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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) 1998-2000 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/* The quick sieve algorithm approach to weeding out primes is
119 * Philip Zimmermann's, as implemented in PGP. I have had a read of
120 * his comments and implemented my own version.
121 */
122#include "bn_prime.h"
123
124static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
125 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont);
126static int probable_prime(BIGNUM *rnd, int bits);
127static int probable_prime_dh(BIGNUM *rnd, int bits,
128 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
129static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
130 BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
131
132BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
133 BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
134 {
135 BIGNUM *rnd=NULL;
136 BIGNUM t;
137 int found=0;
138 int i,j,c1=0;
139 BN_CTX *ctx;
140 int checks = BN_prime_checks_for_size(bits);
141
142 ctx=BN_CTX_new();
143 if (ctx == NULL) goto err;
144 if (ret == NULL)
145 {
146 if ((rnd=BN_new()) == NULL) goto err;
147 }
148 else
149 rnd=ret;
150 BN_init(&t);
151loop:
152 /* make a random number and set the top and bottom bits */
153 if (add == NULL)
154 {
155 if (!probable_prime(rnd,bits)) goto err;
156 }
157 else
158 {
159 if (safe)
160 {
161 if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
162 goto err;
163 }
164 else
165 {
166 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
167 goto err;
168 }
169 }
170 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
171 if (callback != NULL) callback(0,c1++,cb_arg);
172
173 if (!safe)
174 {
175 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
176 if (i == -1) goto err;
177 if (i == 0) goto loop;
178 }
179 else
180 {
181 /* for "safe prime" generation,
182 * check that (p-1)/2 is prime.
183 * Since a prime is odd, We just
184 * need to divide by 2 */
185 if (!BN_rshift1(&t,rnd)) goto err;
186
187 for (i=0; i<checks; i++)
188 {
189 j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
190 if (j == -1) goto err;
191 if (j == 0) goto loop;
192
193 j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
194 if (j == -1) goto err;
195 if (j == 0) goto loop;
196
197 if (callback != NULL) callback(2,c1-1,cb_arg);
198 /* We have a safe prime test pass */
199 }
200 }
201 /* we have a prime :-) */
202 found = 1;
203err:
204 if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
205 BN_free(&t);
206 if (ctx != NULL) BN_CTX_free(ctx);
207 return(found ? rnd : NULL);
208 }
209
210int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
211 BN_CTX *ctx_passed, void *cb_arg)
212 {
213 return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
214 }
215
216int BN_is_prime_fasttest(const BIGNUM *a, int checks,
217 void (*callback)(int,int,void *),
218 BN_CTX *ctx_passed, void *cb_arg,
219 int do_trial_division)
220 {
221 int i, j, ret = -1;
222 int k;
223 BN_CTX *ctx = NULL;
224 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
225 BN_MONT_CTX *mont = NULL;
226 const BIGNUM *A = NULL;
227
228 if (checks == BN_prime_checks)
229 checks = BN_prime_checks_for_size(BN_num_bits(a));
230
231 /* first look for small factors */
232 if (!BN_is_odd(a))
233 return(0);
234 if (do_trial_division)
235 {
236 for (i = 1; i < NUMPRIMES; i++)
237 if (BN_mod_word(a, primes[i]) == 0)
238 return 0;
239 if (callback != NULL) callback(1, -1, cb_arg);
240 }
241
242 if (ctx_passed != NULL)
243 ctx = ctx_passed;
244 else
245 if ((ctx=BN_CTX_new()) == NULL)
246 goto err;
247 BN_CTX_start(ctx);
248
249 /* A := abs(a) */
250 if (a->neg)
251 {
252 BIGNUM *t;
253 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
254 BN_copy(t, a);
255 t->neg = 0;
256 A = t;
257 }
258 else
259 A = a;
260 A1 = BN_CTX_get(ctx);
261 A1_odd = BN_CTX_get(ctx);
262 check = BN_CTX_get(ctx);
263 if (check == NULL) goto err;
264
265 /* compute A1 := A - 1 */
266 if (!BN_copy(A1, A))
267 goto err;
268 if (!BN_sub_word(A1, 1))
269 goto err;
270 if (BN_is_zero(A1))
271 {
272 ret = 0;
273 goto err;
274 }
275
276 /* write A1 as A1_odd * 2^k */
277 k = 1;
278 while (!BN_is_bit_set(A1, k))
279 k++;
280 if (!BN_rshift(A1_odd, A1, k))
281 goto err;
282
283 /* Montgomery setup for computations mod A */
284 mont = BN_MONT_CTX_new();
285 if (mont == NULL)
286 goto err;
287 if (!BN_MONT_CTX_set(mont, A, ctx))
288 goto err;
289
290 for (i = 0; i < checks; i++)
291 {
292 if (!BN_pseudo_rand(check, BN_num_bits(A1), 0, 0))
293 goto err;
294 if (BN_cmp(check, A1) >= 0)
295 if (!BN_sub(check, check, A1))
296 goto err;
297 if (!BN_add_word(check, 1))
298 goto err;
299 /* now 1 <= check < A */
300
301 j = witness(check, A, A1, A1_odd, k, ctx, mont);
302 if (j == -1) goto err;
303 if (j)
304 {
305 ret=0;
306 goto err;
307 }
308 if (callback != NULL) callback(1,i,cb_arg);
309 }
310 ret=1;
311err:
312 if (ctx != NULL)
313 {
314 BN_CTX_end(ctx);
315 if (ctx_passed == NULL)
316 BN_CTX_free(ctx);
317 }
318 if (mont != NULL)
319 BN_MONT_CTX_free(mont);
320
321 return(ret);
322 }
323
324static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
325 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
326 {
327 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
328 return -1;
329 if (BN_is_one(w))
330 return 0; /* probably prime */
331 if (BN_cmp(w, a1) == 0)
332 return 0; /* w == -1 (mod a), 'a' is probably prime */
333 while (--k)
334 {
335 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
336 return -1;
337 if (BN_is_one(w))
338 return 1; /* 'a' is composite, otherwise a previous 'w' would
339 * have been == -1 (mod 'a') */
340 if (BN_cmp(w, a1) == 0)
341 return 0; /* w == -1 (mod a), 'a' is probably prime */
342 }
343 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
344 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
345 return 1;
346 }
347
348static int probable_prime(BIGNUM *rnd, int bits)
349 {
350 int i;
351 BN_ULONG mods[NUMPRIMES];
352 BN_ULONG delta,d;
353
354again:
355 if (!BN_rand(rnd,bits,1,1)) return(0);
356 /* we now have a random number 'rand' to test. */
357 for (i=1; i<NUMPRIMES; i++)
358 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
359 delta=0;
360 loop: for (i=1; i<NUMPRIMES; i++)
361 {
362 /* check that rnd is not a prime and also
363 * that gcd(rnd-1,primes) == 1 (except for 2) */
364 if (((mods[i]+delta)%primes[i]) <= 1)
365 {
366 d=delta;
367 delta+=2;
368 /* perhaps need to check for overflow of
369 * delta (but delta can be up to 2^32)
370 * 21-May-98 eay - added overflow check */
371 if (delta < d) goto again;
372 goto loop;
373 }
374 }
375 if (!BN_add_word(rnd,delta)) return(0);
376 return(1);
377 }
378
379static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
380 BN_CTX *ctx)
381 {
382 int i,ret=0;
383 BIGNUM *t1;
384
385 BN_CTX_start(ctx);
386 if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
387
388 if (!BN_rand(rnd,bits,0,1)) goto err;
389
390 /* we need ((rnd-rem) % add) == 0 */
391
392 if (!BN_mod(t1,rnd,add,ctx)) goto err;
393 if (!BN_sub(rnd,rnd,t1)) goto err;
394 if (rem == NULL)
395 { if (!BN_add_word(rnd,1)) goto err; }
396 else
397 { if (!BN_add(rnd,rnd,rem)) goto err; }
398
399 /* we now have a random number 'rand' to test. */
400
401 loop: for (i=1; i<NUMPRIMES; i++)
402 {
403 /* check that rnd is a prime */
404 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
405 {
406 if (!BN_add(rnd,rnd,add)) goto err;
407 goto loop;
408 }
409 }
410 ret=1;
411err:
412 BN_CTX_end(ctx);
413 return(ret);
414 }
415
416static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
417 BIGNUM *rem, BN_CTX *ctx)
418 {
419 int i,ret=0;
420 BIGNUM *t1,*qadd,*q;
421
422 bits--;
423 BN_CTX_start(ctx);
424 t1 = BN_CTX_get(ctx);
425 q = BN_CTX_get(ctx);
426 qadd = BN_CTX_get(ctx);
427 if (qadd == NULL) goto err;
428
429 if (!BN_rshift1(qadd,padd)) goto err;
430
431 if (!BN_rand(q,bits,0,1)) goto err;
432
433 /* we need ((rnd-rem) % add) == 0 */
434 if (!BN_mod(t1,q,qadd,ctx)) goto err;
435 if (!BN_sub(q,q,t1)) goto err;
436 if (rem == NULL)
437 { if (!BN_add_word(q,1)) goto err; }
438 else
439 {
440 if (!BN_rshift1(t1,rem)) goto err;
441 if (!BN_add(q,q,t1)) goto err;
442 }
443
444 /* we now have a random number 'rand' to test. */
445 if (!BN_lshift1(p,q)) goto err;
446 if (!BN_add_word(p,1)) goto err;
447
448 loop: for (i=1; i<NUMPRIMES; i++)
449 {
450 /* check that p and q are prime */
451 /* check that for p and q
452 * gcd(p-1,primes) == 1 (except for 2) */
453 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
454 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
455 {
456 if (!BN_add(p,p,padd)) goto err;
457 if (!BN_add(q,q,qadd)) goto err;
458 goto loop;
459 }
460 }
461 ret=1;
462err:
463 BN_CTX_end(ctx);
464 return(ret);
465 }
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