moduli.c revision 262566
1/* $OpenBSD: moduli.c,v 1.28 2013/10/24 00:49:49 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#include "misc.h"
60
61#include "openbsd-compat/openssl-compat.h"
62
63/*
64 * File output defines
65 */
66
67/* need line long enough for largest moduli plus headers */
68#define QLINESIZE		(100+8192)
69
70/*
71 * Size: decimal.
72 * Specifies the number of the most significant bit (0 to M).
73 * WARNING: internally, usually 1 to N.
74 */
75#define QSIZE_MINIMUM		(511)
76
77/*
78 * Prime sieving defines
79 */
80
81/* Constant: assuming 8 bit bytes and 32 bit words */
82#define SHIFT_BIT	(3)
83#define SHIFT_BYTE	(2)
84#define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
85#define SHIFT_MEGABYTE	(20)
86#define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
87
88/*
89 * Using virtual memory can cause thrashing.  This should be the largest
90 * number that is supported without a large amount of disk activity --
91 * that would increase the run time from hours to days or weeks!
92 */
93#define LARGE_MINIMUM	(8UL)	/* megabytes */
94
95/*
96 * Do not increase this number beyond the unsigned integer bit size.
97 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
98 */
99#define LARGE_MAXIMUM	(127UL)	/* megabytes */
100
101/*
102 * Constant: when used with 32-bit integers, the largest sieve prime
103 * has to be less than 2**32.
104 */
105#define SMALL_MAXIMUM	(0xffffffffUL)
106
107/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
108#define TINY_NUMBER	(1UL<<16)
109
110/* Ensure enough bit space for testing 2*q. */
111#define TEST_MAXIMUM	(1UL<<16)
112#define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
113/* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
114#define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
115
116/* bit operations on 32-bit words */
117#define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
118#define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
119#define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
120
121/*
122 * Prime testing defines
123 */
124
125/* Minimum number of primality tests to perform */
126#define TRIAL_MINIMUM	(4)
127
128/*
129 * Sieving data (XXX - move to struct)
130 */
131
132/* sieve 2**16 */
133static u_int32_t *TinySieve, tinybits;
134
135/* sieve 2**30 in 2**16 parts */
136static u_int32_t *SmallSieve, smallbits, smallbase;
137
138/* sieve relative to the initial value */
139static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
140static u_int32_t largebits, largememory;	/* megabytes */
141static BIGNUM *largebase;
142
143int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
144int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
145    unsigned long);
146
147/*
148 * print moduli out in consistent form,
149 */
150static int
151qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
152    u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
153{
154	struct tm *gtm;
155	time_t time_now;
156	int res;
157
158	time(&time_now);
159	gtm = gmtime(&time_now);
160
161	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
162	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
163	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
164	    otype, otests, otries, osize, ogenerator);
165
166	if (res < 0)
167		return (-1);
168
169	if (BN_print_fp(ofile, omodulus) < 1)
170		return (-1);
171
172	res = fprintf(ofile, "\n");
173	fflush(ofile);
174
175	return (res > 0 ? 0 : -1);
176}
177
178
179/*
180 ** Sieve p's and q's with small factors
181 */
182static void
183sieve_large(u_int32_t s)
184{
185	u_int32_t r, u;
186
187	debug3("sieve_large %u", s);
188	largetries++;
189	/* r = largebase mod s */
190	r = BN_mod_word(largebase, s);
191	if (r == 0)
192		u = 0; /* s divides into largebase exactly */
193	else
194		u = s - r; /* largebase+u is first entry divisible by s */
195
196	if (u < largebits * 2) {
197		/*
198		 * The sieve omits p's and q's divisible by 2, so ensure that
199		 * largebase+u is odd. Then, step through the sieve in
200		 * increments of 2*s
201		 */
202		if (u & 0x1)
203			u += s; /* Make largebase+u odd, and u even */
204
205		/* Mark all multiples of 2*s */
206		for (u /= 2; u < largebits; u += s)
207			BIT_SET(LargeSieve, u);
208	}
209
210	/* r = p mod s */
211	r = (2 * r + 1) % s;
212	if (r == 0)
213		u = 0; /* s divides p exactly */
214	else
215		u = s - r; /* p+u is first entry divisible by s */
216
217	if (u < largebits * 4) {
218		/*
219		 * The sieve omits p's divisible by 4, so ensure that
220		 * largebase+u is not. Then, step through the sieve in
221		 * increments of 4*s
222		 */
223		while (u & 0x3) {
224			if (SMALL_MAXIMUM - u < s)
225				return;
226			u += s;
227		}
228
229		/* Mark all multiples of 4*s */
230		for (u /= 4; u < largebits; u += s)
231			BIT_SET(LargeSieve, u);
232	}
233}
234
235/*
236 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
237 * to standard output.
238 * The list is checked against small known primes (less than 2**30).
239 */
240int
241gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
242{
243	BIGNUM *q;
244	u_int32_t j, r, s, t;
245	u_int32_t smallwords = TINY_NUMBER >> 6;
246	u_int32_t tinywords = TINY_NUMBER >> 6;
247	time_t time_start, time_stop;
248	u_int32_t i;
249	int ret = 0;
250
251	largememory = memory;
252
253	if (memory != 0 &&
254	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
255		error("Invalid memory amount (min %ld, max %ld)",
256		    LARGE_MINIMUM, LARGE_MAXIMUM);
257		return (-1);
258	}
259
260	/*
261	 * Set power to the length in bits of the prime to be generated.
262	 * This is changed to 1 less than the desired safe prime moduli p.
263	 */
264	if (power > TEST_MAXIMUM) {
265		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
266		return (-1);
267	} else if (power < TEST_MINIMUM) {
268		error("Too few bits: %u < %u", power, TEST_MINIMUM);
269		return (-1);
270	}
271	power--; /* decrement before squaring */
272
273	/*
274	 * The density of ordinary primes is on the order of 1/bits, so the
275	 * density of safe primes should be about (1/bits)**2. Set test range
276	 * to something well above bits**2 to be reasonably sure (but not
277	 * guaranteed) of catching at least one safe prime.
278	 */
279	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
280
281	/*
282	 * Need idea of how much memory is available. We don't have to use all
283	 * of it.
284	 */
285	if (largememory > LARGE_MAXIMUM) {
286		logit("Limited memory: %u MB; limit %lu MB",
287		    largememory, LARGE_MAXIMUM);
288		largememory = LARGE_MAXIMUM;
289	}
290
291	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
292		logit("Increased memory: %u MB; need %u bytes",
293		    largememory, (largewords << SHIFT_BYTE));
294		largewords = (largememory << SHIFT_MEGAWORD);
295	} else if (largememory > 0) {
296		logit("Decreased memory: %u MB; want %u bytes",
297		    largememory, (largewords << SHIFT_BYTE));
298		largewords = (largememory << SHIFT_MEGAWORD);
299	}
300
301	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
302	tinybits = tinywords << SHIFT_WORD;
303
304	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
305	smallbits = smallwords << SHIFT_WORD;
306
307	/*
308	 * dynamically determine available memory
309	 */
310	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
311		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
312
313	largebits = largewords << SHIFT_WORD;
314	largenumbers = largebits * 2;	/* even numbers excluded */
315
316	/* validation check: count the number of primes tried */
317	largetries = 0;
318	if ((q = BN_new()) == NULL)
319		fatal("BN_new failed");
320
321	/*
322	 * Generate random starting point for subprime search, or use
323	 * specified parameter.
324	 */
325	if ((largebase = BN_new()) == NULL)
326		fatal("BN_new failed");
327	if (start == NULL) {
328		if (BN_rand(largebase, power, 1, 1) == 0)
329			fatal("BN_rand failed");
330	} else {
331		if (BN_copy(largebase, start) == NULL)
332			fatal("BN_copy: failed");
333	}
334
335	/* ensure odd */
336	if (BN_set_bit(largebase, 0) == 0)
337		fatal("BN_set_bit: failed");
338
339	time(&time_start);
340
341	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
342	    largenumbers, power);
343	debug2("start point: 0x%s", BN_bn2hex(largebase));
344
345	/*
346	 * TinySieve
347	 */
348	for (i = 0; i < tinybits; i++) {
349		if (BIT_TEST(TinySieve, i))
350			continue; /* 2*i+3 is composite */
351
352		/* The next tiny prime */
353		t = 2 * i + 3;
354
355		/* Mark all multiples of t */
356		for (j = i + t; j < tinybits; j += t)
357			BIT_SET(TinySieve, j);
358
359		sieve_large(t);
360	}
361
362	/*
363	 * Start the small block search at the next possible prime. To avoid
364	 * fencepost errors, the last pass is skipped.
365	 */
366	for (smallbase = TINY_NUMBER + 3;
367	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
368	    smallbase += TINY_NUMBER) {
369		for (i = 0; i < tinybits; i++) {
370			if (BIT_TEST(TinySieve, i))
371				continue; /* 2*i+3 is composite */
372
373			/* The next tiny prime */
374			t = 2 * i + 3;
375			r = smallbase % t;
376
377			if (r == 0) {
378				s = 0; /* t divides into smallbase exactly */
379			} else {
380				/* smallbase+s is first entry divisible by t */
381				s = t - r;
382			}
383
384			/*
385			 * The sieve omits even numbers, so ensure that
386			 * smallbase+s is odd. Then, step through the sieve
387			 * in increments of 2*t
388			 */
389			if (s & 1)
390				s += t; /* Make smallbase+s odd, and s even */
391
392			/* Mark all multiples of 2*t */
393			for (s /= 2; s < smallbits; s += t)
394				BIT_SET(SmallSieve, s);
395		}
396
397		/*
398		 * SmallSieve
399		 */
400		for (i = 0; i < smallbits; i++) {
401			if (BIT_TEST(SmallSieve, i))
402				continue; /* 2*i+smallbase is composite */
403
404			/* The next small prime */
405			sieve_large((2 * i) + smallbase);
406		}
407
408		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
409	}
410
411	time(&time_stop);
412
413	logit("%.24s Sieved with %u small primes in %ld seconds",
414	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
415
416	for (j = r = 0; j < largebits; j++) {
417		if (BIT_TEST(LargeSieve, j))
418			continue; /* Definitely composite, skip */
419
420		debug2("test q = largebase+%u", 2 * j);
421		if (BN_set_word(q, 2 * j) == 0)
422			fatal("BN_set_word failed");
423		if (BN_add(q, q, largebase) == 0)
424			fatal("BN_add failed");
425		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
426		    MODULI_TESTS_SIEVE, largetries,
427		    (power - 1) /* MSB */, (0), q) == -1) {
428			ret = -1;
429			break;
430		}
431
432		r++; /* count q */
433	}
434
435	time(&time_stop);
436
437	free(LargeSieve);
438	free(SmallSieve);
439	free(TinySieve);
440
441	logit("%.24s Found %u candidates", ctime(&time_stop), r);
442
443	return (ret);
444}
445
446static void
447write_checkpoint(char *cpfile, u_int32_t lineno)
448{
449	FILE *fp;
450	char tmp[MAXPATHLEN];
451	int r;
452
453	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
454	if (r == -1 || r >= MAXPATHLEN) {
455		logit("write_checkpoint: temp pathname too long");
456		return;
457	}
458	if ((r = mkstemp(tmp)) == -1) {
459		logit("mkstemp(%s): %s", tmp, strerror(errno));
460		return;
461	}
462	if ((fp = fdopen(r, "w")) == NULL) {
463		logit("write_checkpoint: fdopen: %s", strerror(errno));
464		close(r);
465		return;
466	}
467	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
468	    && rename(tmp, cpfile) == 0)
469		debug3("wrote checkpoint line %lu to '%s'",
470		    (unsigned long)lineno, cpfile);
471	else
472		logit("failed to write to checkpoint file '%s': %s", cpfile,
473		    strerror(errno));
474}
475
476static unsigned long
477read_checkpoint(char *cpfile)
478{
479	FILE *fp;
480	unsigned long lineno = 0;
481
482	if ((fp = fopen(cpfile, "r")) == NULL)
483		return 0;
484	if (fscanf(fp, "%lu\n", &lineno) < 1)
485		logit("Failed to load checkpoint from '%s'", cpfile);
486	else
487		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
488	fclose(fp);
489	return lineno;
490}
491
492static unsigned long
493count_lines(FILE *f)
494{
495	unsigned long count = 0;
496	char lp[QLINESIZE + 1];
497
498	if (fseek(f, 0, SEEK_SET) != 0) {
499		debug("input file is not seekable");
500		return ULONG_MAX;
501	}
502	while (fgets(lp, QLINESIZE + 1, f) != NULL)
503		count++;
504	rewind(f);
505	debug("input file has %lu lines", count);
506	return count;
507}
508
509static char *
510fmt_time(time_t seconds)
511{
512	int day, hr, min;
513	static char buf[128];
514
515	min = (seconds / 60) % 60;
516	hr = (seconds / 60 / 60) % 24;
517	day = seconds / 60 / 60 / 24;
518	if (day > 0)
519		snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min);
520	else
521		snprintf(buf, sizeof buf, "%d:%02d", hr, min);
522	return buf;
523}
524
525static void
526print_progress(unsigned long start_lineno, unsigned long current_lineno,
527    unsigned long end_lineno)
528{
529	static time_t time_start, time_prev;
530	time_t time_now, elapsed;
531	unsigned long num_to_process, processed, remaining, percent, eta;
532	double time_per_line;
533	char *eta_str;
534
535	time_now = monotime();
536	if (time_start == 0) {
537		time_start = time_prev = time_now;
538		return;
539	}
540	/* print progress after 1m then once per 5m */
541	if (time_now - time_prev < 5 * 60)
542		return;
543	time_prev = time_now;
544	elapsed = time_now - time_start;
545	processed = current_lineno - start_lineno;
546	remaining = end_lineno - current_lineno;
547	num_to_process = end_lineno - start_lineno;
548	time_per_line = (double)elapsed / processed;
549	/* if we don't know how many we're processing just report count+time */
550	time(&time_now);
551	if (end_lineno == ULONG_MAX) {
552		logit("%.24s processed %lu in %s", ctime(&time_now),
553		    processed, fmt_time(elapsed));
554		return;
555	}
556	percent = 100 * processed / num_to_process;
557	eta = time_per_line * remaining;
558	eta_str = xstrdup(fmt_time(eta));
559	logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s",
560	    ctime(&time_now), processed, num_to_process, percent,
561	    fmt_time(elapsed), eta_str);
562	free(eta_str);
563}
564
565/*
566 * perform a Miller-Rabin primality test
567 * on the list of candidates
568 * (checking both q and p)
569 * The result is a list of so-call "safe" primes
570 */
571int
572prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
573    char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
574{
575	BIGNUM *q, *p, *a;
576	BN_CTX *ctx;
577	char *cp, *lp;
578	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
579	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
580	unsigned long last_processed = 0, end_lineno;
581	time_t time_start, time_stop;
582	int res;
583
584	if (trials < TRIAL_MINIMUM) {
585		error("Minimum primality trials is %d", TRIAL_MINIMUM);
586		return (-1);
587	}
588
589	if (num_lines == 0)
590		end_lineno = count_lines(in);
591	else
592		end_lineno = start_lineno + num_lines;
593
594	time(&time_start);
595
596	if ((p = BN_new()) == NULL)
597		fatal("BN_new failed");
598	if ((q = BN_new()) == NULL)
599		fatal("BN_new failed");
600	if ((ctx = BN_CTX_new()) == NULL)
601		fatal("BN_CTX_new failed");
602
603	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
604	    ctime(&time_start), trials, generator_wanted);
605
606	if (checkpoint_file != NULL)
607		last_processed = read_checkpoint(checkpoint_file);
608	last_processed = start_lineno = MAX(last_processed, start_lineno);
609	if (end_lineno == ULONG_MAX)
610		debug("process from line %lu from pipe", last_processed);
611	else
612		debug("process from line %lu to line %lu", last_processed,
613		    end_lineno);
614
615	res = 0;
616	lp = xmalloc(QLINESIZE + 1);
617	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
618		count_in++;
619		if (count_in <= last_processed) {
620			debug3("skipping line %u, before checkpoint or "
621			    "specified start line", count_in);
622			continue;
623		}
624		if (checkpoint_file != NULL)
625			write_checkpoint(checkpoint_file, count_in);
626		print_progress(start_lineno, count_in, end_lineno);
627		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
628			debug2("%10u: comment or short line", count_in);
629			continue;
630		}
631
632		/* XXX - fragile parser */
633		/* time */
634		cp = &lp[14];	/* (skip) */
635
636		/* type */
637		in_type = strtoul(cp, &cp, 10);
638
639		/* tests */
640		in_tests = strtoul(cp, &cp, 10);
641
642		if (in_tests & MODULI_TESTS_COMPOSITE) {
643			debug2("%10u: known composite", count_in);
644			continue;
645		}
646
647		/* tries */
648		in_tries = strtoul(cp, &cp, 10);
649
650		/* size (most significant bit) */
651		in_size = strtoul(cp, &cp, 10);
652
653		/* generator (hex) */
654		generator_known = strtoul(cp, &cp, 16);
655
656		/* Skip white space */
657		cp += strspn(cp, " ");
658
659		/* modulus (hex) */
660		switch (in_type) {
661		case MODULI_TYPE_SOPHIE_GERMAIN:
662			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
663			a = q;
664			if (BN_hex2bn(&a, cp) == 0)
665				fatal("BN_hex2bn failed");
666			/* p = 2*q + 1 */
667			if (BN_lshift(p, q, 1) == 0)
668				fatal("BN_lshift failed");
669			if (BN_add_word(p, 1) == 0)
670				fatal("BN_add_word failed");
671			in_size += 1;
672			generator_known = 0;
673			break;
674		case MODULI_TYPE_UNSTRUCTURED:
675		case MODULI_TYPE_SAFE:
676		case MODULI_TYPE_SCHNORR:
677		case MODULI_TYPE_STRONG:
678		case MODULI_TYPE_UNKNOWN:
679			debug2("%10u: (%u)", count_in, in_type);
680			a = p;
681			if (BN_hex2bn(&a, cp) == 0)
682				fatal("BN_hex2bn failed");
683			/* q = (p-1) / 2 */
684			if (BN_rshift(q, p, 1) == 0)
685				fatal("BN_rshift failed");
686			break;
687		default:
688			debug2("Unknown prime type");
689			break;
690		}
691
692		/*
693		 * due to earlier inconsistencies in interpretation, check
694		 * the proposed bit size.
695		 */
696		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
697			debug2("%10u: bit size %u mismatch", count_in, in_size);
698			continue;
699		}
700		if (in_size < QSIZE_MINIMUM) {
701			debug2("%10u: bit size %u too short", count_in, in_size);
702			continue;
703		}
704
705		if (in_tests & MODULI_TESTS_MILLER_RABIN)
706			in_tries += trials;
707		else
708			in_tries = trials;
709
710		/*
711		 * guess unknown generator
712		 */
713		if (generator_known == 0) {
714			if (BN_mod_word(p, 24) == 11)
715				generator_known = 2;
716			else if (BN_mod_word(p, 12) == 5)
717				generator_known = 3;
718			else {
719				u_int32_t r = BN_mod_word(p, 10);
720
721				if (r == 3 || r == 7)
722					generator_known = 5;
723			}
724		}
725		/*
726		 * skip tests when desired generator doesn't match
727		 */
728		if (generator_wanted > 0 &&
729		    generator_wanted != generator_known) {
730			debug2("%10u: generator %d != %d",
731			    count_in, generator_known, generator_wanted);
732			continue;
733		}
734
735		/*
736		 * Primes with no known generator are useless for DH, so
737		 * skip those.
738		 */
739		if (generator_known == 0) {
740			debug2("%10u: no known generator", count_in);
741			continue;
742		}
743
744		count_possible++;
745
746		/*
747		 * The (1/4)^N performance bound on Miller-Rabin is
748		 * extremely pessimistic, so don't spend a lot of time
749		 * really verifying that q is prime until after we know
750		 * that p is also prime. A single pass will weed out the
751		 * vast majority of composite q's.
752		 */
753		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
754			debug("%10u: q failed first possible prime test",
755			    count_in);
756			continue;
757		}
758
759		/*
760		 * q is possibly prime, so go ahead and really make sure
761		 * that p is prime. If it is, then we can go back and do
762		 * the same for q. If p is composite, chances are that
763		 * will show up on the first Rabin-Miller iteration so it
764		 * doesn't hurt to specify a high iteration count.
765		 */
766		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
767			debug("%10u: p is not prime", count_in);
768			continue;
769		}
770		debug("%10u: p is almost certainly prime", count_in);
771
772		/* recheck q more rigorously */
773		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
774			debug("%10u: q is not prime", count_in);
775			continue;
776		}
777		debug("%10u: q is almost certainly prime", count_in);
778
779		if (qfileout(out, MODULI_TYPE_SAFE,
780		    in_tests | MODULI_TESTS_MILLER_RABIN,
781		    in_tries, in_size, generator_known, p)) {
782			res = -1;
783			break;
784		}
785
786		count_out++;
787	}
788
789	time(&time_stop);
790	free(lp);
791	BN_free(p);
792	BN_free(q);
793	BN_CTX_free(ctx);
794
795	if (checkpoint_file != NULL)
796		unlink(checkpoint_file);
797
798	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
799	    ctime(&time_stop), count_out, count_possible,
800	    (long) (time_stop - time_start));
801
802	return (res);
803}
804