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eb7a33b8 | 1 | /* $OpenBSD: moduli.c,v 1.4 2003/12/09 13:52:55 dtucker Exp $ */ |
5ae3dc68 | 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 | ||
5ae3dc68 | 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 | /* Size: decimal. | |
76 | * Specifies the number of the most significant bit (0 to M). | |
77 | ** WARNING: internally, usually 1 to N. | |
78 | */ | |
79 | #define QSIZE_MINIMUM (511) | |
80 | ||
81 | /* | |
82 | * Prime sieving defines | |
83 | */ | |
84 | ||
85 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
86 | #define SHIFT_BIT (3) | |
87 | #define SHIFT_BYTE (2) | |
88 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
89 | #define SHIFT_MEGABYTE (20) | |
90 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
91 | ||
92 | /* | |
93 | * Constant: when used with 32-bit integers, the largest sieve prime | |
94 | * has to be less than 2**32. | |
95 | */ | |
96 | #define SMALL_MAXIMUM (0xffffffffUL) | |
97 | ||
98 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
99 | #define TINY_NUMBER (1UL<<16) | |
100 | ||
101 | /* Ensure enough bit space for testing 2*q. */ | |
102 | #define TEST_MAXIMUM (1UL<<16) | |
103 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
104 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
105 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
106 | ||
107 | /* bit operations on 32-bit words */ | |
108 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) | |
109 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
110 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
111 | ||
112 | /* | |
113 | * Prime testing defines | |
114 | */ | |
115 | ||
116 | /* | |
117 | * Sieving data (XXX - move to struct) | |
118 | */ | |
119 | ||
120 | /* sieve 2**16 */ | |
121 | static u_int32_t *TinySieve, tinybits; | |
122 | ||
123 | /* sieve 2**30 in 2**16 parts */ | |
124 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
125 | ||
126 | /* sieve relative to the initial value */ | |
127 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
128 | static u_int32_t largebits, largememory; /* megabytes */ | |
129 | static BIGNUM *largebase; | |
130 | ||
131 | ||
132 | /* | |
133 | * print moduli out in consistent form, | |
134 | */ | |
135 | static int | |
136 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
137 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
138 | { | |
139 | struct tm *gtm; | |
140 | time_t time_now; | |
141 | int res; | |
142 | ||
143 | time(&time_now); | |
144 | gtm = gmtime(&time_now); | |
b6453d99 | 145 | |
5ae3dc68 | 146 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", |
147 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
148 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
149 | otype, otests, otries, osize, ogenerator); | |
150 | ||
151 | if (res < 0) | |
152 | return (-1); | |
153 | ||
154 | if (BN_print_fp(ofile, omodulus) < 1) | |
155 | return (-1); | |
156 | ||
157 | res = fprintf(ofile, "\n"); | |
158 | fflush(ofile); | |
159 | ||
160 | return (res > 0 ? 0 : -1); | |
161 | } | |
162 | ||
163 | ||
164 | /* | |
165 | ** Sieve p's and q's with small factors | |
166 | */ | |
167 | static void | |
168 | sieve_large(u_int32_t s) | |
169 | { | |
170 | u_int32_t r, u; | |
171 | ||
172 | debug2("sieve_large %u", s); | |
173 | largetries++; | |
174 | /* r = largebase mod s */ | |
175 | r = BN_mod_word(largebase, s); | |
176 | if (r == 0) | |
177 | u = 0; /* s divides into largebase exactly */ | |
178 | else | |
179 | u = s - r; /* largebase+u is first entry divisible by s */ | |
180 | ||
181 | if (u < largebits * 2) { | |
182 | /* | |
183 | * The sieve omits p's and q's divisible by 2, so ensure that | |
184 | * largebase+u is odd. Then, step through the sieve in | |
185 | * increments of 2*s | |
186 | */ | |
187 | if (u & 0x1) | |
188 | u += s; /* Make largebase+u odd, and u even */ | |
189 | ||
190 | /* Mark all multiples of 2*s */ | |
191 | for (u /= 2; u < largebits; u += s) | |
192 | BIT_SET(LargeSieve, u); | |
193 | } | |
194 | ||
195 | /* r = p mod s */ | |
196 | r = (2 * r + 1) % s; | |
197 | if (r == 0) | |
198 | u = 0; /* s divides p exactly */ | |
199 | else | |
200 | u = s - r; /* p+u is first entry divisible by s */ | |
201 | ||
202 | if (u < largebits * 4) { | |
203 | /* | |
204 | * The sieve omits p's divisible by 4, so ensure that | |
205 | * largebase+u is not. Then, step through the sieve in | |
206 | * increments of 4*s | |
207 | */ | |
208 | while (u & 0x3) { | |
209 | if (SMALL_MAXIMUM - u < s) | |
210 | return; | |
211 | u += s; | |
212 | } | |
213 | ||
214 | /* Mark all multiples of 4*s */ | |
215 | for (u /= 4; u < largebits; u += s) | |
216 | BIT_SET(LargeSieve, u); | |
217 | } | |
218 | } | |
219 | ||
220 | /* | |
221 | * list candidates for Sophie-Germaine primes (where q = (p-1)/2) | |
222 | * to standard output. | |
223 | * The list is checked against small known primes (less than 2**30). | |
224 | */ | |
225 | int | |
226 | gen_candidates(FILE *out, int memory, int power, BIGNUM *start) | |
227 | { | |
228 | BIGNUM *q; | |
229 | u_int32_t j, r, s, t; | |
230 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
231 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
232 | time_t time_start, time_stop; | |
233 | int i, ret = 0; | |
234 | ||
235 | largememory = memory; | |
236 | ||
237 | /* | |
aff51935 | 238 | * Set power to the length in bits of the prime to be generated. |
239 | * This is changed to 1 less than the desired safe prime moduli p. | |
240 | */ | |
5ae3dc68 | 241 | if (power > TEST_MAXIMUM) { |
242 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
243 | return (-1); | |
244 | } else if (power < TEST_MINIMUM) { | |
245 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
246 | return (-1); | |
247 | } | |
248 | power--; /* decrement before squaring */ | |
249 | ||
250 | /* | |
aff51935 | 251 | * The density of ordinary primes is on the order of 1/bits, so the |
252 | * density of safe primes should be about (1/bits)**2. Set test range | |
253 | * to something well above bits**2 to be reasonably sure (but not | |
254 | * guaranteed) of catching at least one safe prime. | |
5ae3dc68 | 255 | */ |
256 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
257 | ||
258 | /* | |
aff51935 | 259 | * Need idea of how much memory is available. We don't have to use all |
260 | * of it. | |
5ae3dc68 | 261 | */ |
262 | if (largememory > LARGE_MAXIMUM) { | |
263 | logit("Limited memory: %u MB; limit %lu MB", | |
264 | largememory, LARGE_MAXIMUM); | |
265 | largememory = LARGE_MAXIMUM; | |
266 | } | |
267 | ||
268 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
269 | logit("Increased memory: %u MB; need %u bytes", | |
270 | largememory, (largewords << SHIFT_BYTE)); | |
271 | largewords = (largememory << SHIFT_MEGAWORD); | |
272 | } else if (largememory > 0) { | |
273 | logit("Decreased memory: %u MB; want %u bytes", | |
274 | largememory, (largewords << SHIFT_BYTE)); | |
275 | largewords = (largememory << SHIFT_MEGAWORD); | |
276 | } | |
277 | ||
278 | TinySieve = calloc(tinywords, sizeof(u_int32_t)); | |
279 | if (TinySieve == NULL) { | |
280 | error("Insufficient memory for tiny sieve: need %u bytes", | |
281 | tinywords << SHIFT_BYTE); | |
282 | exit(1); | |
283 | } | |
284 | tinybits = tinywords << SHIFT_WORD; | |
285 | ||
286 | SmallSieve = calloc(smallwords, sizeof(u_int32_t)); | |
287 | if (SmallSieve == NULL) { | |
288 | error("Insufficient memory for small sieve: need %u bytes", | |
289 | smallwords << SHIFT_BYTE); | |
290 | xfree(TinySieve); | |
291 | exit(1); | |
292 | } | |
293 | smallbits = smallwords << SHIFT_WORD; | |
294 | ||
295 | /* | |
296 | * dynamically determine available memory | |
297 | */ | |
298 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
299 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
300 | ||
301 | largebits = largewords << SHIFT_WORD; | |
302 | largenumbers = largebits * 2; /* even numbers excluded */ | |
303 | ||
304 | /* validation check: count the number of primes tried */ | |
305 | largetries = 0; | |
306 | q = BN_new(); | |
307 | ||
308 | /* | |
aff51935 | 309 | * Generate random starting point for subprime search, or use |
310 | * specified parameter. | |
5ae3dc68 | 311 | */ |
312 | largebase = BN_new(); | |
313 | if (start == NULL) | |
314 | BN_rand(largebase, power, 1, 1); | |
315 | else | |
316 | BN_copy(largebase, start); | |
317 | ||
318 | /* ensure odd */ | |
319 | BN_set_bit(largebase, 0); | |
320 | ||
321 | time(&time_start); | |
322 | ||
aff51935 | 323 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
5ae3dc68 | 324 | largenumbers, power); |
325 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
326 | ||
327 | /* | |
aff51935 | 328 | * TinySieve |
329 | */ | |
5ae3dc68 | 330 | for (i = 0; i < tinybits; i++) { |
331 | if (BIT_TEST(TinySieve, i)) | |
332 | continue; /* 2*i+3 is composite */ | |
333 | ||
334 | /* The next tiny prime */ | |
335 | t = 2 * i + 3; | |
336 | ||
337 | /* Mark all multiples of t */ | |
338 | for (j = i + t; j < tinybits; j += t) | |
339 | BIT_SET(TinySieve, j); | |
340 | ||
341 | sieve_large(t); | |
342 | } | |
343 | ||
344 | /* | |
aff51935 | 345 | * Start the small block search at the next possible prime. To avoid |
346 | * fencepost errors, the last pass is skipped. | |
347 | */ | |
5ae3dc68 | 348 | for (smallbase = TINY_NUMBER + 3; |
349 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); | |
350 | smallbase += TINY_NUMBER) { | |
351 | for (i = 0; i < tinybits; i++) { | |
352 | if (BIT_TEST(TinySieve, i)) | |
353 | continue; /* 2*i+3 is composite */ | |
354 | ||
355 | /* The next tiny prime */ | |
356 | t = 2 * i + 3; | |
357 | r = smallbase % t; | |
358 | ||
359 | if (r == 0) { | |
360 | s = 0; /* t divides into smallbase exactly */ | |
361 | } else { | |
362 | /* smallbase+s is first entry divisible by t */ | |
363 | s = t - r; | |
364 | } | |
365 | ||
366 | /* | |
367 | * The sieve omits even numbers, so ensure that | |
368 | * smallbase+s is odd. Then, step through the sieve | |
369 | * in increments of 2*t | |
370 | */ | |
371 | if (s & 1) | |
372 | s += t; /* Make smallbase+s odd, and s even */ | |
373 | ||
374 | /* Mark all multiples of 2*t */ | |
375 | for (s /= 2; s < smallbits; s += t) | |
376 | BIT_SET(SmallSieve, s); | |
377 | } | |
378 | ||
379 | /* | |
aff51935 | 380 | * SmallSieve |
381 | */ | |
5ae3dc68 | 382 | for (i = 0; i < smallbits; i++) { |
383 | if (BIT_TEST(SmallSieve, i)) | |
384 | continue; /* 2*i+smallbase is composite */ | |
385 | ||
386 | /* The next small prime */ | |
387 | sieve_large((2 * i) + smallbase); | |
388 | } | |
389 | ||
390 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
391 | } | |
392 | ||
393 | time(&time_stop); | |
394 | ||
395 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
396 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
397 | ||
398 | for (j = r = 0; j < largebits; j++) { | |
399 | if (BIT_TEST(LargeSieve, j)) | |
400 | continue; /* Definitely composite, skip */ | |
401 | ||
402 | debug2("test q = largebase+%u", 2 * j); | |
403 | BN_set_word(q, 2 * j); | |
404 | BN_add(q, q, largebase); | |
405 | if (qfileout(out, QTYPE_SOPHIE_GERMAINE, QTEST_SIEVE, | |
406 | largetries, (power - 1) /* MSB */, (0), q) == -1) { | |
407 | ret = -1; | |
408 | break; | |
409 | } | |
410 | ||
411 | r++; /* count q */ | |
412 | } | |
413 | ||
414 | time(&time_stop); | |
415 | ||
416 | xfree(LargeSieve); | |
417 | xfree(SmallSieve); | |
418 | xfree(TinySieve); | |
419 | ||
420 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
421 | ||
422 | return (ret); | |
423 | } | |
424 | ||
425 | /* | |
426 | * perform a Miller-Rabin primality test | |
427 | * on the list of candidates | |
428 | * (checking both q and p) | |
429 | * The result is a list of so-call "safe" primes | |
430 | */ | |
431 | int | |
aff51935 | 432 | prime_test(FILE *in, FILE *out, u_int32_t trials, |
5ae3dc68 | 433 | u_int32_t generator_wanted) |
434 | { | |
435 | BIGNUM *q, *p, *a; | |
436 | BN_CTX *ctx; | |
437 | char *cp, *lp; | |
438 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
439 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
440 | time_t time_start, time_stop; | |
441 | int res; | |
442 | ||
443 | time(&time_start); | |
444 | ||
445 | p = BN_new(); | |
446 | q = BN_new(); | |
447 | ctx = BN_CTX_new(); | |
448 | ||
449 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
450 | ctime(&time_start), trials, generator_wanted); | |
451 | ||
452 | res = 0; | |
453 | lp = xmalloc(QLINESIZE + 1); | |
454 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
455 | int ll = strlen(lp); | |
456 | ||
457 | count_in++; | |
458 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
459 | debug2("%10u: comment or short line", count_in); | |
460 | continue; | |
461 | } | |
462 | ||
463 | /* XXX - fragile parser */ | |
464 | /* time */ | |
465 | cp = &lp[14]; /* (skip) */ | |
466 | ||
467 | /* type */ | |
468 | in_type = strtoul(cp, &cp, 10); | |
469 | ||
470 | /* tests */ | |
471 | in_tests = strtoul(cp, &cp, 10); | |
472 | ||
473 | if (in_tests & QTEST_COMPOSITE) { | |
474 | debug2("%10u: known composite", count_in); | |
475 | continue; | |
476 | } | |
477 | /* tries */ | |
478 | in_tries = strtoul(cp, &cp, 10); | |
479 | ||
480 | /* size (most significant bit) */ | |
481 | in_size = strtoul(cp, &cp, 10); | |
482 | ||
483 | /* generator (hex) */ | |
484 | generator_known = strtoul(cp, &cp, 16); | |
485 | ||
486 | /* Skip white space */ | |
487 | cp += strspn(cp, " "); | |
488 | ||
489 | /* modulus (hex) */ | |
490 | switch (in_type) { | |
491 | case QTYPE_SOPHIE_GERMAINE: | |
492 | debug2("%10u: (%u) Sophie-Germaine", count_in, in_type); | |
493 | a = q; | |
494 | BN_hex2bn(&a, cp); | |
495 | /* p = 2*q + 1 */ | |
496 | BN_lshift(p, q, 1); | |
497 | BN_add_word(p, 1); | |
498 | in_size += 1; | |
499 | generator_known = 0; | |
500 | break; | |
501 | default: | |
502 | debug2("%10u: (%u)", count_in, in_type); | |
503 | a = p; | |
504 | BN_hex2bn(&a, cp); | |
505 | /* q = (p-1) / 2 */ | |
506 | BN_rshift(q, p, 1); | |
507 | break; | |
508 | } | |
509 | ||
510 | /* | |
511 | * due to earlier inconsistencies in interpretation, check | |
512 | * the proposed bit size. | |
513 | */ | |
514 | if (BN_num_bits(p) != (in_size + 1)) { | |
515 | debug2("%10u: bit size %u mismatch", count_in, in_size); | |
516 | continue; | |
517 | } | |
518 | if (in_size < QSIZE_MINIMUM) { | |
519 | debug2("%10u: bit size %u too short", count_in, in_size); | |
520 | continue; | |
521 | } | |
522 | ||
523 | if (in_tests & QTEST_MILLER_RABIN) | |
524 | in_tries += trials; | |
525 | else | |
526 | in_tries = trials; | |
527 | /* | |
528 | * guess unknown generator | |
529 | */ | |
530 | if (generator_known == 0) { | |
531 | if (BN_mod_word(p, 24) == 11) | |
532 | generator_known = 2; | |
533 | else if (BN_mod_word(p, 12) == 5) | |
534 | generator_known = 3; | |
535 | else { | |
536 | u_int32_t r = BN_mod_word(p, 10); | |
537 | ||
538 | if (r == 3 || r == 7) { | |
539 | generator_known = 5; | |
540 | } | |
541 | } | |
542 | } | |
543 | /* | |
544 | * skip tests when desired generator doesn't match | |
545 | */ | |
546 | if (generator_wanted > 0 && | |
547 | generator_wanted != generator_known) { | |
548 | debug2("%10u: generator %d != %d", | |
549 | count_in, generator_known, generator_wanted); | |
550 | continue; | |
551 | } | |
552 | ||
eb7a33b8 | 553 | /* |
554 | * Primes with no known generator are useless for DH, so | |
555 | * skip those. | |
556 | */ | |
557 | if (generator_known == 0) { | |
558 | debug2("%10u: no known generator", count_in); | |
559 | continue; | |
560 | } | |
561 | ||
5ae3dc68 | 562 | count_possible++; |
563 | ||
564 | /* | |
aff51935 | 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 | |
5ae3dc68 | 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 | } | |
b6453d99 | 576 | |
5ae3dc68 | 577 | /* |
aff51935 | 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 | |
5ae3dc68 | 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 | ||
aff51935 | 597 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
5ae3dc68 | 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", | |
aff51935 | 613 | ctime(&time_stop), count_out, count_possible, |
5ae3dc68 | 614 | (long) (time_stop - time_start)); |
615 | ||
616 | return (res); | |
617 | } |