i))
336 goto err;
337 }
338 ret=1;
339 err:
340 if (ctx != NULL)
341 {
342 BN_CTX_end(ctx);
343 if (ctx_passed == NULL)
344 BN_CTX_free(ctx);
345 }
346 if (mont != NULL)
347 BN_MONT_CTX_free(mont);
348
349 return(ret);
350 }
351
352 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
353 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
354 {
355 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
356 return -1;
357 if (BN_is_one(w))
358 return 0; /* probably prime */
359 if (BN_cmp(w, a1) == 0)
360 return 0; /* w == -1 (mod a), 'a' is probably prime */
361 while (--k)
362 {
363 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
364 return -1;
365 if (BN_is_one(w))
366 return 1; /* 'a' is composite, otherwise a previous 'w' would
367 * have been == -1 (mod 'a') */
368 if (BN_cmp(w, a1) == 0)
369 return 0; /* w == -1 (mod a), 'a' is probably prime */
370 }
371 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
372 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
373 bn_check_top(w);
374 return 1;
375 }
376
377 static int probable_prime(BIGNUM *rnd, int bits)
378 {
379 int i;
380 prime_t mods[NUMPRIMES];
381 BN_ULONG delta,maxdelta;
382
383 again:
384 if (!BN_rand(rnd,bits,1,1)) return(0);
385 /* we now have a random number 'rand' to test. */
386 for (i=1; i<NUMPRIMES; i++)
387 mods[i]=(prime_t)BN_mod_word(rnd,(BN_ULONG)primes[i]);
388 maxdelta=BN_MASK2 - primes[NUMPRIMES-1];
389 delta=0;
390 loop: for (i=1; i<NUMPRIMES; i++)
391 {
392 /* check that rnd is not a prime and also
393 * that gcd(rnd-1,primes) == 1 (except for 2) */
394 if (((mods[i]+delta)%primes[i]) <= 1)
395 {
396 delta+=2;
397 if (delta > maxdelta) goto again;
398 goto loop;
399 }
400 }
401 if (!BN_add_word(rnd,delta)) return(0);
402 bn_check_top(rnd);
403 return(1);
404 }
405
406 static int probable_prime_dh(BIGNUM *rnd, int bits,
407 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
408 {
409 int i,ret=0;
410 BIGNUM *t1;
411
412 BN_CTX_start(ctx);
413 if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
414
415 if (!BN_rand(rnd,bits,0,1)) goto err;
416
417 /* we need ((rnd-rem) % add) == 0 */
418
419 if (!BN_mod(t1,rnd,add,ctx)) goto err;
420 if (!BN_sub(rnd,rnd,t1)) goto err;
421 if (rem == NULL)
422 { if (!BN_add_word(rnd,1)) goto err; }
423 else
424 { if (!BN_add(rnd,rnd,rem)) goto err; }
425
426 /* we now have a random number 'rand' to test. */
427
428 loop: for (i=1; i<NUMPRIMES; i++)
429 {
430 /* check that rnd is a prime */
431 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
432 {
433 if (!BN_add(rnd,rnd,add)) goto err;
434 goto loop;
435 }
436 }
437 ret=1;
438 err:
439 BN_CTX_end(ctx);
440 bn_check_top(rnd);
441 return(ret);
442 }
443
444 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
445 const BIGNUM *rem, BN_CTX *ctx)
446 {
447 int i,ret=0;
448 BIGNUM *t1,*qadd,*q;
449
450 bits--;
451 BN_CTX_start(ctx);
452 t1 = BN_CTX_get(ctx);
453 q = BN_CTX_get(ctx);
454 qadd = BN_CTX_get(ctx);
455 if (qadd == NULL) goto err;
456
457 if (!BN_rshift1(qadd,padd)) goto err;
458
459 if (!BN_rand(q,bits,0,1)) goto err;
460
461 /* we need ((rnd-rem) % add) == 0 */
462 if (!BN_mod(t1,q,qadd,ctx)) goto err;
463 if (!BN_sub(q,q,t1)) goto err;
464 if (rem == NULL)
465 { if (!BN_add_word(q,1)) goto err; }
466 else
467 {
468 if (!BN_rshift1(t1,rem)) goto err;
469 if (!BN_add(q,q,t1)) goto err;
470 }
471
472 /* we now have a random number 'rand' to test. */
473 if (!BN_lshift1(p,q)) goto err;
474 if (!BN_add_word(p,1)) goto err;
475
476 loop: for (i=1; i<NUMPRIMES; i++)
477 {
478 /* check that p and q are prime */
479 /* check that for p and q
480 * gcd(p-1,primes) == 1 (except for 2) */
481 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
482 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
483 {
484 if (!BN_add(p,p,padd)) goto err;
485 if (!BN_add(q,q,qadd)) goto err;
486 goto loop;
487 }
488 }
489 ret=1;
490 err:
491 BN_CTX_end(ctx);
492 bn_check_top(p);
493 return(ret);
494 }