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1 | /* $OpenBSD: moduli.c,v 1.5 2003/12/22 09:16:57 djm Exp $ */ | |
2 | /* | |
3 | * Copyright 1994 Phil Karn <karn@qualcomm.com> | |
4 | * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> | |
5 | * Copyright 2000 Niels Provos <provos@citi.umich.edu> | |
6 | * All rights reserved. | |
7 | * | |
8 | * Redistribution and use in source and binary forms, with or without | |
9 | * modification, are permitted provided that the following conditions | |
10 | * are met: | |
11 | * 1. Redistributions of source code must retain the above copyright | |
12 | * notice, this list of conditions and the following disclaimer. | |
13 | * 2. Redistributions in binary form must reproduce the above copyright | |
14 | * notice, this list of conditions and the following disclaimer in the | |
15 | * documentation and/or other materials provided with the distribution. | |
16 | * | |
17 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR | |
18 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES | |
19 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. | |
20 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, | |
21 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT | |
22 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | |
23 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | |
24 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | |
25 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF | |
26 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | |
27 | */ | |
28 | ||
29 | /* | |
30 | * Two-step process to generate safe primes for DHGEX | |
31 | * | |
32 | * Sieve candidates for "safe" primes, | |
33 | * suitable for use as Diffie-Hellman moduli; | |
34 | * that is, where q = (p-1)/2 is also prime. | |
35 | * | |
36 | * First step: generate candidate primes (memory intensive) | |
37 | * Second step: test primes' safety (processor intensive) | |
38 | */ | |
39 | ||
40 | #include "includes.h" | |
41 | #include "moduli.h" | |
42 | #include "xmalloc.h" | |
43 | #include "log.h" | |
44 | ||
45 | #include <openssl/bn.h> | |
46 | ||
47 | /* | |
48 | * File output defines | |
49 | */ | |
50 | ||
51 | /* need line long enough for largest moduli plus headers */ | |
52 | #define QLINESIZE (100+8192) | |
53 | ||
54 | /* Type: decimal. | |
55 | * Specifies the internal structure of the prime modulus. | |
56 | */ | |
57 | #define QTYPE_UNKNOWN (0) | |
58 | #define QTYPE_UNSTRUCTURED (1) | |
59 | #define QTYPE_SAFE (2) | |
60 | #define QTYPE_SCHNOOR (3) | |
61 | #define QTYPE_SOPHIE_GERMAINE (4) | |
62 | #define QTYPE_STRONG (5) | |
63 | ||
64 | /* Tests: decimal (bit field). | |
65 | * Specifies the methods used in checking for primality. | |
66 | * Usually, more than one test is used. | |
67 | */ | |
68 | #define QTEST_UNTESTED (0x00) | |
69 | #define QTEST_COMPOSITE (0x01) | |
70 | #define QTEST_SIEVE (0x02) | |
71 | #define QTEST_MILLER_RABIN (0x04) | |
72 | #define QTEST_JACOBI (0x08) | |
73 | #define QTEST_ELLIPTIC (0x10) | |
74 | ||
75 | /* | |
76 | * Size: decimal. | |
77 | * Specifies the number of the most significant bit (0 to M). | |
78 | * WARNING: internally, usually 1 to N. | |
79 | */ | |
80 | #define QSIZE_MINIMUM (511) | |
81 | ||
82 | /* | |
83 | * Prime sieving defines | |
84 | */ | |
85 | ||
86 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
87 | #define SHIFT_BIT (3) | |
88 | #define SHIFT_BYTE (2) | |
89 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
90 | #define SHIFT_MEGABYTE (20) | |
91 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
92 | ||
93 | /* | |
94 | * Constant: when used with 32-bit integers, the largest sieve prime | |
95 | * has to be less than 2**32. | |
96 | */ | |
97 | #define SMALL_MAXIMUM (0xffffffffUL) | |
98 | ||
99 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
100 | #define TINY_NUMBER (1UL<<16) | |
101 | ||
102 | /* Ensure enough bit space for testing 2*q. */ | |
103 | #define TEST_MAXIMUM (1UL<<16) | |
104 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
105 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
106 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
107 | ||
108 | /* bit operations on 32-bit words */ | |
109 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) | |
110 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
111 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
112 | ||
113 | /* | |
114 | * Prime testing defines | |
115 | */ | |
116 | ||
117 | /* | |
118 | * Sieving data (XXX - move to struct) | |
119 | */ | |
120 | ||
121 | /* sieve 2**16 */ | |
122 | static u_int32_t *TinySieve, tinybits; | |
123 | ||
124 | /* sieve 2**30 in 2**16 parts */ | |
125 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
126 | ||
127 | /* sieve relative to the initial value */ | |
128 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
129 | static u_int32_t largebits, largememory; /* megabytes */ | |
130 | static BIGNUM *largebase; | |
131 | ||
132 | ||
133 | /* | |
134 | * print moduli out in consistent form, | |
135 | */ | |
136 | static int | |
137 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
138 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
139 | { | |
140 | struct tm *gtm; | |
141 | time_t time_now; | |
142 | int res; | |
143 | ||
144 | time(&time_now); | |
145 | gtm = gmtime(&time_now); | |
146 | ||
147 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", | |
148 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
149 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
150 | otype, otests, otries, osize, ogenerator); | |
151 | ||
152 | if (res < 0) | |
153 | return (-1); | |
154 | ||
155 | if (BN_print_fp(ofile, omodulus) < 1) | |
156 | return (-1); | |
157 | ||
158 | res = fprintf(ofile, "\n"); | |
159 | fflush(ofile); | |
160 | ||
161 | return (res > 0 ? 0 : -1); | |
162 | } | |
163 | ||
164 | ||
165 | /* | |
166 | ** Sieve p's and q's with small factors | |
167 | */ | |
168 | static void | |
169 | sieve_large(u_int32_t s) | |
170 | { | |
171 | u_int32_t r, u; | |
172 | ||
173 | debug3("sieve_large %u", s); | |
174 | largetries++; | |
175 | /* r = largebase mod s */ | |
176 | r = BN_mod_word(largebase, s); | |
177 | if (r == 0) | |
178 | u = 0; /* s divides into largebase exactly */ | |
179 | else | |
180 | u = s - r; /* largebase+u is first entry divisible by s */ | |
181 | ||
182 | if (u < largebits * 2) { | |
183 | /* | |
184 | * The sieve omits p's and q's divisible by 2, so ensure that | |
185 | * largebase+u is odd. Then, step through the sieve in | |
186 | * increments of 2*s | |
187 | */ | |
188 | if (u & 0x1) | |
189 | u += s; /* Make largebase+u odd, and u even */ | |
190 | ||
191 | /* Mark all multiples of 2*s */ | |
192 | for (u /= 2; u < largebits; u += s) | |
193 | BIT_SET(LargeSieve, u); | |
194 | } | |
195 | ||
196 | /* r = p mod s */ | |
197 | r = (2 * r + 1) % s; | |
198 | if (r == 0) | |
199 | u = 0; /* s divides p exactly */ | |
200 | else | |
201 | u = s - r; /* p+u is first entry divisible by s */ | |
202 | ||
203 | if (u < largebits * 4) { | |
204 | /* | |
205 | * The sieve omits p's divisible by 4, so ensure that | |
206 | * largebase+u is not. Then, step through the sieve in | |
207 | * increments of 4*s | |
208 | */ | |
209 | while (u & 0x3) { | |
210 | if (SMALL_MAXIMUM - u < s) | |
211 | return; | |
212 | u += s; | |
213 | } | |
214 | ||
215 | /* Mark all multiples of 4*s */ | |
216 | for (u /= 4; u < largebits; u += s) | |
217 | BIT_SET(LargeSieve, u); | |
218 | } | |
219 | } | |
220 | ||
221 | /* | |
222 | * list candidates for Sophie-Germaine primes (where q = (p-1)/2) | |
223 | * to standard output. | |
224 | * The list is checked against small known primes (less than 2**30). | |
225 | */ | |
226 | int | |
227 | gen_candidates(FILE *out, int memory, int power, BIGNUM *start) | |
228 | { | |
229 | BIGNUM *q; | |
230 | u_int32_t j, r, s, t; | |
231 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
232 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
233 | time_t time_start, time_stop; | |
234 | int i, ret = 0; | |
235 | ||
236 | largememory = memory; | |
237 | ||
238 | /* | |
239 | * Set power to the length in bits of the prime to be generated. | |
240 | * This is changed to 1 less than the desired safe prime moduli p. | |
241 | */ | |
242 | if (power > TEST_MAXIMUM) { | |
243 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
244 | return (-1); | |
245 | } else if (power < TEST_MINIMUM) { | |
246 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
247 | return (-1); | |
248 | } | |
249 | power--; /* decrement before squaring */ | |
250 | ||
251 | /* | |
252 | * The density of ordinary primes is on the order of 1/bits, so the | |
253 | * density of safe primes should be about (1/bits)**2. Set test range | |
254 | * to something well above bits**2 to be reasonably sure (but not | |
255 | * guaranteed) of catching at least one safe prime. | |
256 | */ | |
257 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
258 | ||
259 | /* | |
260 | * Need idea of how much memory is available. We don't have to use all | |
261 | * of it. | |
262 | */ | |
263 | if (largememory > LARGE_MAXIMUM) { | |
264 | logit("Limited memory: %u MB; limit %lu MB", | |
265 | largememory, LARGE_MAXIMUM); | |
266 | largememory = LARGE_MAXIMUM; | |
267 | } | |
268 | ||
269 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
270 | logit("Increased memory: %u MB; need %u bytes", | |
271 | largememory, (largewords << SHIFT_BYTE)); | |
272 | largewords = (largememory << SHIFT_MEGAWORD); | |
273 | } else if (largememory > 0) { | |
274 | logit("Decreased memory: %u MB; want %u bytes", | |
275 | largememory, (largewords << SHIFT_BYTE)); | |
276 | largewords = (largememory << SHIFT_MEGAWORD); | |
277 | } | |
278 | ||
279 | TinySieve = calloc(tinywords, sizeof(u_int32_t)); | |
280 | if (TinySieve == NULL) { | |
281 | error("Insufficient memory for tiny sieve: need %u bytes", | |
282 | tinywords << SHIFT_BYTE); | |
283 | exit(1); | |
284 | } | |
285 | tinybits = tinywords << SHIFT_WORD; | |
286 | ||
287 | SmallSieve = calloc(smallwords, sizeof(u_int32_t)); | |
288 | if (SmallSieve == NULL) { | |
289 | error("Insufficient memory for small sieve: need %u bytes", | |
290 | smallwords << SHIFT_BYTE); | |
291 | xfree(TinySieve); | |
292 | exit(1); | |
293 | } | |
294 | smallbits = smallwords << SHIFT_WORD; | |
295 | ||
296 | /* | |
297 | * dynamically determine available memory | |
298 | */ | |
299 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
300 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
301 | ||
302 | largebits = largewords << SHIFT_WORD; | |
303 | largenumbers = largebits * 2; /* even numbers excluded */ | |
304 | ||
305 | /* validation check: count the number of primes tried */ | |
306 | largetries = 0; | |
307 | q = BN_new(); | |
308 | ||
309 | /* | |
310 | * Generate random starting point for subprime search, or use | |
311 | * specified parameter. | |
312 | */ | |
313 | largebase = BN_new(); | |
314 | if (start == NULL) | |
315 | BN_rand(largebase, power, 1, 1); | |
316 | else | |
317 | BN_copy(largebase, start); | |
318 | ||
319 | /* ensure odd */ | |
320 | BN_set_bit(largebase, 0); | |
321 | ||
322 | time(&time_start); | |
323 | ||
324 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), | |
325 | largenumbers, power); | |
326 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
327 | ||
328 | /* | |
329 | * TinySieve | |
330 | */ | |
331 | for (i = 0; i < tinybits; i++) { | |
332 | if (BIT_TEST(TinySieve, i)) | |
333 | continue; /* 2*i+3 is composite */ | |
334 | ||
335 | /* The next tiny prime */ | |
336 | t = 2 * i + 3; | |
337 | ||
338 | /* Mark all multiples of t */ | |
339 | for (j = i + t; j < tinybits; j += t) | |
340 | BIT_SET(TinySieve, j); | |
341 | ||
342 | sieve_large(t); | |
343 | } | |
344 | ||
345 | /* | |
346 | * Start the small block search at the next possible prime. To avoid | |
347 | * fencepost errors, the last pass is skipped. | |
348 | */ | |
349 | for (smallbase = TINY_NUMBER + 3; | |
350 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); | |
351 | smallbase += TINY_NUMBER) { | |
352 | for (i = 0; i < tinybits; i++) { | |
353 | if (BIT_TEST(TinySieve, i)) | |
354 | continue; /* 2*i+3 is composite */ | |
355 | ||
356 | /* The next tiny prime */ | |
357 | t = 2 * i + 3; | |
358 | r = smallbase % t; | |
359 | ||
360 | if (r == 0) { | |
361 | s = 0; /* t divides into smallbase exactly */ | |
362 | } else { | |
363 | /* smallbase+s is first entry divisible by t */ | |
364 | s = t - r; | |
365 | } | |
366 | ||
367 | /* | |
368 | * The sieve omits even numbers, so ensure that | |
369 | * smallbase+s is odd. Then, step through the sieve | |
370 | * in increments of 2*t | |
371 | */ | |
372 | if (s & 1) | |
373 | s += t; /* Make smallbase+s odd, and s even */ | |
374 | ||
375 | /* Mark all multiples of 2*t */ | |
376 | for (s /= 2; s < smallbits; s += t) | |
377 | BIT_SET(SmallSieve, s); | |
378 | } | |
379 | ||
380 | /* | |
381 | * SmallSieve | |
382 | */ | |
383 | for (i = 0; i < smallbits; i++) { | |
384 | if (BIT_TEST(SmallSieve, i)) | |
385 | continue; /* 2*i+smallbase is composite */ | |
386 | ||
387 | /* The next small prime */ | |
388 | sieve_large((2 * i) + smallbase); | |
389 | } | |
390 | ||
391 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
392 | } | |
393 | ||
394 | time(&time_stop); | |
395 | ||
396 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
397 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
398 | ||
399 | for (j = r = 0; j < largebits; j++) { | |
400 | if (BIT_TEST(LargeSieve, j)) | |
401 | continue; /* Definitely composite, skip */ | |
402 | ||
403 | debug2("test q = largebase+%u", 2 * j); | |
404 | BN_set_word(q, 2 * j); | |
405 | BN_add(q, q, largebase); | |
406 | if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE, | |
407 | largetries, (power - 1) /* MSB */, (0), q) == -1) { | |
408 | ret = -1; | |
409 | break; | |
410 | } | |
411 | ||
412 | r++; /* count q */ | |
413 | } | |
414 | ||
415 | time(&time_stop); | |
416 | ||
417 | xfree(LargeSieve); | |
418 | xfree(SmallSieve); | |
419 | xfree(TinySieve); | |
420 | ||
421 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
422 | ||
423 | return (ret); | |
424 | } | |
425 | ||
426 | /* | |
427 | * perform a Miller-Rabin primality test | |
428 | * on the list of candidates | |
429 | * (checking both q and p) | |
430 | * The result is a list of so-call "safe" primes | |
431 | */ | |
432 | int | |
433 | prime_test(FILE *in, FILE *out, u_int32_t trials, | |
434 | u_int32_t generator_wanted) | |
435 | { | |
436 | BIGNUM *q, *p, *a; | |
437 | BN_CTX *ctx; | |
438 | char *cp, *lp; | |
439 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
440 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
441 | time_t time_start, time_stop; | |
442 | int res; | |
443 | ||
444 | time(&time_start); | |
445 | ||
446 | p = BN_new(); | |
447 | q = BN_new(); | |
448 | ctx = BN_CTX_new(); | |
449 | ||
450 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
451 | ctime(&time_start), trials, generator_wanted); | |
452 | ||
453 | res = 0; | |
454 | lp = xmalloc(QLINESIZE + 1); | |
455 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
456 | int ll = strlen(lp); | |
457 | ||
458 | count_in++; | |
459 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
460 | debug2("%10u: comment or short line", count_in); | |
461 | continue; | |
462 | } | |
463 | ||
464 | /* XXX - fragile parser */ | |
465 | /* time */ | |
466 | cp = &lp[14]; /* (skip) */ | |
467 | ||
468 | /* type */ | |
469 | in_type = strtoul(cp, &cp, 10); | |
470 | ||
471 | /* tests */ | |
472 | in_tests = strtoul(cp, &cp, 10); | |
473 | ||
474 | if (in_tests & QTEST_COMPOSITE) { | |
475 | debug2("%10u: known composite", count_in); | |
476 | continue; | |
477 | } | |
478 | ||
479 | /* tries */ | |
480 | in_tries = strtoul(cp, &cp, 10); | |
481 | ||
482 | /* size (most significant bit) */ | |
483 | in_size = strtoul(cp, &cp, 10); | |
484 | ||
485 | /* generator (hex) */ | |
486 | generator_known = strtoul(cp, &cp, 16); | |
487 | ||
488 | /* Skip white space */ | |
489 | cp += strspn(cp, " "); | |
490 | ||
491 | /* modulus (hex) */ | |
492 | switch (in_type) { | |
493 | case QTYPE_SOPHIE_GERMAINE: | |
494 | debug2("%10u: (%u) Sophie-Germaine", count_in, in_type); | |
495 | a = q; | |
496 | BN_hex2bn(&a, cp); | |
497 | /* p = 2*q + 1 */ | |
498 | BN_lshift(p, q, 1); | |
499 | BN_add_word(p, 1); | |
500 | in_size += 1; | |
501 | generator_known = 0; | |
502 | break; | |
503 | case QTYPE_UNSTRUCTURED: | |
504 | case QTYPE_SAFE: | |
505 | case QTYPE_SCHNOOR: | |
506 | case QTYPE_STRONG: | |
507 | case QTYPE_UNKNOWN: | |
508 | debug2("%10u: (%u)", count_in, in_type); | |
509 | a = p; | |
510 | BN_hex2bn(&a, cp); | |
511 | /* q = (p-1) / 2 */ | |
512 | BN_rshift(q, p, 1); | |
513 | break; | |
514 | default: | |
515 | debug2("Unknown prime type"); | |
516 | break; | |
517 | } | |
518 | ||
519 | /* | |
520 | * due to earlier inconsistencies in interpretation, check | |
521 | * the proposed bit size. | |
522 | */ | |
523 | if (BN_num_bits(p) != (in_size + 1)) { | |
524 | debug2("%10u: bit size %u mismatch", count_in, in_size); | |
525 | continue; | |
526 | } | |
527 | if (in_size < QSIZE_MINIMUM) { | |
528 | debug2("%10u: bit size %u too short", count_in, in_size); | |
529 | continue; | |
530 | } | |
531 | ||
532 | if (in_tests & QTEST_MILLER_RABIN) | |
533 | in_tries += trials; | |
534 | else | |
535 | in_tries = trials; | |
536 | ||
537 | /* | |
538 | * guess unknown generator | |
539 | */ | |
540 | if (generator_known == 0) { | |
541 | if (BN_mod_word(p, 24) == 11) | |
542 | generator_known = 2; | |
543 | else if (BN_mod_word(p, 12) == 5) | |
544 | generator_known = 3; | |
545 | else { | |
546 | u_int32_t r = BN_mod_word(p, 10); | |
547 | ||
548 | if (r == 3 || r == 7) | |
549 | generator_known = 5; | |
550 | } | |
551 | } | |
552 | /* | |
553 | * skip tests when desired generator doesn't match | |
554 | */ | |
555 | if (generator_wanted > 0 && | |
556 | generator_wanted != generator_known) { | |
557 | debug2("%10u: generator %d != %d", | |
558 | count_in, generator_known, generator_wanted); | |
559 | continue; | |
560 | } | |
561 | ||
562 | /* | |
563 | * Primes with no known generator are useless for DH, so | |
564 | * skip those. | |
565 | */ | |
566 | if (generator_known == 0) { | |
567 | debug2("%10u: no known generator", count_in); | |
568 | continue; | |
569 | } | |
570 | ||
571 | count_possible++; | |
572 | ||
573 | /* | |
574 | * The (1/4)^N performance bound on Miller-Rabin is | |
575 | * extremely pessimistic, so don't spend a lot of time | |
576 | * really verifying that q is prime until after we know | |
577 | * that p is also prime. A single pass will weed out the | |
578 | * vast majority of composite q's. | |
579 | */ | |
580 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
581 | debug("%10u: q failed first possible prime test", | |
582 | count_in); | |
583 | continue; | |
584 | } | |
585 | ||
586 | /* | |
587 | * q is possibly prime, so go ahead and really make sure | |
588 | * that p is prime. If it is, then we can go back and do | |
589 | * the same for q. If p is composite, chances are that | |
590 | * will show up on the first Rabin-Miller iteration so it | |
591 | * doesn't hurt to specify a high iteration count. | |
592 | */ | |
593 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
594 | debug("%10u: p is not prime", count_in); | |
595 | continue; | |
596 | } | |
597 | debug("%10u: p is almost certainly prime", count_in); | |
598 | ||
599 | /* recheck q more rigorously */ | |
600 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
601 | debug("%10u: q is not prime", count_in); | |
602 | continue; | |
603 | } | |
604 | debug("%10u: q is almost certainly prime", count_in); | |
605 | ||
606 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), | |
607 | in_tries, in_size, generator_known, p)) { | |
608 | res = -1; | |
609 | break; | |
610 | } | |
611 | ||
612 | count_out++; | |
613 | } | |
614 | ||
615 | time(&time_stop); | |
616 | xfree(lp); | |
617 | BN_free(p); | |
618 | BN_free(q); | |
619 | BN_CTX_free(ctx); | |
620 | ||
621 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
622 | ctime(&time_stop), count_out, count_possible, | |
623 | (long) (time_stop - time_start)); | |
624 | ||
625 | return (res); | |
626 | } |