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5ae3dc68 | 1 | /* $OpenBSD: moduli.c,v 1.1 2003/07/28 09:49:56 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 | /* | |
49 | * Debugging defines | |
50 | */ | |
51 | ||
52 | /* define DEBUG_LARGE 1 */ | |
53 | /* define DEBUG_SMALL 1 */ | |
54 | /* define DEBUG_TEST 1 */ | |
55 | ||
56 | /* | |
57 | * File output defines | |
58 | */ | |
59 | ||
60 | /* need line long enough for largest moduli plus headers */ | |
61 | #define QLINESIZE (100+8192) | |
62 | ||
63 | /* Type: decimal. | |
64 | * Specifies the internal structure of the prime modulus. | |
65 | */ | |
66 | #define QTYPE_UNKNOWN (0) | |
67 | #define QTYPE_UNSTRUCTURED (1) | |
68 | #define QTYPE_SAFE (2) | |
69 | #define QTYPE_SCHNOOR (3) | |
70 | #define QTYPE_SOPHIE_GERMAINE (4) | |
71 | #define QTYPE_STRONG (5) | |
72 | ||
73 | /* Tests: decimal (bit field). | |
74 | * Specifies the methods used in checking for primality. | |
75 | * Usually, more than one test is used. | |
76 | */ | |
77 | #define QTEST_UNTESTED (0x00) | |
78 | #define QTEST_COMPOSITE (0x01) | |
79 | #define QTEST_SIEVE (0x02) | |
80 | #define QTEST_MILLER_RABIN (0x04) | |
81 | #define QTEST_JACOBI (0x08) | |
82 | #define QTEST_ELLIPTIC (0x10) | |
83 | ||
84 | /* Size: decimal. | |
85 | * Specifies the number of the most significant bit (0 to M). | |
86 | ** WARNING: internally, usually 1 to N. | |
87 | */ | |
88 | #define QSIZE_MINIMUM (511) | |
89 | ||
90 | /* | |
91 | * Prime sieving defines | |
92 | */ | |
93 | ||
94 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
95 | #define SHIFT_BIT (3) | |
96 | #define SHIFT_BYTE (2) | |
97 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
98 | #define SHIFT_MEGABYTE (20) | |
99 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
100 | ||
101 | /* | |
102 | * Constant: when used with 32-bit integers, the largest sieve prime | |
103 | * has to be less than 2**32. | |
104 | */ | |
105 | #define SMALL_MAXIMUM (0xffffffffUL) | |
106 | ||
107 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
108 | #define TINY_NUMBER (1UL<<16) | |
109 | ||
110 | /* Ensure enough bit space for testing 2*q. */ | |
111 | #define TEST_MAXIMUM (1UL<<16) | |
112 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
113 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
114 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
115 | ||
116 | /* bit operations on 32-bit words */ | |
117 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) | |
118 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
119 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
120 | ||
121 | /* | |
122 | * Prime testing defines | |
123 | */ | |
124 | ||
125 | /* | |
126 | * Sieving data (XXX - move to struct) | |
127 | */ | |
128 | ||
129 | /* sieve 2**16 */ | |
130 | static u_int32_t *TinySieve, tinybits; | |
131 | ||
132 | /* sieve 2**30 in 2**16 parts */ | |
133 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
134 | ||
135 | /* sieve relative to the initial value */ | |
136 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
137 | static u_int32_t largebits, largememory; /* megabytes */ | |
138 | static BIGNUM *largebase; | |
139 | ||
140 | ||
141 | /* | |
142 | * print moduli out in consistent form, | |
143 | */ | |
144 | static int | |
145 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
146 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
147 | { | |
148 | struct tm *gtm; | |
149 | time_t time_now; | |
150 | int res; | |
151 | ||
152 | time(&time_now); | |
153 | gtm = gmtime(&time_now); | |
154 | ||
155 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", | |
156 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
157 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
158 | otype, otests, otries, osize, ogenerator); | |
159 | ||
160 | if (res < 0) | |
161 | return (-1); | |
162 | ||
163 | if (BN_print_fp(ofile, omodulus) < 1) | |
164 | return (-1); | |
165 | ||
166 | res = fprintf(ofile, "\n"); | |
167 | fflush(ofile); | |
168 | ||
169 | return (res > 0 ? 0 : -1); | |
170 | } | |
171 | ||
172 | ||
173 | /* | |
174 | ** Sieve p's and q's with small factors | |
175 | */ | |
176 | static void | |
177 | sieve_large(u_int32_t s) | |
178 | { | |
179 | u_int32_t r, u; | |
180 | ||
181 | debug2("sieve_large %u", s); | |
182 | largetries++; | |
183 | /* r = largebase mod s */ | |
184 | r = BN_mod_word(largebase, s); | |
185 | if (r == 0) | |
186 | u = 0; /* s divides into largebase exactly */ | |
187 | else | |
188 | u = s - r; /* largebase+u is first entry divisible by s */ | |
189 | ||
190 | if (u < largebits * 2) { | |
191 | /* | |
192 | * The sieve omits p's and q's divisible by 2, so ensure that | |
193 | * largebase+u is odd. Then, step through the sieve in | |
194 | * increments of 2*s | |
195 | */ | |
196 | if (u & 0x1) | |
197 | u += s; /* Make largebase+u odd, and u even */ | |
198 | ||
199 | /* Mark all multiples of 2*s */ | |
200 | for (u /= 2; u < largebits; u += s) | |
201 | BIT_SET(LargeSieve, u); | |
202 | } | |
203 | ||
204 | /* r = p mod s */ | |
205 | r = (2 * r + 1) % s; | |
206 | if (r == 0) | |
207 | u = 0; /* s divides p exactly */ | |
208 | else | |
209 | u = s - r; /* p+u is first entry divisible by s */ | |
210 | ||
211 | if (u < largebits * 4) { | |
212 | /* | |
213 | * The sieve omits p's divisible by 4, so ensure that | |
214 | * largebase+u is not. Then, step through the sieve in | |
215 | * increments of 4*s | |
216 | */ | |
217 | while (u & 0x3) { | |
218 | if (SMALL_MAXIMUM - u < s) | |
219 | return; | |
220 | u += s; | |
221 | } | |
222 | ||
223 | /* Mark all multiples of 4*s */ | |
224 | for (u /= 4; u < largebits; u += s) | |
225 | BIT_SET(LargeSieve, u); | |
226 | } | |
227 | } | |
228 | ||
229 | /* | |
230 | * list candidates for Sophie-Germaine primes (where q = (p-1)/2) | |
231 | * to standard output. | |
232 | * The list is checked against small known primes (less than 2**30). | |
233 | */ | |
234 | int | |
235 | gen_candidates(FILE *out, int memory, int power, BIGNUM *start) | |
236 | { | |
237 | BIGNUM *q; | |
238 | u_int32_t j, r, s, t; | |
239 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
240 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
241 | time_t time_start, time_stop; | |
242 | int i, ret = 0; | |
243 | ||
244 | largememory = memory; | |
245 | ||
246 | /* | |
247 | * Set power to the length in bits of the prime to be generated. | |
248 | * This is changed to 1 less than the desired safe prime moduli p. | |
249 | */ | |
250 | if (power > TEST_MAXIMUM) { | |
251 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
252 | return (-1); | |
253 | } else if (power < TEST_MINIMUM) { | |
254 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
255 | return (-1); | |
256 | } | |
257 | power--; /* decrement before squaring */ | |
258 | ||
259 | /* | |
260 | * The density of ordinary primes is on the order of 1/bits, so the | |
261 | * density of safe primes should be about (1/bits)**2. Set test range | |
262 | * to something well above bits**2 to be reasonably sure (but not | |
263 | * guaranteed) of catching at least one safe prime. | |
264 | */ | |
265 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
266 | ||
267 | /* | |
268 | * Need idea of how much memory is available. We don't have to use all | |
269 | * of it. | |
270 | */ | |
271 | if (largememory > LARGE_MAXIMUM) { | |
272 | logit("Limited memory: %u MB; limit %lu MB", | |
273 | largememory, LARGE_MAXIMUM); | |
274 | largememory = LARGE_MAXIMUM; | |
275 | } | |
276 | ||
277 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
278 | logit("Increased memory: %u MB; need %u bytes", | |
279 | largememory, (largewords << SHIFT_BYTE)); | |
280 | largewords = (largememory << SHIFT_MEGAWORD); | |
281 | } else if (largememory > 0) { | |
282 | logit("Decreased memory: %u MB; want %u bytes", | |
283 | largememory, (largewords << SHIFT_BYTE)); | |
284 | largewords = (largememory << SHIFT_MEGAWORD); | |
285 | } | |
286 | ||
287 | TinySieve = calloc(tinywords, sizeof(u_int32_t)); | |
288 | if (TinySieve == NULL) { | |
289 | error("Insufficient memory for tiny sieve: need %u bytes", | |
290 | tinywords << SHIFT_BYTE); | |
291 | exit(1); | |
292 | } | |
293 | tinybits = tinywords << SHIFT_WORD; | |
294 | ||
295 | SmallSieve = calloc(smallwords, sizeof(u_int32_t)); | |
296 | if (SmallSieve == NULL) { | |
297 | error("Insufficient memory for small sieve: need %u bytes", | |
298 | smallwords << SHIFT_BYTE); | |
299 | xfree(TinySieve); | |
300 | exit(1); | |
301 | } | |
302 | smallbits = smallwords << SHIFT_WORD; | |
303 | ||
304 | /* | |
305 | * dynamically determine available memory | |
306 | */ | |
307 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
308 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
309 | ||
310 | largebits = largewords << SHIFT_WORD; | |
311 | largenumbers = largebits * 2; /* even numbers excluded */ | |
312 | ||
313 | /* validation check: count the number of primes tried */ | |
314 | largetries = 0; | |
315 | q = BN_new(); | |
316 | ||
317 | /* | |
318 | * Generate random starting point for subprime search, or use | |
319 | * specified parameter. | |
320 | */ | |
321 | largebase = BN_new(); | |
322 | if (start == NULL) | |
323 | BN_rand(largebase, power, 1, 1); | |
324 | else | |
325 | BN_copy(largebase, start); | |
326 | ||
327 | /* ensure odd */ | |
328 | BN_set_bit(largebase, 0); | |
329 | ||
330 | time(&time_start); | |
331 | ||
332 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), | |
333 | largenumbers, power); | |
334 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
335 | ||
336 | /* | |
337 | * TinySieve | |
338 | */ | |
339 | for (i = 0; i < tinybits; i++) { | |
340 | if (BIT_TEST(TinySieve, i)) | |
341 | continue; /* 2*i+3 is composite */ | |
342 | ||
343 | /* The next tiny prime */ | |
344 | t = 2 * i + 3; | |
345 | ||
346 | /* Mark all multiples of t */ | |
347 | for (j = i + t; j < tinybits; j += t) | |
348 | BIT_SET(TinySieve, j); | |
349 | ||
350 | sieve_large(t); | |
351 | } | |
352 | ||
353 | /* | |
354 | * Start the small block search at the next possible prime. To avoid | |
355 | * fencepost errors, the last pass is skipped. | |
356 | */ | |
357 | for (smallbase = TINY_NUMBER + 3; | |
358 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); | |
359 | smallbase += TINY_NUMBER) { | |
360 | for (i = 0; i < tinybits; i++) { | |
361 | if (BIT_TEST(TinySieve, i)) | |
362 | continue; /* 2*i+3 is composite */ | |
363 | ||
364 | /* The next tiny prime */ | |
365 | t = 2 * i + 3; | |
366 | r = smallbase % t; | |
367 | ||
368 | if (r == 0) { | |
369 | s = 0; /* t divides into smallbase exactly */ | |
370 | } else { | |
371 | /* smallbase+s is first entry divisible by t */ | |
372 | s = t - r; | |
373 | } | |
374 | ||
375 | /* | |
376 | * The sieve omits even numbers, so ensure that | |
377 | * smallbase+s is odd. Then, step through the sieve | |
378 | * in increments of 2*t | |
379 | */ | |
380 | if (s & 1) | |
381 | s += t; /* Make smallbase+s odd, and s even */ | |
382 | ||
383 | /* Mark all multiples of 2*t */ | |
384 | for (s /= 2; s < smallbits; s += t) | |
385 | BIT_SET(SmallSieve, s); | |
386 | } | |
387 | ||
388 | /* | |
389 | * SmallSieve | |
390 | */ | |
391 | for (i = 0; i < smallbits; i++) { | |
392 | if (BIT_TEST(SmallSieve, i)) | |
393 | continue; /* 2*i+smallbase is composite */ | |
394 | ||
395 | /* The next small prime */ | |
396 | sieve_large((2 * i) + smallbase); | |
397 | } | |
398 | ||
399 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
400 | } | |
401 | ||
402 | time(&time_stop); | |
403 | ||
404 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
405 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
406 | ||
407 | for (j = r = 0; j < largebits; j++) { | |
408 | if (BIT_TEST(LargeSieve, j)) | |
409 | continue; /* Definitely composite, skip */ | |
410 | ||
411 | debug2("test q = largebase+%u", 2 * j); | |
412 | BN_set_word(q, 2 * j); | |
413 | BN_add(q, q, largebase); | |
414 | if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE, | |
415 | largetries, (power - 1) /* MSB */, (0), q) == -1) { | |
416 | ret = -1; | |
417 | break; | |
418 | } | |
419 | ||
420 | r++; /* count q */ | |
421 | } | |
422 | ||
423 | time(&time_stop); | |
424 | ||
425 | xfree(LargeSieve); | |
426 | xfree(SmallSieve); | |
427 | xfree(TinySieve); | |
428 | ||
429 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
430 | ||
431 | return (ret); | |
432 | } | |
433 | ||
434 | /* | |
435 | * perform a Miller-Rabin primality test | |
436 | * on the list of candidates | |
437 | * (checking both q and p) | |
438 | * The result is a list of so-call "safe" primes | |
439 | */ | |
440 | int | |
441 | prime_test(FILE *in, FILE *out, u_int32_t trials, | |
442 | u_int32_t generator_wanted) | |
443 | { | |
444 | BIGNUM *q, *p, *a; | |
445 | BN_CTX *ctx; | |
446 | char *cp, *lp; | |
447 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
448 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
449 | time_t time_start, time_stop; | |
450 | int res; | |
451 | ||
452 | time(&time_start); | |
453 | ||
454 | p = BN_new(); | |
455 | q = BN_new(); | |
456 | ctx = BN_CTX_new(); | |
457 | ||
458 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
459 | ctime(&time_start), trials, generator_wanted); | |
460 | ||
461 | res = 0; | |
462 | lp = xmalloc(QLINESIZE + 1); | |
463 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
464 | int ll = strlen(lp); | |
465 | ||
466 | count_in++; | |
467 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
468 | debug2("%10u: comment or short line", count_in); | |
469 | continue; | |
470 | } | |
471 | ||
472 | /* XXX - fragile parser */ | |
473 | /* time */ | |
474 | cp = &lp[14]; /* (skip) */ | |
475 | ||
476 | /* type */ | |
477 | in_type = strtoul(cp, &cp, 10); | |
478 | ||
479 | /* tests */ | |
480 | in_tests = strtoul(cp, &cp, 10); | |
481 | ||
482 | if (in_tests & QTEST_COMPOSITE) { | |
483 | debug2("%10u: known composite", count_in); | |
484 | continue; | |
485 | } | |
486 | /* tries */ | |
487 | in_tries = strtoul(cp, &cp, 10); | |
488 | ||
489 | /* size (most significant bit) */ | |
490 | in_size = strtoul(cp, &cp, 10); | |
491 | ||
492 | /* generator (hex) */ | |
493 | generator_known = strtoul(cp, &cp, 16); | |
494 | ||
495 | /* Skip white space */ | |
496 | cp += strspn(cp, " "); | |
497 | ||
498 | /* modulus (hex) */ | |
499 | switch (in_type) { | |
500 | case QTYPE_SOPHIE_GERMAINE: | |
501 | debug2("%10u: (%u) Sophie-Germaine", count_in, in_type); | |
502 | a = q; | |
503 | BN_hex2bn(&a, cp); | |
504 | /* p = 2*q + 1 */ | |
505 | BN_lshift(p, q, 1); | |
506 | BN_add_word(p, 1); | |
507 | in_size += 1; | |
508 | generator_known = 0; | |
509 | break; | |
510 | default: | |
511 | debug2("%10u: (%u)", count_in, in_type); | |
512 | a = p; | |
513 | BN_hex2bn(&a, cp); | |
514 | /* q = (p-1) / 2 */ | |
515 | BN_rshift(q, p, 1); | |
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 | * guess unknown generator | |
538 | */ | |
539 | if (generator_known == 0) { | |
540 | if (BN_mod_word(p, 24) == 11) | |
541 | generator_known = 2; | |
542 | else if (BN_mod_word(p, 12) == 5) | |
543 | generator_known = 3; | |
544 | else { | |
545 | u_int32_t r = BN_mod_word(p, 10); | |
546 | ||
547 | if (r == 3 || r == 7) { | |
548 | generator_known = 5; | |
549 | } | |
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 | count_possible++; | |
563 | ||
564 | /* | |
565 | * The (1/4)^N performance bound on Miller-Rabin is | |
566 | * extremely pessimistic, so don't spend a lot of time | |
567 | * really verifying that q is prime until after we know | |
568 | * that p is also prime. A single pass will weed out the | |
569 | * vast majority of composite q's. | |
570 | */ | |
571 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
572 | debug2("%10u: q failed first possible prime test", | |
573 | count_in); | |
574 | continue; | |
575 | } | |
576 | ||
577 | /* | |
578 | * q is possibly prime, so go ahead and really make sure | |
579 | * that p is prime. If it is, then we can go back and do | |
580 | * the same for q. If p is composite, chances are that | |
581 | * will show up on the first Rabin-Miller iteration so it | |
582 | * doesn't hurt to specify a high iteration count. | |
583 | */ | |
584 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
585 | debug2("%10u: p is not prime", count_in); | |
586 | continue; | |
587 | } | |
588 | debug("%10u: p is almost certainly prime", count_in); | |
589 | ||
590 | /* recheck q more rigorously */ | |
591 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
592 | debug("%10u: q is not prime", count_in); | |
593 | continue; | |
594 | } | |
595 | debug("%10u: q is almost certainly prime", count_in); | |
596 | ||
597 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), | |
598 | in_tries, in_size, generator_known, p)) { | |
599 | res = -1; | |
600 | break; | |
601 | } | |
602 | ||
603 | count_out++; | |
604 | } | |
605 | ||
606 | time(&time_stop); | |
607 | xfree(lp); | |
608 | BN_free(p); | |
609 | BN_free(q); | |
610 | BN_CTX_free(ctx); | |
611 | ||
612 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
613 | ctime(&time_stop), count_out, count_possible, | |
614 | (long) (time_stop - time_start)); | |
615 | ||
616 | return (res); | |
617 | } |