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1 | /* $OpenBSD: moduli.c,v 1.21 2008/06/26 09:19:40 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 | ||
42 | #include <sys/types.h> | |
43 | ||
44 | #include <openssl/bn.h> | |
45 | #include <openssl/dh.h> | |
46 | ||
47 | #include <stdio.h> | |
48 | #include <stdlib.h> | |
49 | #include <string.h> | |
50 | #include <stdarg.h> | |
51 | #include <time.h> | |
52 | ||
53 | #include "xmalloc.h" | |
54 | #include "dh.h" | |
55 | #include "log.h" | |
56 | ||
57 | /* | |
58 | * File output defines | |
59 | */ | |
60 | ||
61 | /* need line long enough for largest moduli plus headers */ | |
62 | #define QLINESIZE (100+8192) | |
63 | ||
64 | /* | |
65 | * Size: decimal. | |
66 | * Specifies the number of the most significant bit (0 to M). | |
67 | * WARNING: internally, usually 1 to N. | |
68 | */ | |
69 | #define QSIZE_MINIMUM (511) | |
70 | ||
71 | /* | |
72 | * Prime sieving defines | |
73 | */ | |
74 | ||
75 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
76 | #define SHIFT_BIT (3) | |
77 | #define SHIFT_BYTE (2) | |
78 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
79 | #define SHIFT_MEGABYTE (20) | |
80 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
81 | ||
82 | /* | |
83 | * Using virtual memory can cause thrashing. This should be the largest | |
84 | * number that is supported without a large amount of disk activity -- | |
85 | * that would increase the run time from hours to days or weeks! | |
86 | */ | |
87 | #define LARGE_MINIMUM (8UL) /* megabytes */ | |
88 | ||
89 | /* | |
90 | * Do not increase this number beyond the unsigned integer bit size. | |
91 | * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). | |
92 | */ | |
93 | #define LARGE_MAXIMUM (127UL) /* megabytes */ | |
94 | ||
95 | /* | |
96 | * Constant: when used with 32-bit integers, the largest sieve prime | |
97 | * has to be less than 2**32. | |
98 | */ | |
99 | #define SMALL_MAXIMUM (0xffffffffUL) | |
100 | ||
101 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
102 | #define TINY_NUMBER (1UL<<16) | |
103 | ||
104 | /* Ensure enough bit space for testing 2*q. */ | |
105 | #define TEST_MAXIMUM (1UL<<16) | |
106 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
107 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
108 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
109 | ||
110 | /* bit operations on 32-bit words */ | |
111 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) | |
112 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
113 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
114 | ||
115 | /* | |
116 | * Prime testing defines | |
117 | */ | |
118 | ||
119 | /* Minimum number of primality tests to perform */ | |
120 | #define TRIAL_MINIMUM (4) | |
121 | ||
122 | /* | |
123 | * Sieving data (XXX - move to struct) | |
124 | */ | |
125 | ||
126 | /* sieve 2**16 */ | |
127 | static u_int32_t *TinySieve, tinybits; | |
128 | ||
129 | /* sieve 2**30 in 2**16 parts */ | |
130 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
131 | ||
132 | /* sieve relative to the initial value */ | |
133 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
134 | static u_int32_t largebits, largememory; /* megabytes */ | |
135 | static BIGNUM *largebase; | |
136 | ||
137 | int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); | |
138 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); | |
139 | ||
140 | /* | |
141 | * print moduli out in consistent form, | |
142 | */ | |
143 | static int | |
144 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
145 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
146 | { | |
147 | struct tm *gtm; | |
148 | time_t time_now; | |
149 | int res; | |
150 | ||
151 | time(&time_now); | |
152 | gtm = gmtime(&time_now); | |
153 | ||
154 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", | |
155 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
156 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
157 | otype, otests, otries, osize, ogenerator); | |
158 | ||
159 | if (res < 0) | |
160 | return (-1); | |
161 | ||
162 | if (BN_print_fp(ofile, omodulus) < 1) | |
163 | return (-1); | |
164 | ||
165 | res = fprintf(ofile, "\n"); | |
166 | fflush(ofile); | |
167 | ||
168 | return (res > 0 ? 0 : -1); | |
169 | } | |
170 | ||
171 | ||
172 | /* | |
173 | ** Sieve p's and q's with small factors | |
174 | */ | |
175 | static void | |
176 | sieve_large(u_int32_t s) | |
177 | { | |
178 | u_int32_t r, u; | |
179 | ||
180 | debug3("sieve_large %u", s); | |
181 | largetries++; | |
182 | /* r = largebase mod s */ | |
183 | r = BN_mod_word(largebase, s); | |
184 | if (r == 0) | |
185 | u = 0; /* s divides into largebase exactly */ | |
186 | else | |
187 | u = s - r; /* largebase+u is first entry divisible by s */ | |
188 | ||
189 | if (u < largebits * 2) { | |
190 | /* | |
191 | * The sieve omits p's and q's divisible by 2, so ensure that | |
192 | * largebase+u is odd. Then, step through the sieve in | |
193 | * increments of 2*s | |
194 | */ | |
195 | if (u & 0x1) | |
196 | u += s; /* Make largebase+u odd, and u even */ | |
197 | ||
198 | /* Mark all multiples of 2*s */ | |
199 | for (u /= 2; u < largebits; u += s) | |
200 | BIT_SET(LargeSieve, u); | |
201 | } | |
202 | ||
203 | /* r = p mod s */ | |
204 | r = (2 * r + 1) % s; | |
205 | if (r == 0) | |
206 | u = 0; /* s divides p exactly */ | |
207 | else | |
208 | u = s - r; /* p+u is first entry divisible by s */ | |
209 | ||
210 | if (u < largebits * 4) { | |
211 | /* | |
212 | * The sieve omits p's divisible by 4, so ensure that | |
213 | * largebase+u is not. Then, step through the sieve in | |
214 | * increments of 4*s | |
215 | */ | |
216 | while (u & 0x3) { | |
217 | if (SMALL_MAXIMUM - u < s) | |
218 | return; | |
219 | u += s; | |
220 | } | |
221 | ||
222 | /* Mark all multiples of 4*s */ | |
223 | for (u /= 4; u < largebits; u += s) | |
224 | BIT_SET(LargeSieve, u); | |
225 | } | |
226 | } | |
227 | ||
228 | /* | |
229 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) | |
230 | * to standard output. | |
231 | * The list is checked against small known primes (less than 2**30). | |
232 | */ | |
233 | int | |
234 | gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) | |
235 | { | |
236 | BIGNUM *q; | |
237 | u_int32_t j, r, s, t; | |
238 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
239 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
240 | time_t time_start, time_stop; | |
241 | u_int32_t i; | |
242 | int ret = 0; | |
243 | ||
244 | largememory = memory; | |
245 | ||
246 | if (memory != 0 && | |
247 | (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { | |
248 | error("Invalid memory amount (min %ld, max %ld)", | |
249 | LARGE_MINIMUM, LARGE_MAXIMUM); | |
250 | return (-1); | |
251 | } | |
252 | ||
253 | /* | |
254 | * Set power to the length in bits of the prime to be generated. | |
255 | * This is changed to 1 less than the desired safe prime moduli p. | |
256 | */ | |
257 | if (power > TEST_MAXIMUM) { | |
258 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
259 | return (-1); | |
260 | } else if (power < TEST_MINIMUM) { | |
261 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
262 | return (-1); | |
263 | } | |
264 | power--; /* decrement before squaring */ | |
265 | ||
266 | /* | |
267 | * The density of ordinary primes is on the order of 1/bits, so the | |
268 | * density of safe primes should be about (1/bits)**2. Set test range | |
269 | * to something well above bits**2 to be reasonably sure (but not | |
270 | * guaranteed) of catching at least one safe prime. | |
271 | */ | |
272 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
273 | ||
274 | /* | |
275 | * Need idea of how much memory is available. We don't have to use all | |
276 | * of it. | |
277 | */ | |
278 | if (largememory > LARGE_MAXIMUM) { | |
279 | logit("Limited memory: %u MB; limit %lu MB", | |
280 | largememory, LARGE_MAXIMUM); | |
281 | largememory = LARGE_MAXIMUM; | |
282 | } | |
283 | ||
284 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
285 | logit("Increased memory: %u MB; need %u bytes", | |
286 | largememory, (largewords << SHIFT_BYTE)); | |
287 | largewords = (largememory << SHIFT_MEGAWORD); | |
288 | } else if (largememory > 0) { | |
289 | logit("Decreased memory: %u MB; want %u bytes", | |
290 | largememory, (largewords << SHIFT_BYTE)); | |
291 | largewords = (largememory << SHIFT_MEGAWORD); | |
292 | } | |
293 | ||
294 | TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); | |
295 | tinybits = tinywords << SHIFT_WORD; | |
296 | ||
297 | SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); | |
298 | smallbits = smallwords << SHIFT_WORD; | |
299 | ||
300 | /* | |
301 | * dynamically determine available memory | |
302 | */ | |
303 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
304 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
305 | ||
306 | largebits = largewords << SHIFT_WORD; | |
307 | largenumbers = largebits * 2; /* even numbers excluded */ | |
308 | ||
309 | /* validation check: count the number of primes tried */ | |
310 | largetries = 0; | |
311 | if ((q = BN_new()) == NULL) | |
312 | fatal("BN_new failed"); | |
313 | ||
314 | /* | |
315 | * Generate random starting point for subprime search, or use | |
316 | * specified parameter. | |
317 | */ | |
318 | if ((largebase = BN_new()) == NULL) | |
319 | fatal("BN_new failed"); | |
320 | if (start == NULL) { | |
321 | if (BN_rand(largebase, power, 1, 1) == 0) | |
322 | fatal("BN_rand failed"); | |
323 | } else { | |
324 | if (BN_copy(largebase, start) == NULL) | |
325 | fatal("BN_copy: failed"); | |
326 | } | |
327 | ||
328 | /* ensure odd */ | |
329 | if (BN_set_bit(largebase, 0) == 0) | |
330 | fatal("BN_set_bit: failed"); | |
331 | ||
332 | time(&time_start); | |
333 | ||
334 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), | |
335 | largenumbers, power); | |
336 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
337 | ||
338 | /* | |
339 | * TinySieve | |
340 | */ | |
341 | for (i = 0; i < tinybits; i++) { | |
342 | if (BIT_TEST(TinySieve, i)) | |
343 | continue; /* 2*i+3 is composite */ | |
344 | ||
345 | /* The next tiny prime */ | |
346 | t = 2 * i + 3; | |
347 | ||
348 | /* Mark all multiples of t */ | |
349 | for (j = i + t; j < tinybits; j += t) | |
350 | BIT_SET(TinySieve, j); | |
351 | ||
352 | sieve_large(t); | |
353 | } | |
354 | ||
355 | /* | |
356 | * Start the small block search at the next possible prime. To avoid | |
357 | * fencepost errors, the last pass is skipped. | |
358 | */ | |
359 | for (smallbase = TINY_NUMBER + 3; | |
360 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); | |
361 | smallbase += TINY_NUMBER) { | |
362 | for (i = 0; i < tinybits; i++) { | |
363 | if (BIT_TEST(TinySieve, i)) | |
364 | continue; /* 2*i+3 is composite */ | |
365 | ||
366 | /* The next tiny prime */ | |
367 | t = 2 * i + 3; | |
368 | r = smallbase % t; | |
369 | ||
370 | if (r == 0) { | |
371 | s = 0; /* t divides into smallbase exactly */ | |
372 | } else { | |
373 | /* smallbase+s is first entry divisible by t */ | |
374 | s = t - r; | |
375 | } | |
376 | ||
377 | /* | |
378 | * The sieve omits even numbers, so ensure that | |
379 | * smallbase+s is odd. Then, step through the sieve | |
380 | * in increments of 2*t | |
381 | */ | |
382 | if (s & 1) | |
383 | s += t; /* Make smallbase+s odd, and s even */ | |
384 | ||
385 | /* Mark all multiples of 2*t */ | |
386 | for (s /= 2; s < smallbits; s += t) | |
387 | BIT_SET(SmallSieve, s); | |
388 | } | |
389 | ||
390 | /* | |
391 | * SmallSieve | |
392 | */ | |
393 | for (i = 0; i < smallbits; i++) { | |
394 | if (BIT_TEST(SmallSieve, i)) | |
395 | continue; /* 2*i+smallbase is composite */ | |
396 | ||
397 | /* The next small prime */ | |
398 | sieve_large((2 * i) + smallbase); | |
399 | } | |
400 | ||
401 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
402 | } | |
403 | ||
404 | time(&time_stop); | |
405 | ||
406 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
407 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
408 | ||
409 | for (j = r = 0; j < largebits; j++) { | |
410 | if (BIT_TEST(LargeSieve, j)) | |
411 | continue; /* Definitely composite, skip */ | |
412 | ||
413 | debug2("test q = largebase+%u", 2 * j); | |
414 | if (BN_set_word(q, 2 * j) == 0) | |
415 | fatal("BN_set_word failed"); | |
416 | if (BN_add(q, q, largebase) == 0) | |
417 | fatal("BN_add failed"); | |
418 | if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, | |
419 | MODULI_TESTS_SIEVE, largetries, | |
420 | (power - 1) /* MSB */, (0), q) == -1) { | |
421 | ret = -1; | |
422 | break; | |
423 | } | |
424 | ||
425 | r++; /* count q */ | |
426 | } | |
427 | ||
428 | time(&time_stop); | |
429 | ||
430 | xfree(LargeSieve); | |
431 | xfree(SmallSieve); | |
432 | xfree(TinySieve); | |
433 | ||
434 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
435 | ||
436 | return (ret); | |
437 | } | |
438 | ||
439 | /* | |
440 | * perform a Miller-Rabin primality test | |
441 | * on the list of candidates | |
442 | * (checking both q and p) | |
443 | * The result is a list of so-call "safe" primes | |
444 | */ | |
445 | int | |
446 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) | |
447 | { | |
448 | BIGNUM *q, *p, *a; | |
449 | BN_CTX *ctx; | |
450 | char *cp, *lp; | |
451 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
452 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
453 | time_t time_start, time_stop; | |
454 | int res; | |
455 | ||
456 | if (trials < TRIAL_MINIMUM) { | |
457 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
458 | return (-1); | |
459 | } | |
460 | ||
461 | time(&time_start); | |
462 | ||
463 | if ((p = BN_new()) == NULL) | |
464 | fatal("BN_new failed"); | |
465 | if ((q = BN_new()) == NULL) | |
466 | fatal("BN_new failed"); | |
467 | if ((ctx = BN_CTX_new()) == NULL) | |
468 | fatal("BN_CTX_new failed"); | |
469 | ||
470 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
471 | ctime(&time_start), trials, generator_wanted); | |
472 | ||
473 | res = 0; | |
474 | lp = xmalloc(QLINESIZE + 1); | |
475 | while (fgets(lp, QLINESIZE + 1, in) != NULL) { | |
476 | count_in++; | |
477 | if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { | |
478 | debug2("%10u: comment or short line", count_in); | |
479 | continue; | |
480 | } | |
481 | ||
482 | /* XXX - fragile parser */ | |
483 | /* time */ | |
484 | cp = &lp[14]; /* (skip) */ | |
485 | ||
486 | /* type */ | |
487 | in_type = strtoul(cp, &cp, 10); | |
488 | ||
489 | /* tests */ | |
490 | in_tests = strtoul(cp, &cp, 10); | |
491 | ||
492 | if (in_tests & MODULI_TESTS_COMPOSITE) { | |
493 | debug2("%10u: known composite", count_in); | |
494 | continue; | |
495 | } | |
496 | ||
497 | /* tries */ | |
498 | in_tries = strtoul(cp, &cp, 10); | |
499 | ||
500 | /* size (most significant bit) */ | |
501 | in_size = strtoul(cp, &cp, 10); | |
502 | ||
503 | /* generator (hex) */ | |
504 | generator_known = strtoul(cp, &cp, 16); | |
505 | ||
506 | /* Skip white space */ | |
507 | cp += strspn(cp, " "); | |
508 | ||
509 | /* modulus (hex) */ | |
510 | switch (in_type) { | |
511 | case MODULI_TYPE_SOPHIE_GERMAIN: | |
512 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
513 | a = q; | |
514 | if (BN_hex2bn(&a, cp) == 0) | |
515 | fatal("BN_hex2bn failed"); | |
516 | /* p = 2*q + 1 */ | |
517 | if (BN_lshift(p, q, 1) == 0) | |
518 | fatal("BN_lshift failed"); | |
519 | if (BN_add_word(p, 1) == 0) | |
520 | fatal("BN_add_word failed"); | |
521 | in_size += 1; | |
522 | generator_known = 0; | |
523 | break; | |
524 | case MODULI_TYPE_UNSTRUCTURED: | |
525 | case MODULI_TYPE_SAFE: | |
526 | case MODULI_TYPE_SCHNORR: | |
527 | case MODULI_TYPE_STRONG: | |
528 | case MODULI_TYPE_UNKNOWN: | |
529 | debug2("%10u: (%u)", count_in, in_type); | |
530 | a = p; | |
531 | if (BN_hex2bn(&a, cp) == 0) | |
532 | fatal("BN_hex2bn failed"); | |
533 | /* q = (p-1) / 2 */ | |
534 | if (BN_rshift(q, p, 1) == 0) | |
535 | fatal("BN_rshift failed"); | |
536 | break; | |
537 | default: | |
538 | debug2("Unknown prime type"); | |
539 | break; | |
540 | } | |
541 | ||
542 | /* | |
543 | * due to earlier inconsistencies in interpretation, check | |
544 | * the proposed bit size. | |
545 | */ | |
546 | if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { | |
547 | debug2("%10u: bit size %u mismatch", count_in, in_size); | |
548 | continue; | |
549 | } | |
550 | if (in_size < QSIZE_MINIMUM) { | |
551 | debug2("%10u: bit size %u too short", count_in, in_size); | |
552 | continue; | |
553 | } | |
554 | ||
555 | if (in_tests & MODULI_TESTS_MILLER_RABIN) | |
556 | in_tries += trials; | |
557 | else | |
558 | in_tries = trials; | |
559 | ||
560 | /* | |
561 | * guess unknown generator | |
562 | */ | |
563 | if (generator_known == 0) { | |
564 | if (BN_mod_word(p, 24) == 11) | |
565 | generator_known = 2; | |
566 | else if (BN_mod_word(p, 12) == 5) | |
567 | generator_known = 3; | |
568 | else { | |
569 | u_int32_t r = BN_mod_word(p, 10); | |
570 | ||
571 | if (r == 3 || r == 7) | |
572 | generator_known = 5; | |
573 | } | |
574 | } | |
575 | /* | |
576 | * skip tests when desired generator doesn't match | |
577 | */ | |
578 | if (generator_wanted > 0 && | |
579 | generator_wanted != generator_known) { | |
580 | debug2("%10u: generator %d != %d", | |
581 | count_in, generator_known, generator_wanted); | |
582 | continue; | |
583 | } | |
584 | ||
585 | /* | |
586 | * Primes with no known generator are useless for DH, so | |
587 | * skip those. | |
588 | */ | |
589 | if (generator_known == 0) { | |
590 | debug2("%10u: no known generator", count_in); | |
591 | continue; | |
592 | } | |
593 | ||
594 | count_possible++; | |
595 | ||
596 | /* | |
597 | * The (1/4)^N performance bound on Miller-Rabin is | |
598 | * extremely pessimistic, so don't spend a lot of time | |
599 | * really verifying that q is prime until after we know | |
600 | * that p is also prime. A single pass will weed out the | |
601 | * vast majority of composite q's. | |
602 | */ | |
603 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
604 | debug("%10u: q failed first possible prime test", | |
605 | count_in); | |
606 | continue; | |
607 | } | |
608 | ||
609 | /* | |
610 | * q is possibly prime, so go ahead and really make sure | |
611 | * that p is prime. If it is, then we can go back and do | |
612 | * the same for q. If p is composite, chances are that | |
613 | * will show up on the first Rabin-Miller iteration so it | |
614 | * doesn't hurt to specify a high iteration count. | |
615 | */ | |
616 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
617 | debug("%10u: p is not prime", count_in); | |
618 | continue; | |
619 | } | |
620 | debug("%10u: p is almost certainly prime", count_in); | |
621 | ||
622 | /* recheck q more rigorously */ | |
623 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
624 | debug("%10u: q is not prime", count_in); | |
625 | continue; | |
626 | } | |
627 | debug("%10u: q is almost certainly prime", count_in); | |
628 | ||
629 | if (qfileout(out, MODULI_TYPE_SAFE, | |
630 | in_tests | MODULI_TESTS_MILLER_RABIN, | |
631 | in_tries, in_size, generator_known, p)) { | |
632 | res = -1; | |
633 | break; | |
634 | } | |
635 | ||
636 | count_out++; | |
637 | } | |
638 | ||
639 | time(&time_stop); | |
640 | xfree(lp); | |
641 | BN_free(p); | |
642 | BN_free(q); | |
643 | BN_CTX_free(ctx); | |
644 | ||
645 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
646 | ctime(&time_stop), count_out, count_possible, | |
647 | (long) (time_stop - time_start)); | |
648 | ||
649 | return (res); | |
650 | } |