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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) 1998-2001 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/* 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 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
129static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
130 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
131
132BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe,
133 const BIGNUM *add, const BIGNUM *rem,
134 void (*callback)(int,int,void *), void *cb_arg)
135 {
136 BIGNUM *rnd=NULL;
137 BIGNUM t;
138 int found=0;
139 int i,j,c1=0;
140 BN_CTX *ctx;
141 int checks = BN_prime_checks_for_size(bits);
142
143 BN_init(&t);
144 ctx=BN_CTX_new();
145 if (ctx == NULL) goto err;
146 if (ret == NULL)
147 {
148 if ((rnd=BN_new()) == NULL) goto err;
149 }
150 else
151 rnd=ret;
152loop:
153 /* make a random number and set the top and bottom bits */
154 if (add == NULL)
155 {
156 if (!probable_prime(rnd,bits)) goto err;
157 }
158 else
159 {
160 if (safe)
161 {
162 if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
163 goto err;
164 }
165 else
166 {
167 if (!probable_prime_dh(rnd,bits,add,rem,ctx))
168 goto err;
169 }
170 }
171 /* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
172 if (callback != NULL) callback(0,c1++,cb_arg);
173
174 if (!safe)
175 {
176 i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
177 if (i == -1) goto err;
178 if (i == 0) goto loop;
179 }
180 else
181 {
182 /* for "safe prime" generation,
183 * check that (p-1)/2 is prime.
184 * Since a prime is odd, We just
185 * need to divide by 2 */
186 if (!BN_rshift1(&t,rnd)) goto err;
187
188 for (i=0; i<checks; i++)
189 {
190 j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
191 if (j == -1) goto err;
192 if (j == 0) goto loop;
193
194 j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
195 if (j == -1) goto err;
196 if (j == 0) goto loop;
197
198 if (callback != NULL) callback(2,c1-1,cb_arg);
199 /* We have a safe prime test pass */
200 }
201 }
202 /* we have a prime :-) */
203 found = 1;
204err:
205 if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
206 BN_free(&t);
207 if (ctx != NULL) BN_CTX_free(ctx);
208 return(found ? rnd : NULL);
209 }
210
211int BN_is_prime(const BIGNUM *a, int checks, void (*callback)(int,int,void *),
212 BN_CTX *ctx_passed, void *cb_arg)
213 {
214 return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
215 }
216
217int BN_is_prime_fasttest(const BIGNUM *a, int checks,
218 void (*callback)(int,int,void *),
219 BN_CTX *ctx_passed, void *cb_arg,
220 int do_trial_division)
221 {
222 int i, j, ret = -1;
223 int k;
224 BN_CTX *ctx = NULL;
225 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
226 BN_MONT_CTX *mont = NULL;
227 const BIGNUM *A = NULL;
228
229 if (BN_cmp(a, BN_value_one()) <= 0)
230 return 0;
231
232 if (checks == BN_prime_checks)
233 checks = BN_prime_checks_for_size(BN_num_bits(a));
234
235 /* first look for small factors */
236 if (!BN_is_odd(a))
237 /* a is even => a is prime if and only if a == 2 */
238 return BN_is_word(a, 2);
239
240 if (do_trial_division)
241 {
242 for (i = 1; i < NUMPRIMES; i++)
243 if (BN_mod_word(a, primes[i]) == 0)
244 return 0;
245 if (callback != NULL) callback(1, -1, cb_arg);
246 }
247
248 if (ctx_passed != NULL)
249 ctx = ctx_passed;
250 else
251 if ((ctx=BN_CTX_new()) == NULL)
252 goto err;
253 BN_CTX_start(ctx);
254
255 /* A := abs(a) */
256 if (a->neg)
257 {
258 BIGNUM *t;
259 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
260 BN_copy(t, a);
261 t->neg = 0;
262 A = t;
263 }
264 else
265 A = a;
266 A1 = BN_CTX_get(ctx);
267 A1_odd = BN_CTX_get(ctx);
268 check = BN_CTX_get(ctx);
269 if (check == NULL) goto err;
270
271 /* compute A1 := A - 1 */
272 if (!BN_copy(A1, A))
273 goto err;
274 if (!BN_sub_word(A1, 1))
275 goto err;
276 if (BN_is_zero(A1))
277 {
278 ret = 0;
279 goto err;
280 }
281
282 /* write A1 as A1_odd * 2^k */
283 k = 1;
284 while (!BN_is_bit_set(A1, k))
285 k++;
286 if (!BN_rshift(A1_odd, A1, k))
287 goto err;
288
289 /* Montgomery setup for computations mod A */
290 mont = BN_MONT_CTX_new();
291 if (mont == NULL)
292 goto err;
293 if (!BN_MONT_CTX_set(mont, A, ctx))
294 goto err;
295
296 for (i = 0; i < checks; i++)
297 {
298 if (!BN_pseudo_rand_range(check, A1))
299 goto err;
300 if (!BN_add_word(check, 1))
301 goto err;
302 /* now 1 <= check < A */
303
304 j = witness(check, A, A1, A1_odd, k, ctx, mont);
305 if (j == -1) goto err;
306 if (j)
307 {
308 ret=0;
309 goto err;
310 }
311 if (callback != NULL) callback(1,i,cb_arg);
312 }
313 ret=1;
314err:
315 if (ctx != NULL)
316 {
317 BN_CTX_end(ctx);
318 if (ctx_passed == NULL)
319 BN_CTX_free(ctx);
320 }
321 if (mont != NULL)
322 BN_MONT_CTX_free(mont);
323
324 return(ret);
325 }
326
327static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
328 const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont)
329 {
330 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
331 return -1;
332 if (BN_is_one(w))
333 return 0; /* probably prime */
334 if (BN_cmp(w, a1) == 0)
335 return 0; /* w == -1 (mod a), 'a' is probably prime */
336 while (--k)
337 {
338 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
339 return -1;
340 if (BN_is_one(w))
341 return 1; /* 'a' is composite, otherwise a previous 'w' would
342 * have been == -1 (mod 'a') */
343 if (BN_cmp(w, a1) == 0)
344 return 0; /* w == -1 (mod a), 'a' is probably prime */
345 }
346 /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
347 * and it is neither -1 nor +1 -- so 'a' cannot be prime */
348 return 1;
349 }
350
351static int probable_prime(BIGNUM *rnd, int bits)
352 {
353 int i;
354 BN_ULONG mods[NUMPRIMES];
355 BN_ULONG delta,d;
356
357again:
358 if (!BN_rand(rnd,bits,1,1)) return(0);
359 /* we now have a random number 'rand' to test. */
360 for (i=1; i<NUMPRIMES; i++)
361 mods[i]=BN_mod_word(rnd,(BN_ULONG)primes[i]);
362 delta=0;
363 loop: for (i=1; i<NUMPRIMES; i++)
364 {
365 /* check that rnd is not a prime and also
366 * that gcd(rnd-1,primes) == 1 (except for 2) */
367 if (((mods[i]+delta)%primes[i]) <= 1)
368 {
369 d=delta;
370 delta+=2;
371 /* perhaps need to check for overflow of
372 * delta (but delta can be up to 2^32)
373 * 21-May-98 eay - added overflow check */
374 if (delta < d) goto again;
375 goto loop;
376 }
377 }
378 if (!BN_add_word(rnd,delta)) return(0);
379 return(1);
380 }
381
382static int probable_prime_dh(BIGNUM *rnd, int bits,
383 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
384 {
385 int i,ret=0;
386 BIGNUM *t1;
387
388 BN_CTX_start(ctx);
389 if ((t1 = BN_CTX_get(ctx)) == NULL) goto err;
390
391 if (!BN_rand(rnd,bits,0,1)) goto err;
392
393 /* we need ((rnd-rem) % add) == 0 */
394
395 if (!BN_mod(t1,rnd,add,ctx)) goto err;
396 if (!BN_sub(rnd,rnd,t1)) goto err;
397 if (rem == NULL)
398 { if (!BN_add_word(rnd,1)) goto err; }
399 else
400 { if (!BN_add(rnd,rnd,rem)) goto err; }
401
402 /* we now have a random number 'rand' to test. */
403
404 loop: for (i=1; i<NUMPRIMES; i++)
405 {
406 /* check that rnd is a prime */
407 if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
408 {
409 if (!BN_add(rnd,rnd,add)) goto err;
410 goto loop;
411 }
412 }
413 ret=1;
414err:
415 BN_CTX_end(ctx);
416 return(ret);
417 }
418
419static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
420 const BIGNUM *rem, BN_CTX *ctx)
421 {
422 int i,ret=0;
423 BIGNUM *t1,*qadd,*q;
424
425 bits--;
426 BN_CTX_start(ctx);
427 t1 = BN_CTX_get(ctx);
428 q = BN_CTX_get(ctx);
429 qadd = BN_CTX_get(ctx);
430 if (qadd == NULL) goto err;
431
432 if (!BN_rshift1(qadd,padd)) goto err;
433
434 if (!BN_rand(q,bits,0,1)) goto err;
435
436 /* we need ((rnd-rem) % add) == 0 */
437 if (!BN_mod(t1,q,qadd,ctx)) goto err;
438 if (!BN_sub(q,q,t1)) goto err;
439 if (rem == NULL)
440 { if (!BN_add_word(q,1)) goto err; }
441 else
442 {
443 if (!BN_rshift1(t1,rem)) goto err;
444 if (!BN_add(q,q,t1)) goto err;
445 }
446
447 /* we now have a random number 'rand' to test. */
448 if (!BN_lshift1(p,q)) goto err;
449 if (!BN_add_word(p,1)) goto err;
450
451 loop: for (i=1; i<NUMPRIMES; i++)
452 {
453 /* check that p and q are prime */
454 /* check that for p and q
455 * gcd(p-1,primes) == 1 (except for 2) */
456 if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
457 (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
458 {
459 if (!BN_add(p,p,padd)) goto err;
460 if (!BN_add(q,q,qadd)) goto err;
461 goto loop;
462 }
463 }
464 ret=1;
465err:
466 BN_CTX_end(ctx);
467 return(ret);
468 }
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