xref: /netbsd-src/crypto/external/bsd/openssh/dist/moduli.c (revision 6a493d6bc668897c91594964a732d38505b70cbb)
1 /*	$NetBSD: moduli.c,v 1.6 2013/11/08 19:18:25 christos Exp $	*/
2 /* $OpenBSD: moduli.c,v 1.27 2013/05/17 00:13:13 djm Exp $ */
3 /*
4  * Copyright 1994 Phil Karn <karn@qualcomm.com>
5  * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com>
6  * Copyright 2000 Niels Provos <provos@citi.umich.edu>
7  * All rights reserved.
8  *
9  * Redistribution and use in source and binary forms, with or without
10  * modification, are permitted provided that the following conditions
11  * are met:
12  * 1. Redistributions of source code must retain the above copyright
13  *    notice, this list of conditions and the following disclaimer.
14  * 2. Redistributions in binary form must reproduce the above copyright
15  *    notice, this list of conditions and the following disclaimer in the
16  *    documentation and/or other materials provided with the distribution.
17  *
18  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
19  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
20  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
21  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
22  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
23  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
24  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
25  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
26  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
27  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28  */
29 
30 /*
31  * Two-step process to generate safe primes for DHGEX
32  *
33  *  Sieve candidates for "safe" primes,
34  *  suitable for use as Diffie-Hellman moduli;
35  *  that is, where q = (p-1)/2 is also prime.
36  *
37  * First step: generate candidate primes (memory intensive)
38  * Second step: test primes' safety (processor intensive)
39  */
40 #include "includes.h"
41 __RCSID("$NetBSD: moduli.c,v 1.6 2013/11/08 19:18:25 christos Exp $");
42 
43 #include <sys/param.h>
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 
57 #include "xmalloc.h"
58 #include "dh.h"
59 #include "log.h"
60 
61 /*
62  * File output defines
63  */
64 
65 /* need line long enough for largest moduli plus headers */
66 #define QLINESIZE		(100+8192)
67 
68 /*
69  * Size: decimal.
70  * Specifies the number of the most significant bit (0 to M).
71  * WARNING: internally, usually 1 to N.
72  */
73 #define QSIZE_MINIMUM		(511)
74 
75 /*
76  * Prime sieving defines
77  */
78 
79 /* Constant: assuming 8 bit bytes and 32 bit words */
80 #define SHIFT_BIT	(3)
81 #define SHIFT_BYTE	(2)
82 #define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
83 #define SHIFT_MEGABYTE	(20)
84 #define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
85 
86 /*
87  * Using virtual memory can cause thrashing.  This should be the largest
88  * number that is supported without a large amount of disk activity --
89  * that would increase the run time from hours to days or weeks!
90  */
91 #define LARGE_MINIMUM	(8UL)	/* megabytes */
92 
93 /*
94  * Do not increase this number beyond the unsigned integer bit size.
95  * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
96  */
97 #define LARGE_MAXIMUM	(127UL)	/* megabytes */
98 
99 /*
100  * Constant: when used with 32-bit integers, the largest sieve prime
101  * has to be less than 2**32.
102  */
103 #define SMALL_MAXIMUM	(0xffffffffUL)
104 
105 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
106 #define TINY_NUMBER	(1UL<<16)
107 
108 /* Ensure enough bit space for testing 2*q. */
109 #define TEST_MAXIMUM	(1UL<<16)
110 #define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
111 /* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
112 #define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
113 
114 /* bit operations on 32-bit words */
115 #define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
116 #define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
117 #define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
118 
119 /*
120  * Prime testing defines
121  */
122 
123 /* Minimum number of primality tests to perform */
124 #define TRIAL_MINIMUM	(4)
125 
126 /*
127  * Sieving data (XXX - move to struct)
128  */
129 
130 /* sieve 2**16 */
131 static u_int32_t *TinySieve, tinybits;
132 
133 /* sieve 2**30 in 2**16 parts */
134 static u_int32_t *SmallSieve, smallbits, smallbase;
135 
136 /* sieve relative to the initial value */
137 static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
138 static u_int32_t largebits, largememory;	/* megabytes */
139 static BIGNUM *largebase;
140 
141 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
142 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
143     unsigned long);
144 
145 /*
146  * print moduli out in consistent form,
147  */
148 static int
149 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
150     u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
151 {
152 	struct tm *gtm;
153 	time_t time_now;
154 	int res;
155 
156 	time(&time_now);
157 	gtm = gmtime(&time_now);
158 
159 	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
160 	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
161 	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
162 	    otype, otests, otries, osize, ogenerator);
163 
164 	if (res < 0)
165 		return (-1);
166 
167 	if (BN_print_fp(ofile, omodulus) < 1)
168 		return (-1);
169 
170 	res = fprintf(ofile, "\n");
171 	fflush(ofile);
172 
173 	return (res > 0 ? 0 : -1);
174 }
175 
176 
177 /*
178  ** Sieve p's and q's with small factors
179  */
180 static void
181 sieve_large(u_int32_t s)
182 {
183 	u_int32_t r, u;
184 
185 	debug3("sieve_large %u", s);
186 	largetries++;
187 	/* r = largebase mod s */
188 	r = BN_mod_word(largebase, s);
189 	if (r == 0)
190 		u = 0; /* s divides into largebase exactly */
191 	else
192 		u = s - r; /* largebase+u is first entry divisible by s */
193 
194 	if (u < largebits * 2) {
195 		/*
196 		 * The sieve omits p's and q's divisible by 2, so ensure that
197 		 * largebase+u is odd. Then, step through the sieve in
198 		 * increments of 2*s
199 		 */
200 		if (u & 0x1)
201 			u += s; /* Make largebase+u odd, and u even */
202 
203 		/* Mark all multiples of 2*s */
204 		for (u /= 2; u < largebits; u += s)
205 			BIT_SET(LargeSieve, u);
206 	}
207 
208 	/* r = p mod s */
209 	r = (2 * r + 1) % s;
210 	if (r == 0)
211 		u = 0; /* s divides p exactly */
212 	else
213 		u = s - r; /* p+u is first entry divisible by s */
214 
215 	if (u < largebits * 4) {
216 		/*
217 		 * The sieve omits p's divisible by 4, so ensure that
218 		 * largebase+u is not. Then, step through the sieve in
219 		 * increments of 4*s
220 		 */
221 		while (u & 0x3) {
222 			if (SMALL_MAXIMUM - u < s)
223 				return;
224 			u += s;
225 		}
226 
227 		/* Mark all multiples of 4*s */
228 		for (u /= 4; u < largebits; u += s)
229 			BIT_SET(LargeSieve, u);
230 	}
231 }
232 
233 /*
234  * list candidates for Sophie-Germain primes (where q = (p-1)/2)
235  * to standard output.
236  * The list is checked against small known primes (less than 2**30).
237  */
238 int
239 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
240 {
241 	BIGNUM *q;
242 	u_int32_t j, r, s, t;
243 	u_int32_t smallwords = TINY_NUMBER >> 6;
244 	u_int32_t tinywords = TINY_NUMBER >> 6;
245 	time_t time_start, time_stop;
246 	u_int32_t i;
247 	int ret = 0;
248 
249 	largememory = memory;
250 
251 	if (memory != 0 &&
252 	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
253 		error("Invalid memory amount (min %ld, max %ld)",
254 		    LARGE_MINIMUM, LARGE_MAXIMUM);
255 		return (-1);
256 	}
257 
258 	/*
259 	 * Set power to the length in bits of the prime to be generated.
260 	 * This is changed to 1 less than the desired safe prime moduli p.
261 	 */
262 	if (power > TEST_MAXIMUM) {
263 		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
264 		return (-1);
265 	} else if (power < TEST_MINIMUM) {
266 		error("Too few bits: %u < %u", power, TEST_MINIMUM);
267 		return (-1);
268 	}
269 	power--; /* decrement before squaring */
270 
271 	/*
272 	 * The density of ordinary primes is on the order of 1/bits, so the
273 	 * density of safe primes should be about (1/bits)**2. Set test range
274 	 * to something well above bits**2 to be reasonably sure (but not
275 	 * guaranteed) of catching at least one safe prime.
276 	 */
277 	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
278 
279 	/*
280 	 * Need idea of how much memory is available. We don't have to use all
281 	 * of it.
282 	 */
283 	if (largememory > LARGE_MAXIMUM) {
284 		logit("Limited memory: %u MB; limit %lu MB",
285 		    largememory, LARGE_MAXIMUM);
286 		largememory = LARGE_MAXIMUM;
287 	}
288 
289 	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
290 		logit("Increased memory: %u MB; need %u bytes",
291 		    largememory, (largewords << SHIFT_BYTE));
292 		largewords = (largememory << SHIFT_MEGAWORD);
293 	} else if (largememory > 0) {
294 		logit("Decreased memory: %u MB; want %u bytes",
295 		    largememory, (largewords << SHIFT_BYTE));
296 		largewords = (largememory << SHIFT_MEGAWORD);
297 	}
298 
299 	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
300 	tinybits = tinywords << SHIFT_WORD;
301 
302 	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
303 	smallbits = smallwords << SHIFT_WORD;
304 
305 	/*
306 	 * dynamically determine available memory
307 	 */
308 	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
309 		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
310 
311 	largebits = largewords << SHIFT_WORD;
312 	largenumbers = largebits * 2;	/* even numbers excluded */
313 
314 	/* validation check: count the number of primes tried */
315 	largetries = 0;
316 	if ((q = BN_new()) == NULL)
317 		fatal("BN_new failed");
318 
319 	/*
320 	 * Generate random starting point for subprime search, or use
321 	 * specified parameter.
322 	 */
323 	if ((largebase = BN_new()) == NULL)
324 		fatal("BN_new failed");
325 	if (start == NULL) {
326 		if (BN_rand(largebase, power, 1, 1) == 0)
327 			fatal("BN_rand failed");
328 	} else {
329 		if (BN_copy(largebase, start) == NULL)
330 			fatal("BN_copy: failed");
331 	}
332 
333 	/* ensure odd */
334 	if (BN_set_bit(largebase, 0) == 0)
335 		fatal("BN_set_bit: failed");
336 
337 	time(&time_start);
338 
339 	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
340 	    largenumbers, power);
341 	debug2("start point: 0x%s", BN_bn2hex(largebase));
342 
343 	/*
344 	 * TinySieve
345 	 */
346 	for (i = 0; i < tinybits; i++) {
347 		if (BIT_TEST(TinySieve, i))
348 			continue; /* 2*i+3 is composite */
349 
350 		/* The next tiny prime */
351 		t = 2 * i + 3;
352 
353 		/* Mark all multiples of t */
354 		for (j = i + t; j < tinybits; j += t)
355 			BIT_SET(TinySieve, j);
356 
357 		sieve_large(t);
358 	}
359 
360 	/*
361 	 * Start the small block search at the next possible prime. To avoid
362 	 * fencepost errors, the last pass is skipped.
363 	 */
364 	for (smallbase = TINY_NUMBER + 3;
365 	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
366 	    smallbase += TINY_NUMBER) {
367 		for (i = 0; i < tinybits; i++) {
368 			if (BIT_TEST(TinySieve, i))
369 				continue; /* 2*i+3 is composite */
370 
371 			/* The next tiny prime */
372 			t = 2 * i + 3;
373 			r = smallbase % t;
374 
375 			if (r == 0) {
376 				s = 0; /* t divides into smallbase exactly */
377 			} else {
378 				/* smallbase+s is first entry divisible by t */
379 				s = t - r;
380 			}
381 
382 			/*
383 			 * The sieve omits even numbers, so ensure that
384 			 * smallbase+s is odd. Then, step through the sieve
385 			 * in increments of 2*t
386 			 */
387 			if (s & 1)
388 				s += t; /* Make smallbase+s odd, and s even */
389 
390 			/* Mark all multiples of 2*t */
391 			for (s /= 2; s < smallbits; s += t)
392 				BIT_SET(SmallSieve, s);
393 		}
394 
395 		/*
396 		 * SmallSieve
397 		 */
398 		for (i = 0; i < smallbits; i++) {
399 			if (BIT_TEST(SmallSieve, i))
400 				continue; /* 2*i+smallbase is composite */
401 
402 			/* The next small prime */
403 			sieve_large((2 * i) + smallbase);
404 		}
405 
406 		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
407 	}
408 
409 	time(&time_stop);
410 
411 	logit("%.24s Sieved with %u small primes in %ld seconds",
412 	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
413 
414 	for (j = r = 0; j < largebits; j++) {
415 		if (BIT_TEST(LargeSieve, j))
416 			continue; /* Definitely composite, skip */
417 
418 		debug2("test q = largebase+%u", 2 * j);
419 		if (BN_set_word(q, 2 * j) == 0)
420 			fatal("BN_set_word failed");
421 		if (BN_add(q, q, largebase) == 0)
422 			fatal("BN_add failed");
423 		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
424 		    MODULI_TESTS_SIEVE, largetries,
425 		    (power - 1) /* MSB */, (0), q) == -1) {
426 			ret = -1;
427 			break;
428 		}
429 
430 		r++; /* count q */
431 	}
432 
433 	time(&time_stop);
434 
435 	free(LargeSieve);
436 	free(SmallSieve);
437 	free(TinySieve);
438 
439 	logit("%.24s Found %u candidates", ctime(&time_stop), r);
440 
441 	return (ret);
442 }
443 
444 static void
445 write_checkpoint(char *cpfile, u_int32_t lineno)
446 {
447 	FILE *fp;
448 	char tmp[MAXPATHLEN];
449 	int r;
450 
451 	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
452 	if (r == -1 || r >= MAXPATHLEN) {
453 		logit("write_checkpoint: temp pathname too long");
454 		return;
455 	}
456 	if ((r = mkstemp(tmp)) == -1) {
457 		logit("mkstemp(%s): %s", tmp, strerror(errno));
458 		return;
459 	}
460 	if ((fp = fdopen(r, "w")) == NULL) {
461 		logit("write_checkpoint: fdopen: %s", strerror(errno));
462 		close(r);
463 		return;
464 	}
465 	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
466 	    && rename(tmp, cpfile) == 0)
467 		debug3("wrote checkpoint line %lu to '%s'",
468 		    (unsigned long)lineno, cpfile);
469 	else
470 		logit("failed to write to checkpoint file '%s': %s", cpfile,
471 		    strerror(errno));
472 }
473 
474 static unsigned long
475 read_checkpoint(char *cpfile)
476 {
477 	FILE *fp;
478 	unsigned long lineno = 0;
479 
480 	if ((fp = fopen(cpfile, "r")) == NULL)
481 		return 0;
482 	if (fscanf(fp, "%lu\n", &lineno) < 1)
483 		logit("Failed to load checkpoint from '%s'", cpfile);
484 	else
485 		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
486 	fclose(fp);
487 	return lineno;
488 }
489 
490 /*
491  * perform a Miller-Rabin primality test
492  * on the list of candidates
493  * (checking both q and p)
494  * The result is a list of so-call "safe" primes
495  */
496 int
497 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
498     char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
499 {
500 	BIGNUM *q, *p, *a;
501 	BN_CTX *ctx;
502 	char *cp, *lp;
503 	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
504 	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
505 	unsigned long last_processed = 0, end_lineno;
506 	time_t time_start, time_stop;
507 	int res;
508 
509 	if (trials < TRIAL_MINIMUM) {
510 		error("Minimum primality trials is %d", TRIAL_MINIMUM);
511 		return (-1);
512 	}
513 
514 	time(&time_start);
515 
516 	if ((p = BN_new()) == NULL)
517 		fatal("BN_new failed");
518 	if ((q = BN_new()) == NULL)
519 		fatal("BN_new failed");
520 	if ((ctx = BN_CTX_new()) == NULL)
521 		fatal("BN_CTX_new failed");
522 
523 	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
524 	    ctime(&time_start), trials, generator_wanted);
525 
526 	if (checkpoint_file != NULL)
527 		last_processed = read_checkpoint(checkpoint_file);
528 	if (start_lineno > last_processed)
529 		last_processed = start_lineno;
530 	if (num_lines == 0)
531 		end_lineno = ULONG_MAX;
532 	else
533 		end_lineno = last_processed + num_lines;
534 	debug2("process line %lu to line %lu", last_processed, end_lineno);
535 
536 	res = 0;
537 	lp = xmalloc(QLINESIZE + 1);
538 	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
539 		count_in++;
540 		if (checkpoint_file != NULL) {
541 			if (count_in <= last_processed) {
542 				debug3("skipping line %u, before checkpoint",
543 				    count_in);
544 				continue;
545 			}
546 			write_checkpoint(checkpoint_file, count_in);
547 		}
548 		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
549 			debug2("%10u: comment or short line", count_in);
550 			continue;
551 		}
552 
553 		/* XXX - fragile parser */
554 		/* time */
555 		cp = &lp[14];	/* (skip) */
556 
557 		/* type */
558 		in_type = strtoul(cp, &cp, 10);
559 
560 		/* tests */
561 		in_tests = strtoul(cp, &cp, 10);
562 
563 		if (in_tests & MODULI_TESTS_COMPOSITE) {
564 			debug2("%10u: known composite", count_in);
565 			continue;
566 		}
567 
568 		/* tries */
569 		in_tries = strtoul(cp, &cp, 10);
570 
571 		/* size (most significant bit) */
572 		in_size = strtoul(cp, &cp, 10);
573 
574 		/* generator (hex) */
575 		generator_known = strtoul(cp, &cp, 16);
576 
577 		/* Skip white space */
578 		cp += strspn(cp, " ");
579 
580 		/* modulus (hex) */
581 		switch (in_type) {
582 		case MODULI_TYPE_SOPHIE_GERMAIN:
583 			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
584 			a = q;
585 			if (BN_hex2bn(&a, cp) == 0)
586 				fatal("BN_hex2bn failed");
587 			/* p = 2*q + 1 */
588 			if (BN_lshift(p, q, 1) == 0)
589 				fatal("BN_lshift failed");
590 			if (BN_add_word(p, 1) == 0)
591 				fatal("BN_add_word failed");
592 			in_size += 1;
593 			generator_known = 0;
594 			break;
595 		case MODULI_TYPE_UNSTRUCTURED:
596 		case MODULI_TYPE_SAFE:
597 		case MODULI_TYPE_SCHNORR:
598 		case MODULI_TYPE_STRONG:
599 		case MODULI_TYPE_UNKNOWN:
600 			debug2("%10u: (%u)", count_in, in_type);
601 			a = p;
602 			if (BN_hex2bn(&a, cp) == 0)
603 				fatal("BN_hex2bn failed");
604 			/* q = (p-1) / 2 */
605 			if (BN_rshift(q, p, 1) == 0)
606 				fatal("BN_rshift failed");
607 			break;
608 		default:
609 			debug2("Unknown prime type");
610 			break;
611 		}
612 
613 		/*
614 		 * due to earlier inconsistencies in interpretation, check
615 		 * the proposed bit size.
616 		 */
617 		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
618 			debug2("%10u: bit size %u mismatch", count_in, in_size);
619 			continue;
620 		}
621 		if (in_size < QSIZE_MINIMUM) {
622 			debug2("%10u: bit size %u too short", count_in, in_size);
623 			continue;
624 		}
625 
626 		if (in_tests & MODULI_TESTS_MILLER_RABIN)
627 			in_tries += trials;
628 		else
629 			in_tries = trials;
630 
631 		/*
632 		 * guess unknown generator
633 		 */
634 		if (generator_known == 0) {
635 			if (BN_mod_word(p, 24) == 11)
636 				generator_known = 2;
637 			else if (BN_mod_word(p, 12) == 5)
638 				generator_known = 3;
639 			else {
640 				u_int32_t r = BN_mod_word(p, 10);
641 
642 				if (r == 3 || r == 7)
643 					generator_known = 5;
644 			}
645 		}
646 		/*
647 		 * skip tests when desired generator doesn't match
648 		 */
649 		if (generator_wanted > 0 &&
650 		    generator_wanted != generator_known) {
651 			debug2("%10u: generator %d != %d",
652 			    count_in, generator_known, generator_wanted);
653 			continue;
654 		}
655 
656 		/*
657 		 * Primes with no known generator are useless for DH, so
658 		 * skip those.
659 		 */
660 		if (generator_known == 0) {
661 			debug2("%10u: no known generator", count_in);
662 			continue;
663 		}
664 
665 		count_possible++;
666 
667 		/*
668 		 * The (1/4)^N performance bound on Miller-Rabin is
669 		 * extremely pessimistic, so don't spend a lot of time
670 		 * really verifying that q is prime until after we know
671 		 * that p is also prime. A single pass will weed out the
672 		 * vast majority of composite q's.
673 		 */
674 		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
675 			debug("%10u: q failed first possible prime test",
676 			    count_in);
677 			continue;
678 		}
679 
680 		/*
681 		 * q is possibly prime, so go ahead and really make sure
682 		 * that p is prime. If it is, then we can go back and do
683 		 * the same for q. If p is composite, chances are that
684 		 * will show up on the first Rabin-Miller iteration so it
685 		 * doesn't hurt to specify a high iteration count.
686 		 */
687 		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
688 			debug("%10u: p is not prime", count_in);
689 			continue;
690 		}
691 		debug("%10u: p is almost certainly prime", count_in);
692 
693 		/* recheck q more rigorously */
694 		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
695 			debug("%10u: q is not prime", count_in);
696 			continue;
697 		}
698 		debug("%10u: q is almost certainly prime", count_in);
699 
700 		if (qfileout(out, MODULI_TYPE_SAFE,
701 		    in_tests | MODULI_TESTS_MILLER_RABIN,
702 		    in_tries, in_size, generator_known, p)) {
703 			res = -1;
704 			break;
705 		}
706 
707 		count_out++;
708 	}
709 
710 	time(&time_stop);
711 	free(lp);
712 	BN_free(p);
713 	BN_free(q);
714 	BN_CTX_free(ctx);
715 
716 	if (checkpoint_file != NULL)
717 		unlink(checkpoint_file);
718 
719 	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
720 	    ctime(&time_stop), count_out, count_possible,
721 	    (long) (time_stop - time_start));
722 
723 	return (res);
724 }
725