1 /* $OpenBSD: moduli.c,v 1.41 2026/03/03 09:57:25 dtucker 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 #ifdef WITH_OPENSSL
43
44 #include <sys/types.h>
45
46 #include <openssl/bn.h>
47 #include <openssl/dh.h>
48
49 #include <errno.h>
50 #include <stdio.h>
51 #include <stdlib.h>
52 #include <string.h>
53 #include <stdarg.h>
54 #include <time.h>
55 #include <unistd.h>
56 #include <limits.h>
57
58 #include "xmalloc.h"
59 #include "dh.h"
60 #include "log.h"
61 #include "misc.h"
62
63 #include "openbsd-compat/openssl-compat.h"
64
65 /*
66 * File output defines
67 */
68
69 /* need line long enough for largest moduli plus headers */
70 #define QLINESIZE (100+8192)
71
72 /*
73 * Size: decimal.
74 * Specifies the number of the most significant bit (0 to M).
75 * WARNING: internally, usually 1 to N.
76 */
77 #define QSIZE_MINIMUM (511)
78
79 /*
80 * Prime sieving defines
81 */
82
83 /* Constant: assuming 8 bit bytes and 32 bit words */
84 #define SHIFT_BIT (3)
85 #define SHIFT_BYTE (2)
86 #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE)
87 #define SHIFT_MEGABYTE (20)
88 #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE)
89
90 /*
91 * Do not increase this number beyond the unsigned integer bit size.
92 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
93 */
94 #define LARGE_MAXIMUM (127UL) /* megabytes */
95
96 /*
97 * Constant: when used with 32-bit integers, the largest sieve prime
98 * has to be less than 2**32.
99 */
100 #define SMALL_MAXIMUM (0xffffffffUL)
101
102 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
103 #define TINY_NUMBER (1UL<<16)
104
105 /* Ensure enough bit space for testing 2*q. */
106 #define TEST_MAXIMUM (1UL<<16)
107 #define TEST_MINIMUM (QSIZE_MINIMUM + 1)
108 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */
109 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */
110
111 /* bit operations on 32-bit words */
112 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
113 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
114 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
115
116 /*
117 * Prime testing defines
118 */
119
120 /* Minimum number of primality tests to perform */
121 #define TRIAL_MINIMUM (4)
122
123 /*
124 * Sieving data (XXX - move to struct)
125 */
126
127 /* sieve 2**16 */
128 static uint32_t *TinySieve, tinybits;
129
130 /* sieve 2**30 in 2**16 parts */
131 static uint32_t *SmallSieve, smallbits, smallbase;
132
133 /* sieve relative to the initial value */
134 static uint32_t *LargeSieve, largewords, largetries, largenumbers;
135 static uint32_t largebits, largememory; /* megabytes */
136 static BIGNUM *largebase;
137
138 int gen_candidates(FILE *, uint32_t, BIGNUM *);
139 int prime_test(FILE *, FILE *, uint32_t, uint32_t, char *, unsigned long,
140 unsigned long);
141
142 /*
143 * print moduli out in consistent form,
144 */
145 static int
qfileout(FILE * ofile,uint32_t otype,uint32_t otests,uint32_t otries,uint32_t osize,uint32_t ogenerator,BIGNUM * omodulus)146 qfileout(FILE * ofile, uint32_t otype, uint32_t otests, uint32_t otries,
147 uint32_t osize, uint32_t ogenerator, BIGNUM * omodulus)
148 {
149 struct tm *gtm;
150 time_t time_now;
151 int res;
152
153 time(&time_now);
154 gtm = gmtime(&time_now);
155 if (gtm == NULL)
156 return -1;
157
158 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
159 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
160 gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
161 otype, otests, otries, osize, ogenerator);
162
163 if (res < 0)
164 return (-1);
165
166 if (BN_print_fp(ofile, omodulus) < 1)
167 return (-1);
168
169 res = fprintf(ofile, "\n");
170 fflush(ofile);
171
172 return (res > 0 ? 0 : -1);
173 }
174
175
176 /*
177 ** Sieve p's and q's with small factors
178 */
179 static void
sieve_large(uint32_t s32)180 sieve_large(uint32_t s32)
181 {
182 uint64_t r, u, s = s32;
183
184 debug3("sieve_large %u", s32);
185 largetries++;
186 /* r = largebase mod s */
187 r = BN_mod_word(largebase, s32);
188 if (r == 0)
189 u = 0; /* s divides into largebase exactly */
190 else
191 u = s - r; /* largebase+u is first entry divisible by s */
192
193 if (u < largebits * 2ULL) {
194 /*
195 * The sieve omits p's and q's divisible by 2, so ensure that
196 * largebase+u is odd. Then, step through the sieve in
197 * increments of 2*s
198 */
199 if (u & 0x1)
200 u += s; /* Make largebase+u odd, and u even */
201
202 /* Mark all multiples of 2*s */
203 for (u /= 2; u < largebits; u += s)
204 BIT_SET(LargeSieve, u);
205 }
206
207 /* r = p mod s */
208 r = (2 * r + 1) % s;
209 if (r == 0)
210 u = 0; /* s divides p exactly */
211 else
212 u = s - r; /* p+u is first entry divisible by s */
213
214 if (u < largebits * 4ULL) {
215 /*
216 * The sieve omits p's divisible by 4, so ensure that
217 * largebase+u is not. Then, step through the sieve in
218 * increments of 4*s
219 */
220 while (u & 0x3) {
221 if (SMALL_MAXIMUM - u < s)
222 return;
223 u += s;
224 }
225
226 /* Mark all multiples of 4*s */
227 for (u /= 4; u < largebits; u += s)
228 BIT_SET(LargeSieve, u);
229 }
230 }
231
232 /*
233 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
234 * to standard output.
235 * The list is checked against small known primes (less than 2**30).
236 */
237 int
gen_candidates(FILE * out,uint32_t power,BIGNUM * start)238 gen_candidates(FILE *out, uint32_t power, BIGNUM *start)
239 {
240 BIGNUM *q;
241 uint32_t j, r, s, t;
242 uint32_t smallwords = TINY_NUMBER >> 6;
243 uint32_t tinywords = TINY_NUMBER >> 6;
244 time_t time_start, time_stop;
245 uint32_t i;
246 int ret = 0;
247
248 /*
249 * Set power to the length in bits of the prime to be generated.
250 * This is changed to 1 less than the desired safe prime moduli p.
251 */
252 if (power > TEST_MAXIMUM) {
253 error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
254 return (-1);
255 } else if (power < TEST_MINIMUM) {
256 error("Too few bits: %u < %u", power, TEST_MINIMUM);
257 return (-1);
258 }
259 power--; /* decrement before squaring */
260
261 /* Always use the maximum amount of memory supported by the algorithm. */
262 largememory = LARGE_MAXIMUM;
263 largewords = (largememory << SHIFT_MEGAWORD);
264
265 TinySieve = xcalloc(tinywords, sizeof(uint32_t));
266 tinybits = tinywords << SHIFT_WORD;
267
268 SmallSieve = xcalloc(smallwords, sizeof(uint32_t));
269 smallbits = smallwords << SHIFT_WORD;
270
271 LargeSieve = xcalloc(largewords, sizeof(uint32_t));
272 largebits = largewords << SHIFT_WORD;
273 largenumbers = largebits * 2; /* even numbers excluded */
274
275 /* validation check: count the number of primes tried */
276 largetries = 0;
277 if ((q = BN_new()) == NULL)
278 fatal("BN_new failed");
279
280 /*
281 * Generate random starting point for subprime search, or use
282 * specified parameter.
283 */
284 if ((largebase = BN_new()) == NULL)
285 fatal("BN_new failed");
286 if (start == NULL) {
287 if (BN_rand(largebase, power, 1, 1) == 0)
288 fatal("BN_rand failed");
289 } else {
290 if (BN_copy(largebase, start) == NULL)
291 fatal("BN_copy: failed");
292 }
293
294 /* ensure odd */
295 if (BN_set_bit(largebase, 0) == 0)
296 fatal("BN_set_bit: failed");
297
298 time(&time_start);
299
300 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
301 largenumbers, power);
302 debug2("start point: 0x%s", BN_bn2hex(largebase));
303
304 /*
305 * TinySieve
306 */
307 for (i = 0; i < tinybits; i++) {
308 if (BIT_TEST(TinySieve, i))
309 continue; /* 2*i+3 is composite */
310
311 /* The next tiny prime */
312 t = 2 * i + 3;
313
314 /* Mark all multiples of t */
315 for (j = i + t; j < tinybits; j += t)
316 BIT_SET(TinySieve, j);
317
318 sieve_large(t);
319 }
320
321 /*
322 * Start the small block search at the next possible prime. To avoid
323 * fencepost errors, the last pass is skipped.
324 */
325 for (smallbase = TINY_NUMBER + 3;
326 smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
327 smallbase += TINY_NUMBER) {
328 for (i = 0; i < tinybits; i++) {
329 if (BIT_TEST(TinySieve, i))
330 continue; /* 2*i+3 is composite */
331
332 /* The next tiny prime */
333 t = 2 * i + 3;
334 r = smallbase % t;
335
336 if (r == 0) {
337 s = 0; /* t divides into smallbase exactly */
338 } else {
339 /* smallbase+s is first entry divisible by t */
340 s = t - r;
341 }
342
343 /*
344 * The sieve omits even numbers, so ensure that
345 * smallbase+s is odd. Then, step through the sieve
346 * in increments of 2*t
347 */
348 if (s & 1)
349 s += t; /* Make smallbase+s odd, and s even */
350
351 /* Mark all multiples of 2*t */
352 for (s /= 2; s < smallbits; s += t)
353 BIT_SET(SmallSieve, s);
354 }
355
356 /*
357 * SmallSieve
358 */
359 for (i = 0; i < smallbits; i++) {
360 if (BIT_TEST(SmallSieve, i))
361 continue; /* 2*i+smallbase is composite */
362
363 /* The next small prime */
364 sieve_large((2 * i) + smallbase);
365 }
366
367 memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
368 }
369
370 time(&time_stop);
371
372 logit("%.24s Sieved with %u small primes in %lld seconds",
373 ctime(&time_stop), largetries, (long long)(time_stop - time_start));
374
375 for (j = r = 0; j < largebits; j++) {
376 if (BIT_TEST(LargeSieve, j))
377 continue; /* Definitely composite, skip */
378
379 debug2("test q = largebase+%u", 2 * j);
380 if (BN_set_word(q, 2 * j) == 0)
381 fatal("BN_set_word failed");
382 if (BN_add(q, q, largebase) == 0)
383 fatal("BN_add failed");
384 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
385 MODULI_TESTS_SIEVE, largetries,
386 (power - 1) /* MSB */, (0), q) == -1) {
387 ret = -1;
388 break;
389 }
390
391 r++; /* count q */
392 }
393
394 time(&time_stop);
395
396 free(LargeSieve);
397 free(SmallSieve);
398 free(TinySieve);
399
400 logit("%.24s Found %u candidates", ctime(&time_stop), r);
401
402 return (ret);
403 }
404
405 static void
write_checkpoint(char * cpfile,uint32_t lineno)406 write_checkpoint(char *cpfile, uint32_t lineno)
407 {
408 FILE *fp;
409 char tmp[PATH_MAX];
410 int r, writeok, closeok;
411
412 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
413 if (r < 0 || r >= PATH_MAX) {
414 logit("write_checkpoint: temp pathname too long");
415 return;
416 }
417 if ((r = mkstemp(tmp)) == -1) {
418 logit("mkstemp(%s): %s", tmp, strerror(errno));
419 return;
420 }
421 if ((fp = fdopen(r, "w")) == NULL) {
422 logit("write_checkpoint: fdopen: %s", strerror(errno));
423 unlink(tmp);
424 close(r);
425 return;
426 }
427 writeok = (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0);
428 closeok = (fclose(fp) == 0);
429 if (writeok && closeok && rename(tmp, cpfile) == 0) {
430 debug3("wrote checkpoint line %lu to '%s'",
431 (unsigned long)lineno, cpfile);
432 } else {
433 logit("failed to write to checkpoint file '%s': %s", cpfile,
434 strerror(errno));
435 (void)unlink(tmp);
436 }
437 }
438
439 static unsigned long
read_checkpoint(char * cpfile)440 read_checkpoint(char *cpfile)
441 {
442 FILE *fp;
443 unsigned long lineno = 0;
444
445 if ((fp = fopen(cpfile, "r")) == NULL)
446 return 0;
447 if (fscanf(fp, "%lu\n", &lineno) < 1)
448 logit("Failed to load checkpoint from '%s'", cpfile);
449 else
450 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
451 fclose(fp);
452 return lineno;
453 }
454
455 static unsigned long
count_lines(FILE * f)456 count_lines(FILE *f)
457 {
458 unsigned long count = 0;
459 char lp[QLINESIZE + 1];
460
461 if (fseek(f, 0, SEEK_SET) != 0) {
462 debug("input file is not seekable");
463 return ULONG_MAX;
464 }
465 while (fgets(lp, QLINESIZE + 1, f) != NULL)
466 count++;
467 rewind(f);
468 debug("input file has %lu lines", count);
469 return count;
470 }
471
472 static char *
fmt_time(time_t seconds)473 fmt_time(time_t seconds)
474 {
475 int day, hr, min;
476 static char buf[128];
477
478 min = (seconds / 60) % 60;
479 hr = (seconds / 60 / 60) % 24;
480 day = seconds / 60 / 60 / 24;
481 if (day > 0)
482 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min);
483 else
484 snprintf(buf, sizeof buf, "%d:%02d", hr, min);
485 return buf;
486 }
487
488 static void
print_progress(unsigned long start_lineno,unsigned long current_lineno,unsigned long end_lineno)489 print_progress(unsigned long start_lineno, unsigned long current_lineno,
490 unsigned long end_lineno)
491 {
492 static time_t time_start, time_prev;
493 time_t time_now, elapsed;
494 unsigned long num_to_process, processed, remaining, percent, eta;
495 double time_per_line;
496 char *eta_str;
497
498 time_now = monotime();
499 if (time_start == 0) {
500 time_start = time_prev = time_now;
501 return;
502 }
503 /* print progress after 1m then once per 5m */
504 if (time_now - time_prev < 5 * 60)
505 return;
506 time_prev = time_now;
507 elapsed = time_now - time_start;
508 processed = current_lineno - start_lineno;
509 remaining = end_lineno - current_lineno;
510 num_to_process = end_lineno - start_lineno;
511 time_per_line = (double)elapsed / processed;
512 /* if we don't know how many we're processing just report count+time */
513 time(&time_now);
514 if (end_lineno == ULONG_MAX) {
515 logit("%.24s processed %lu in %s", ctime(&time_now),
516 processed, fmt_time(elapsed));
517 return;
518 }
519 percent = 100 * processed / num_to_process;
520 eta = time_per_line * remaining;
521 eta_str = xstrdup(fmt_time(eta));
522 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s",
523 ctime(&time_now), processed, num_to_process, percent,
524 fmt_time(elapsed), eta_str);
525 free(eta_str);
526 }
527
528 /*
529 * perform a Miller-Rabin primality test
530 * on the list of candidates
531 * (checking both q and p)
532 * The result is a list of so-call "safe" primes
533 */
534 int
prime_test(FILE * in,FILE * out,uint32_t trials,uint32_t generator_wanted,char * checkpoint_file,unsigned long start_lineno,unsigned long num_lines)535 prime_test(FILE *in, FILE *out, uint32_t trials, uint32_t generator_wanted,
536 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
537 {
538 BIGNUM *q, *p, *a;
539 char *cp, *lp;
540 uint32_t count_in = 0, count_out = 0, count_possible = 0;
541 uint32_t generator_known, in_tests, in_tries, in_type, in_size;
542 unsigned long last_processed = 0, end_lineno;
543 time_t time_start, time_stop;
544 int res, is_prime;
545
546 if (trials < TRIAL_MINIMUM) {
547 error("Minimum primality trials is %d", TRIAL_MINIMUM);
548 return (-1);
549 }
550
551 if (num_lines == 0)
552 end_lineno = count_lines(in);
553 else
554 end_lineno = start_lineno + num_lines;
555
556 time(&time_start);
557
558 if ((p = BN_new()) == NULL)
559 fatal("BN_new failed");
560 if ((q = BN_new()) == NULL)
561 fatal("BN_new failed");
562
563 debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
564 ctime(&time_start), trials, generator_wanted);
565
566 if (checkpoint_file != NULL)
567 last_processed = read_checkpoint(checkpoint_file);
568 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno);
569 if (end_lineno == ULONG_MAX)
570 debug("process from line %lu from pipe", last_processed);
571 else
572 debug("process from line %lu to line %lu", last_processed,
573 end_lineno);
574
575 res = 0;
576 lp = xmalloc(QLINESIZE + 1);
577 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
578 count_in++;
579 if (count_in <= last_processed) {
580 debug3("skipping line %u, before checkpoint or "
581 "specified start line", count_in);
582 continue;
583 }
584 if (checkpoint_file != NULL)
585 write_checkpoint(checkpoint_file, count_in);
586 print_progress(start_lineno, count_in, end_lineno);
587 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
588 debug2("%10u: comment or short line", count_in);
589 continue;
590 }
591
592 /* XXX - fragile parser */
593 /* time */
594 cp = &lp[14]; /* (skip) */
595
596 /* type */
597 in_type = strtoul(cp, &cp, 10);
598
599 /* tests */
600 in_tests = strtoul(cp, &cp, 10);
601
602 if (in_tests & MODULI_TESTS_COMPOSITE) {
603 debug2("%10u: known composite", count_in);
604 continue;
605 }
606
607 /* tries */
608 in_tries = strtoul(cp, &cp, 10);
609
610 /* size (most significant bit) */
611 in_size = strtoul(cp, &cp, 10);
612
613 /* generator (hex) */
614 generator_known = strtoul(cp, &cp, 16);
615
616 /* Skip white space */
617 cp += strspn(cp, " ");
618
619 /* modulus (hex) */
620 switch (in_type) {
621 case MODULI_TYPE_SOPHIE_GERMAIN:
622 debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
623 a = q;
624 if (BN_hex2bn(&a, cp) == 0)
625 fatal("BN_hex2bn failed");
626 /* p = 2*q + 1 */
627 if (BN_lshift(p, q, 1) == 0)
628 fatal("BN_lshift failed");
629 if (BN_add_word(p, 1) == 0)
630 fatal("BN_add_word failed");
631 in_size += 1;
632 generator_known = 0;
633 break;
634 case MODULI_TYPE_UNSTRUCTURED:
635 case MODULI_TYPE_SAFE:
636 case MODULI_TYPE_SCHNORR:
637 case MODULI_TYPE_STRONG:
638 case MODULI_TYPE_UNKNOWN:
639 debug2("%10u: (%u)", count_in, in_type);
640 a = p;
641 if (BN_hex2bn(&a, cp) == 0)
642 fatal("BN_hex2bn failed");
643 /* q = (p-1) / 2 */
644 if (BN_rshift(q, p, 1) == 0)
645 fatal("BN_rshift failed");
646 break;
647 default:
648 debug2("Unknown prime type");
649 break;
650 }
651
652 /*
653 * due to earlier inconsistencies in interpretation, check
654 * the proposed bit size.
655 */
656 if ((uint32_t)BN_num_bits(p) != (in_size + 1)) {
657 debug2("%10u: bit size %u mismatch", count_in, in_size);
658 continue;
659 }
660 if (in_size < QSIZE_MINIMUM) {
661 debug2("%10u: bit size %u too short", count_in, in_size);
662 continue;
663 }
664
665 if (in_tests & MODULI_TESTS_MILLER_RABIN)
666 in_tries += trials;
667 else
668 in_tries = trials;
669
670 /*
671 * guess unknown generator
672 */
673 if (generator_known == 0) {
674 if (BN_mod_word(p, 24) == 11)
675 generator_known = 2;
676 else {
677 uint32_t r = BN_mod_word(p, 10);
678
679 if (r == 3 || r == 7)
680 generator_known = 5;
681 }
682 }
683 /*
684 * skip tests when desired generator doesn't match
685 */
686 if (generator_wanted > 0 &&
687 generator_wanted != generator_known) {
688 debug2("%10u: generator %d != %d",
689 count_in, generator_known, generator_wanted);
690 continue;
691 }
692
693 /*
694 * Primes with no known generator are useless for DH, so
695 * skip those.
696 */
697 if (generator_known == 0) {
698 debug2("%10u: no known generator", count_in);
699 continue;
700 }
701
702 count_possible++;
703
704 /*
705 * The (1/4)^N performance bound on Miller-Rabin is
706 * extremely pessimistic, so don't spend a lot of time
707 * really verifying that q is prime until after we know
708 * that p is also prime. A single pass will weed out the
709 * vast majority of composite q's.
710 */
711 is_prime = BN_is_prime_ex(q, 1, NULL, NULL);
712 if (is_prime < 0)
713 fatal("BN_is_prime_ex failed");
714 if (is_prime == 0) {
715 debug("%10u: q failed first possible prime test",
716 count_in);
717 continue;
718 }
719
720 /*
721 * q is possibly prime, so go ahead and really make sure
722 * that p is prime. If it is, then we can go back and do
723 * the same for q. If p is composite, chances are that
724 * will show up on the first Rabin-Miller iteration so it
725 * doesn't hurt to specify a high iteration count.
726 */
727 is_prime = BN_is_prime_ex(p, trials, NULL, NULL);
728 if (is_prime < 0)
729 fatal("BN_is_prime_ex failed");
730 if (is_prime == 0) {
731 debug("%10u: p is not prime", count_in);
732 continue;
733 }
734 debug("%10u: p is almost certainly prime", count_in);
735
736 /* recheck q more rigorously */
737 is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL);
738 if (is_prime < 0)
739 fatal("BN_is_prime_ex failed");
740 if (is_prime == 0) {
741 debug("%10u: q is not prime", count_in);
742 continue;
743 }
744 debug("%10u: q is almost certainly prime", count_in);
745
746 if (qfileout(out, MODULI_TYPE_SAFE,
747 in_tests | MODULI_TESTS_MILLER_RABIN,
748 in_tries, in_size, generator_known, p)) {
749 res = -1;
750 break;
751 }
752
753 count_out++;
754 }
755
756 time(&time_stop);
757 free(lp);
758 BN_free(p);
759 BN_free(q);
760
761 if (checkpoint_file != NULL)
762 unlink(checkpoint_file);
763
764 logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
765 ctime(&time_stop), count_out, count_possible,
766 (long) (time_stop - time_start));
767
768 return (res);
769 }
770
771 #endif /* WITH_OPENSSL */
772