xref: /freebsd/crypto/openssh/moduli.c (revision 839f11a4fe18e4ae2dd930766b551fa67e354735)
1 /* $OpenBSD: moduli.c,v 1.26 2012/07/06 00:41:59 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 #include <sys/param.h>
43 #include <sys/types.h>
44 
45 #include <openssl/bn.h>
46 #include <openssl/dh.h>
47 
48 #include <errno.h>
49 #include <stdio.h>
50 #include <stdlib.h>
51 #include <string.h>
52 #include <stdarg.h>
53 #include <time.h>
54 #include <unistd.h>
55 
56 #include "xmalloc.h"
57 #include "dh.h"
58 #include "log.h"
59 
60 #include "openbsd-compat/openssl-compat.h"
61 
62 /*
63  * File output defines
64  */
65 
66 /* need line long enough for largest moduli plus headers */
67 #define QLINESIZE		(100+8192)
68 
69 /*
70  * Size: decimal.
71  * Specifies the number of the most significant bit (0 to M).
72  * WARNING: internally, usually 1 to N.
73  */
74 #define QSIZE_MINIMUM		(511)
75 
76 /*
77  * Prime sieving defines
78  */
79 
80 /* Constant: assuming 8 bit bytes and 32 bit words */
81 #define SHIFT_BIT	(3)
82 #define SHIFT_BYTE	(2)
83 #define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
84 #define SHIFT_MEGABYTE	(20)
85 #define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
86 
87 /*
88  * Using virtual memory can cause thrashing.  This should be the largest
89  * number that is supported without a large amount of disk activity --
90  * that would increase the run time from hours to days or weeks!
91  */
92 #define LARGE_MINIMUM	(8UL)	/* megabytes */
93 
94 /*
95  * Do not increase this number beyond the unsigned integer bit size.
96  * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
97  */
98 #define LARGE_MAXIMUM	(127UL)	/* megabytes */
99 
100 /*
101  * Constant: when used with 32-bit integers, the largest sieve prime
102  * has to be less than 2**32.
103  */
104 #define SMALL_MAXIMUM	(0xffffffffUL)
105 
106 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
107 #define TINY_NUMBER	(1UL<<16)
108 
109 /* Ensure enough bit space for testing 2*q. */
110 #define TEST_MAXIMUM	(1UL<<16)
111 #define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
112 /* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
113 #define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
114 
115 /* bit operations on 32-bit words */
116 #define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
117 #define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
118 #define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
119 
120 /*
121  * Prime testing defines
122  */
123 
124 /* Minimum number of primality tests to perform */
125 #define TRIAL_MINIMUM	(4)
126 
127 /*
128  * Sieving data (XXX - move to struct)
129  */
130 
131 /* sieve 2**16 */
132 static u_int32_t *TinySieve, tinybits;
133 
134 /* sieve 2**30 in 2**16 parts */
135 static u_int32_t *SmallSieve, smallbits, smallbase;
136 
137 /* sieve relative to the initial value */
138 static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
139 static u_int32_t largebits, largememory;	/* megabytes */
140 static BIGNUM *largebase;
141 
142 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
143 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
144     unsigned long);
145 
146 /*
147  * print moduli out in consistent form,
148  */
149 static int
150 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
151     u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
152 {
153 	struct tm *gtm;
154 	time_t time_now;
155 	int res;
156 
157 	time(&time_now);
158 	gtm = gmtime(&time_now);
159 
160 	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
161 	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
162 	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
163 	    otype, otests, otries, osize, ogenerator);
164 
165 	if (res < 0)
166 		return (-1);
167 
168 	if (BN_print_fp(ofile, omodulus) < 1)
169 		return (-1);
170 
171 	res = fprintf(ofile, "\n");
172 	fflush(ofile);
173 
174 	return (res > 0 ? 0 : -1);
175 }
176 
177 
178 /*
179  ** Sieve p's and q's with small factors
180  */
181 static void
182 sieve_large(u_int32_t s)
183 {
184 	u_int32_t r, u;
185 
186 	debug3("sieve_large %u", s);
187 	largetries++;
188 	/* r = largebase mod s */
189 	r = BN_mod_word(largebase, s);
190 	if (r == 0)
191 		u = 0; /* s divides into largebase exactly */
192 	else
193 		u = s - r; /* largebase+u is first entry divisible by s */
194 
195 	if (u < largebits * 2) {
196 		/*
197 		 * The sieve omits p's and q's divisible by 2, so ensure that
198 		 * largebase+u is odd. Then, step through the sieve in
199 		 * increments of 2*s
200 		 */
201 		if (u & 0x1)
202 			u += s; /* Make largebase+u odd, and u even */
203 
204 		/* Mark all multiples of 2*s */
205 		for (u /= 2; u < largebits; u += s)
206 			BIT_SET(LargeSieve, u);
207 	}
208 
209 	/* r = p mod s */
210 	r = (2 * r + 1) % s;
211 	if (r == 0)
212 		u = 0; /* s divides p exactly */
213 	else
214 		u = s - r; /* p+u is first entry divisible by s */
215 
216 	if (u < largebits * 4) {
217 		/*
218 		 * The sieve omits p's divisible by 4, so ensure that
219 		 * largebase+u is not. Then, step through the sieve in
220 		 * increments of 4*s
221 		 */
222 		while (u & 0x3) {
223 			if (SMALL_MAXIMUM - u < s)
224 				return;
225 			u += s;
226 		}
227 
228 		/* Mark all multiples of 4*s */
229 		for (u /= 4; u < largebits; u += s)
230 			BIT_SET(LargeSieve, u);
231 	}
232 }
233 
234 /*
235  * list candidates for Sophie-Germain primes (where q = (p-1)/2)
236  * to standard output.
237  * The list is checked against small known primes (less than 2**30).
238  */
239 int
240 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
241 {
242 	BIGNUM *q;
243 	u_int32_t j, r, s, t;
244 	u_int32_t smallwords = TINY_NUMBER >> 6;
245 	u_int32_t tinywords = TINY_NUMBER >> 6;
246 	time_t time_start, time_stop;
247 	u_int32_t i;
248 	int ret = 0;
249 
250 	largememory = memory;
251 
252 	if (memory != 0 &&
253 	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
254 		error("Invalid memory amount (min %ld, max %ld)",
255 		    LARGE_MINIMUM, LARGE_MAXIMUM);
256 		return (-1);
257 	}
258 
259 	/*
260 	 * Set power to the length in bits of the prime to be generated.
261 	 * This is changed to 1 less than the desired safe prime moduli p.
262 	 */
263 	if (power > TEST_MAXIMUM) {
264 		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
265 		return (-1);
266 	} else if (power < TEST_MINIMUM) {
267 		error("Too few bits: %u < %u", power, TEST_MINIMUM);
268 		return (-1);
269 	}
270 	power--; /* decrement before squaring */
271 
272 	/*
273 	 * The density of ordinary primes is on the order of 1/bits, so the
274 	 * density of safe primes should be about (1/bits)**2. Set test range
275 	 * to something well above bits**2 to be reasonably sure (but not
276 	 * guaranteed) of catching at least one safe prime.
277 	 */
278 	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
279 
280 	/*
281 	 * Need idea of how much memory is available. We don't have to use all
282 	 * of it.
283 	 */
284 	if (largememory > LARGE_MAXIMUM) {
285 		logit("Limited memory: %u MB; limit %lu MB",
286 		    largememory, LARGE_MAXIMUM);
287 		largememory = LARGE_MAXIMUM;
288 	}
289 
290 	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
291 		logit("Increased memory: %u MB; need %u bytes",
292 		    largememory, (largewords << SHIFT_BYTE));
293 		largewords = (largememory << SHIFT_MEGAWORD);
294 	} else if (largememory > 0) {
295 		logit("Decreased memory: %u MB; want %u bytes",
296 		    largememory, (largewords << SHIFT_BYTE));
297 		largewords = (largememory << SHIFT_MEGAWORD);
298 	}
299 
300 	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
301 	tinybits = tinywords << SHIFT_WORD;
302 
303 	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
304 	smallbits = smallwords << SHIFT_WORD;
305 
306 	/*
307 	 * dynamically determine available memory
308 	 */
309 	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
310 		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
311 
312 	largebits = largewords << SHIFT_WORD;
313 	largenumbers = largebits * 2;	/* even numbers excluded */
314 
315 	/* validation check: count the number of primes tried */
316 	largetries = 0;
317 	if ((q = BN_new()) == NULL)
318 		fatal("BN_new failed");
319 
320 	/*
321 	 * Generate random starting point for subprime search, or use
322 	 * specified parameter.
323 	 */
324 	if ((largebase = BN_new()) == NULL)
325 		fatal("BN_new failed");
326 	if (start == NULL) {
327 		if (BN_rand(largebase, power, 1, 1) == 0)
328 			fatal("BN_rand failed");
329 	} else {
330 		if (BN_copy(largebase, start) == NULL)
331 			fatal("BN_copy: failed");
332 	}
333 
334 	/* ensure odd */
335 	if (BN_set_bit(largebase, 0) == 0)
336 		fatal("BN_set_bit: failed");
337 
338 	time(&time_start);
339 
340 	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
341 	    largenumbers, power);
342 	debug2("start point: 0x%s", BN_bn2hex(largebase));
343 
344 	/*
345 	 * TinySieve
346 	 */
347 	for (i = 0; i < tinybits; i++) {
348 		if (BIT_TEST(TinySieve, i))
349 			continue; /* 2*i+3 is composite */
350 
351 		/* The next tiny prime */
352 		t = 2 * i + 3;
353 
354 		/* Mark all multiples of t */
355 		for (j = i + t; j < tinybits; j += t)
356 			BIT_SET(TinySieve, j);
357 
358 		sieve_large(t);
359 	}
360 
361 	/*
362 	 * Start the small block search at the next possible prime. To avoid
363 	 * fencepost errors, the last pass is skipped.
364 	 */
365 	for (smallbase = TINY_NUMBER + 3;
366 	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
367 	    smallbase += TINY_NUMBER) {
368 		for (i = 0; i < tinybits; i++) {
369 			if (BIT_TEST(TinySieve, i))
370 				continue; /* 2*i+3 is composite */
371 
372 			/* The next tiny prime */
373 			t = 2 * i + 3;
374 			r = smallbase % t;
375 
376 			if (r == 0) {
377 				s = 0; /* t divides into smallbase exactly */
378 			} else {
379 				/* smallbase+s is first entry divisible by t */
380 				s = t - r;
381 			}
382 
383 			/*
384 			 * The sieve omits even numbers, so ensure that
385 			 * smallbase+s is odd. Then, step through the sieve
386 			 * in increments of 2*t
387 			 */
388 			if (s & 1)
389 				s += t; /* Make smallbase+s odd, and s even */
390 
391 			/* Mark all multiples of 2*t */
392 			for (s /= 2; s < smallbits; s += t)
393 				BIT_SET(SmallSieve, s);
394 		}
395 
396 		/*
397 		 * SmallSieve
398 		 */
399 		for (i = 0; i < smallbits; i++) {
400 			if (BIT_TEST(SmallSieve, i))
401 				continue; /* 2*i+smallbase is composite */
402 
403 			/* The next small prime */
404 			sieve_large((2 * i) + smallbase);
405 		}
406 
407 		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
408 	}
409 
410 	time(&time_stop);
411 
412 	logit("%.24s Sieved with %u small primes in %ld seconds",
413 	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
414 
415 	for (j = r = 0; j < largebits; j++) {
416 		if (BIT_TEST(LargeSieve, j))
417 			continue; /* Definitely composite, skip */
418 
419 		debug2("test q = largebase+%u", 2 * j);
420 		if (BN_set_word(q, 2 * j) == 0)
421 			fatal("BN_set_word failed");
422 		if (BN_add(q, q, largebase) == 0)
423 			fatal("BN_add failed");
424 		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
425 		    MODULI_TESTS_SIEVE, largetries,
426 		    (power - 1) /* MSB */, (0), q) == -1) {
427 			ret = -1;
428 			break;
429 		}
430 
431 		r++; /* count q */
432 	}
433 
434 	time(&time_stop);
435 
436 	xfree(LargeSieve);
437 	xfree(SmallSieve);
438 	xfree(TinySieve);
439 
440 	logit("%.24s Found %u candidates", ctime(&time_stop), r);
441 
442 	return (ret);
443 }
444 
445 static void
446 write_checkpoint(char *cpfile, u_int32_t lineno)
447 {
448 	FILE *fp;
449 	char tmp[MAXPATHLEN];
450 	int r;
451 
452 	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
453 	if (r == -1 || r >= MAXPATHLEN) {
454 		logit("write_checkpoint: temp pathname too long");
455 		return;
456 	}
457 	if ((r = mkstemp(tmp)) == -1) {
458 		logit("mkstemp(%s): %s", tmp, strerror(errno));
459 		return;
460 	}
461 	if ((fp = fdopen(r, "w")) == NULL) {
462 		logit("write_checkpoint: fdopen: %s", strerror(errno));
463 		close(r);
464 		return;
465 	}
466 	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
467 	    && rename(tmp, cpfile) == 0)
468 		debug3("wrote checkpoint line %lu to '%s'",
469 		    (unsigned long)lineno, cpfile);
470 	else
471 		logit("failed to write to checkpoint file '%s': %s", cpfile,
472 		    strerror(errno));
473 }
474 
475 static unsigned long
476 read_checkpoint(char *cpfile)
477 {
478 	FILE *fp;
479 	unsigned long lineno = 0;
480 
481 	if ((fp = fopen(cpfile, "r")) == NULL)
482 		return 0;
483 	if (fscanf(fp, "%lu\n", &lineno) < 1)
484 		logit("Failed to load checkpoint from '%s'", cpfile);
485 	else
486 		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
487 	fclose(fp);
488 	return lineno;
489 }
490 
491 /*
492  * perform a Miller-Rabin primality test
493  * on the list of candidates
494  * (checking both q and p)
495  * The result is a list of so-call "safe" primes
496  */
497 int
498 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
499     char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
500 {
501 	BIGNUM *q, *p, *a;
502 	BN_CTX *ctx;
503 	char *cp, *lp;
504 	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
505 	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
506 	unsigned long last_processed = 0, end_lineno;
507 	time_t time_start, time_stop;
508 	int res;
509 
510 	if (trials < TRIAL_MINIMUM) {
511 		error("Minimum primality trials is %d", TRIAL_MINIMUM);
512 		return (-1);
513 	}
514 
515 	time(&time_start);
516 
517 	if ((p = BN_new()) == NULL)
518 		fatal("BN_new failed");
519 	if ((q = BN_new()) == NULL)
520 		fatal("BN_new failed");
521 	if ((ctx = BN_CTX_new()) == NULL)
522 		fatal("BN_CTX_new failed");
523 
524 	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
525 	    ctime(&time_start), trials, generator_wanted);
526 
527 	if (checkpoint_file != NULL)
528 		last_processed = read_checkpoint(checkpoint_file);
529 	if (start_lineno > last_processed)
530 		last_processed = start_lineno;
531 	if (num_lines == 0)
532 		end_lineno = ULONG_MAX;
533 	else
534 		end_lineno = last_processed + num_lines;
535 	debug2("process line %lu to line %lu", last_processed, end_lineno);
536 
537 	res = 0;
538 	lp = xmalloc(QLINESIZE + 1);
539 	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
540 		count_in++;
541 		if (checkpoint_file != NULL) {
542 			if (count_in <= last_processed) {
543 				debug3("skipping line %u, before checkpoint",
544 				    count_in);
545 				continue;
546 			}
547 			write_checkpoint(checkpoint_file, count_in);
548 		}
549 		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
550 			debug2("%10u: comment or short line", count_in);
551 			continue;
552 		}
553 
554 		/* XXX - fragile parser */
555 		/* time */
556 		cp = &lp[14];	/* (skip) */
557 
558 		/* type */
559 		in_type = strtoul(cp, &cp, 10);
560 
561 		/* tests */
562 		in_tests = strtoul(cp, &cp, 10);
563 
564 		if (in_tests & MODULI_TESTS_COMPOSITE) {
565 			debug2("%10u: known composite", count_in);
566 			continue;
567 		}
568 
569 		/* tries */
570 		in_tries = strtoul(cp, &cp, 10);
571 
572 		/* size (most significant bit) */
573 		in_size = strtoul(cp, &cp, 10);
574 
575 		/* generator (hex) */
576 		generator_known = strtoul(cp, &cp, 16);
577 
578 		/* Skip white space */
579 		cp += strspn(cp, " ");
580 
581 		/* modulus (hex) */
582 		switch (in_type) {
583 		case MODULI_TYPE_SOPHIE_GERMAIN:
584 			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
585 			a = q;
586 			if (BN_hex2bn(&a, cp) == 0)
587 				fatal("BN_hex2bn failed");
588 			/* p = 2*q + 1 */
589 			if (BN_lshift(p, q, 1) == 0)
590 				fatal("BN_lshift failed");
591 			if (BN_add_word(p, 1) == 0)
592 				fatal("BN_add_word failed");
593 			in_size += 1;
594 			generator_known = 0;
595 			break;
596 		case MODULI_TYPE_UNSTRUCTURED:
597 		case MODULI_TYPE_SAFE:
598 		case MODULI_TYPE_SCHNORR:
599 		case MODULI_TYPE_STRONG:
600 		case MODULI_TYPE_UNKNOWN:
601 			debug2("%10u: (%u)", count_in, in_type);
602 			a = p;
603 			if (BN_hex2bn(&a, cp) == 0)
604 				fatal("BN_hex2bn failed");
605 			/* q = (p-1) / 2 */
606 			if (BN_rshift(q, p, 1) == 0)
607 				fatal("BN_rshift failed");
608 			break;
609 		default:
610 			debug2("Unknown prime type");
611 			break;
612 		}
613 
614 		/*
615 		 * due to earlier inconsistencies in interpretation, check
616 		 * the proposed bit size.
617 		 */
618 		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
619 			debug2("%10u: bit size %u mismatch", count_in, in_size);
620 			continue;
621 		}
622 		if (in_size < QSIZE_MINIMUM) {
623 			debug2("%10u: bit size %u too short", count_in, in_size);
624 			continue;
625 		}
626 
627 		if (in_tests & MODULI_TESTS_MILLER_RABIN)
628 			in_tries += trials;
629 		else
630 			in_tries = trials;
631 
632 		/*
633 		 * guess unknown generator
634 		 */
635 		if (generator_known == 0) {
636 			if (BN_mod_word(p, 24) == 11)
637 				generator_known = 2;
638 			else if (BN_mod_word(p, 12) == 5)
639 				generator_known = 3;
640 			else {
641 				u_int32_t r = BN_mod_word(p, 10);
642 
643 				if (r == 3 || r == 7)
644 					generator_known = 5;
645 			}
646 		}
647 		/*
648 		 * skip tests when desired generator doesn't match
649 		 */
650 		if (generator_wanted > 0 &&
651 		    generator_wanted != generator_known) {
652 			debug2("%10u: generator %d != %d",
653 			    count_in, generator_known, generator_wanted);
654 			continue;
655 		}
656 
657 		/*
658 		 * Primes with no known generator are useless for DH, so
659 		 * skip those.
660 		 */
661 		if (generator_known == 0) {
662 			debug2("%10u: no known generator", count_in);
663 			continue;
664 		}
665 
666 		count_possible++;
667 
668 		/*
669 		 * The (1/4)^N performance bound on Miller-Rabin is
670 		 * extremely pessimistic, so don't spend a lot of time
671 		 * really verifying that q is prime until after we know
672 		 * that p is also prime. A single pass will weed out the
673 		 * vast majority of composite q's.
674 		 */
675 		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
676 			debug("%10u: q failed first possible prime test",
677 			    count_in);
678 			continue;
679 		}
680 
681 		/*
682 		 * q is possibly prime, so go ahead and really make sure
683 		 * that p is prime. If it is, then we can go back and do
684 		 * the same for q. If p is composite, chances are that
685 		 * will show up on the first Rabin-Miller iteration so it
686 		 * doesn't hurt to specify a high iteration count.
687 		 */
688 		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
689 			debug("%10u: p is not prime", count_in);
690 			continue;
691 		}
692 		debug("%10u: p is almost certainly prime", count_in);
693 
694 		/* recheck q more rigorously */
695 		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
696 			debug("%10u: q is not prime", count_in);
697 			continue;
698 		}
699 		debug("%10u: q is almost certainly prime", count_in);
700 
701 		if (qfileout(out, MODULI_TYPE_SAFE,
702 		    in_tests | MODULI_TESTS_MILLER_RABIN,
703 		    in_tries, in_size, generator_known, p)) {
704 			res = -1;
705 			break;
706 		}
707 
708 		count_out++;
709 	}
710 
711 	time(&time_stop);
712 	xfree(lp);
713 	BN_free(p);
714 	BN_free(q);
715 	BN_CTX_free(ctx);
716 
717 	if (checkpoint_file != NULL)
718 		unlink(checkpoint_file);
719 
720 	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
721 	    ctime(&time_stop), count_out, count_possible,
722 	    (long) (time_stop - time_start));
723 
724 	return (res);
725 }
726