xref: /freebsd/crypto/openssh/moduli.c (revision 243e928310d073338c5ec089f0dce238a80b9866)
1 /* $OpenBSD: moduli.c,v 1.30 2015/01/20 23:14:00 deraadt 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/param.h>	/* MAX */
45 #include <sys/types.h>
46 
47 #include <openssl/bn.h>
48 #include <openssl/dh.h>
49 
50 #include <errno.h>
51 #include <stdio.h>
52 #include <stdlib.h>
53 #include <string.h>
54 #include <stdarg.h>
55 #include <time.h>
56 #include <unistd.h>
57 #include <limits.h>
58 
59 #include "xmalloc.h"
60 #include "dh.h"
61 #include "log.h"
62 #include "misc.h"
63 
64 #include "openbsd-compat/openssl-compat.h"
65 
66 /*
67  * File output defines
68  */
69 
70 /* need line long enough for largest moduli plus headers */
71 #define QLINESIZE		(100+8192)
72 
73 /*
74  * Size: decimal.
75  * Specifies the number of the most significant bit (0 to M).
76  * WARNING: internally, usually 1 to N.
77  */
78 #define QSIZE_MINIMUM		(511)
79 
80 /*
81  * Prime sieving defines
82  */
83 
84 /* Constant: assuming 8 bit bytes and 32 bit words */
85 #define SHIFT_BIT	(3)
86 #define SHIFT_BYTE	(2)
87 #define SHIFT_WORD	(SHIFT_BIT+SHIFT_BYTE)
88 #define SHIFT_MEGABYTE	(20)
89 #define SHIFT_MEGAWORD	(SHIFT_MEGABYTE-SHIFT_BYTE)
90 
91 /*
92  * Using virtual memory can cause thrashing.  This should be the largest
93  * number that is supported without a large amount of disk activity --
94  * that would increase the run time from hours to days or weeks!
95  */
96 #define LARGE_MINIMUM	(8UL)	/* megabytes */
97 
98 /*
99  * Do not increase this number beyond the unsigned integer bit size.
100  * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits).
101  */
102 #define LARGE_MAXIMUM	(127UL)	/* megabytes */
103 
104 /*
105  * Constant: when used with 32-bit integers, the largest sieve prime
106  * has to be less than 2**32.
107  */
108 #define SMALL_MAXIMUM	(0xffffffffUL)
109 
110 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
111 #define TINY_NUMBER	(1UL<<16)
112 
113 /* Ensure enough bit space for testing 2*q. */
114 #define TEST_MAXIMUM	(1UL<<16)
115 #define TEST_MINIMUM	(QSIZE_MINIMUM + 1)
116 /* real TEST_MINIMUM	(1UL << (SHIFT_WORD - TEST_POWER)) */
117 #define TEST_POWER	(3)	/* 2**n, n < SHIFT_WORD */
118 
119 /* bit operations on 32-bit words */
120 #define BIT_CLEAR(a,n)	((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31)))
121 #define BIT_SET(a,n)	((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31)))
122 #define BIT_TEST(a,n)	((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31)))
123 
124 /*
125  * Prime testing defines
126  */
127 
128 /* Minimum number of primality tests to perform */
129 #define TRIAL_MINIMUM	(4)
130 
131 /*
132  * Sieving data (XXX - move to struct)
133  */
134 
135 /* sieve 2**16 */
136 static u_int32_t *TinySieve, tinybits;
137 
138 /* sieve 2**30 in 2**16 parts */
139 static u_int32_t *SmallSieve, smallbits, smallbase;
140 
141 /* sieve relative to the initial value */
142 static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
143 static u_int32_t largebits, largememory;	/* megabytes */
144 static BIGNUM *largebase;
145 
146 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
147 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
148     unsigned long);
149 
150 /*
151  * print moduli out in consistent form,
152  */
153 static int
154 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries,
155     u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus)
156 {
157 	struct tm *gtm;
158 	time_t time_now;
159 	int res;
160 
161 	time(&time_now);
162 	gtm = gmtime(&time_now);
163 
164 	res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ",
165 	    gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday,
166 	    gtm->tm_hour, gtm->tm_min, gtm->tm_sec,
167 	    otype, otests, otries, osize, ogenerator);
168 
169 	if (res < 0)
170 		return (-1);
171 
172 	if (BN_print_fp(ofile, omodulus) < 1)
173 		return (-1);
174 
175 	res = fprintf(ofile, "\n");
176 	fflush(ofile);
177 
178 	return (res > 0 ? 0 : -1);
179 }
180 
181 
182 /*
183  ** Sieve p's and q's with small factors
184  */
185 static void
186 sieve_large(u_int32_t s)
187 {
188 	u_int32_t r, u;
189 
190 	debug3("sieve_large %u", s);
191 	largetries++;
192 	/* r = largebase mod s */
193 	r = BN_mod_word(largebase, s);
194 	if (r == 0)
195 		u = 0; /* s divides into largebase exactly */
196 	else
197 		u = s - r; /* largebase+u is first entry divisible by s */
198 
199 	if (u < largebits * 2) {
200 		/*
201 		 * The sieve omits p's and q's divisible by 2, so ensure that
202 		 * largebase+u is odd. Then, step through the sieve in
203 		 * increments of 2*s
204 		 */
205 		if (u & 0x1)
206 			u += s; /* Make largebase+u odd, and u even */
207 
208 		/* Mark all multiples of 2*s */
209 		for (u /= 2; u < largebits; u += s)
210 			BIT_SET(LargeSieve, u);
211 	}
212 
213 	/* r = p mod s */
214 	r = (2 * r + 1) % s;
215 	if (r == 0)
216 		u = 0; /* s divides p exactly */
217 	else
218 		u = s - r; /* p+u is first entry divisible by s */
219 
220 	if (u < largebits * 4) {
221 		/*
222 		 * The sieve omits p's divisible by 4, so ensure that
223 		 * largebase+u is not. Then, step through the sieve in
224 		 * increments of 4*s
225 		 */
226 		while (u & 0x3) {
227 			if (SMALL_MAXIMUM - u < s)
228 				return;
229 			u += s;
230 		}
231 
232 		/* Mark all multiples of 4*s */
233 		for (u /= 4; u < largebits; u += s)
234 			BIT_SET(LargeSieve, u);
235 	}
236 }
237 
238 /*
239  * list candidates for Sophie-Germain primes (where q = (p-1)/2)
240  * to standard output.
241  * The list is checked against small known primes (less than 2**30).
242  */
243 int
244 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
245 {
246 	BIGNUM *q;
247 	u_int32_t j, r, s, t;
248 	u_int32_t smallwords = TINY_NUMBER >> 6;
249 	u_int32_t tinywords = TINY_NUMBER >> 6;
250 	time_t time_start, time_stop;
251 	u_int32_t i;
252 	int ret = 0;
253 
254 	largememory = memory;
255 
256 	if (memory != 0 &&
257 	    (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
258 		error("Invalid memory amount (min %ld, max %ld)",
259 		    LARGE_MINIMUM, LARGE_MAXIMUM);
260 		return (-1);
261 	}
262 
263 	/*
264 	 * Set power to the length in bits of the prime to be generated.
265 	 * This is changed to 1 less than the desired safe prime moduli p.
266 	 */
267 	if (power > TEST_MAXIMUM) {
268 		error("Too many bits: %u > %lu", power, TEST_MAXIMUM);
269 		return (-1);
270 	} else if (power < TEST_MINIMUM) {
271 		error("Too few bits: %u < %u", power, TEST_MINIMUM);
272 		return (-1);
273 	}
274 	power--; /* decrement before squaring */
275 
276 	/*
277 	 * The density of ordinary primes is on the order of 1/bits, so the
278 	 * density of safe primes should be about (1/bits)**2. Set test range
279 	 * to something well above bits**2 to be reasonably sure (but not
280 	 * guaranteed) of catching at least one safe prime.
281 	 */
282 	largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
283 
284 	/*
285 	 * Need idea of how much memory is available. We don't have to use all
286 	 * of it.
287 	 */
288 	if (largememory > LARGE_MAXIMUM) {
289 		logit("Limited memory: %u MB; limit %lu MB",
290 		    largememory, LARGE_MAXIMUM);
291 		largememory = LARGE_MAXIMUM;
292 	}
293 
294 	if (largewords <= (largememory << SHIFT_MEGAWORD)) {
295 		logit("Increased memory: %u MB; need %u bytes",
296 		    largememory, (largewords << SHIFT_BYTE));
297 		largewords = (largememory << SHIFT_MEGAWORD);
298 	} else if (largememory > 0) {
299 		logit("Decreased memory: %u MB; want %u bytes",
300 		    largememory, (largewords << SHIFT_BYTE));
301 		largewords = (largememory << SHIFT_MEGAWORD);
302 	}
303 
304 	TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
305 	tinybits = tinywords << SHIFT_WORD;
306 
307 	SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
308 	smallbits = smallwords << SHIFT_WORD;
309 
310 	/*
311 	 * dynamically determine available memory
312 	 */
313 	while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL)
314 		largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */
315 
316 	largebits = largewords << SHIFT_WORD;
317 	largenumbers = largebits * 2;	/* even numbers excluded */
318 
319 	/* validation check: count the number of primes tried */
320 	largetries = 0;
321 	if ((q = BN_new()) == NULL)
322 		fatal("BN_new failed");
323 
324 	/*
325 	 * Generate random starting point for subprime search, or use
326 	 * specified parameter.
327 	 */
328 	if ((largebase = BN_new()) == NULL)
329 		fatal("BN_new failed");
330 	if (start == NULL) {
331 		if (BN_rand(largebase, power, 1, 1) == 0)
332 			fatal("BN_rand failed");
333 	} else {
334 		if (BN_copy(largebase, start) == NULL)
335 			fatal("BN_copy: failed");
336 	}
337 
338 	/* ensure odd */
339 	if (BN_set_bit(largebase, 0) == 0)
340 		fatal("BN_set_bit: failed");
341 
342 	time(&time_start);
343 
344 	logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
345 	    largenumbers, power);
346 	debug2("start point: 0x%s", BN_bn2hex(largebase));
347 
348 	/*
349 	 * TinySieve
350 	 */
351 	for (i = 0; i < tinybits; i++) {
352 		if (BIT_TEST(TinySieve, i))
353 			continue; /* 2*i+3 is composite */
354 
355 		/* The next tiny prime */
356 		t = 2 * i + 3;
357 
358 		/* Mark all multiples of t */
359 		for (j = i + t; j < tinybits; j += t)
360 			BIT_SET(TinySieve, j);
361 
362 		sieve_large(t);
363 	}
364 
365 	/*
366 	 * Start the small block search at the next possible prime. To avoid
367 	 * fencepost errors, the last pass is skipped.
368 	 */
369 	for (smallbase = TINY_NUMBER + 3;
370 	    smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
371 	    smallbase += TINY_NUMBER) {
372 		for (i = 0; i < tinybits; i++) {
373 			if (BIT_TEST(TinySieve, i))
374 				continue; /* 2*i+3 is composite */
375 
376 			/* The next tiny prime */
377 			t = 2 * i + 3;
378 			r = smallbase % t;
379 
380 			if (r == 0) {
381 				s = 0; /* t divides into smallbase exactly */
382 			} else {
383 				/* smallbase+s is first entry divisible by t */
384 				s = t - r;
385 			}
386 
387 			/*
388 			 * The sieve omits even numbers, so ensure that
389 			 * smallbase+s is odd. Then, step through the sieve
390 			 * in increments of 2*t
391 			 */
392 			if (s & 1)
393 				s += t; /* Make smallbase+s odd, and s even */
394 
395 			/* Mark all multiples of 2*t */
396 			for (s /= 2; s < smallbits; s += t)
397 				BIT_SET(SmallSieve, s);
398 		}
399 
400 		/*
401 		 * SmallSieve
402 		 */
403 		for (i = 0; i < smallbits; i++) {
404 			if (BIT_TEST(SmallSieve, i))
405 				continue; /* 2*i+smallbase is composite */
406 
407 			/* The next small prime */
408 			sieve_large((2 * i) + smallbase);
409 		}
410 
411 		memset(SmallSieve, 0, smallwords << SHIFT_BYTE);
412 	}
413 
414 	time(&time_stop);
415 
416 	logit("%.24s Sieved with %u small primes in %ld seconds",
417 	    ctime(&time_stop), largetries, (long) (time_stop - time_start));
418 
419 	for (j = r = 0; j < largebits; j++) {
420 		if (BIT_TEST(LargeSieve, j))
421 			continue; /* Definitely composite, skip */
422 
423 		debug2("test q = largebase+%u", 2 * j);
424 		if (BN_set_word(q, 2 * j) == 0)
425 			fatal("BN_set_word failed");
426 		if (BN_add(q, q, largebase) == 0)
427 			fatal("BN_add failed");
428 		if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
429 		    MODULI_TESTS_SIEVE, largetries,
430 		    (power - 1) /* MSB */, (0), q) == -1) {
431 			ret = -1;
432 			break;
433 		}
434 
435 		r++; /* count q */
436 	}
437 
438 	time(&time_stop);
439 
440 	free(LargeSieve);
441 	free(SmallSieve);
442 	free(TinySieve);
443 
444 	logit("%.24s Found %u candidates", ctime(&time_stop), r);
445 
446 	return (ret);
447 }
448 
449 static void
450 write_checkpoint(char *cpfile, u_int32_t lineno)
451 {
452 	FILE *fp;
453 	char tmp[PATH_MAX];
454 	int r;
455 
456 	r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
457 	if (r == -1 || r >= PATH_MAX) {
458 		logit("write_checkpoint: temp pathname too long");
459 		return;
460 	}
461 	if ((r = mkstemp(tmp)) == -1) {
462 		logit("mkstemp(%s): %s", tmp, strerror(errno));
463 		return;
464 	}
465 	if ((fp = fdopen(r, "w")) == NULL) {
466 		logit("write_checkpoint: fdopen: %s", strerror(errno));
467 		unlink(tmp);
468 		close(r);
469 		return;
470 	}
471 	if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0
472 	    && rename(tmp, cpfile) == 0)
473 		debug3("wrote checkpoint line %lu to '%s'",
474 		    (unsigned long)lineno, cpfile);
475 	else
476 		logit("failed to write to checkpoint file '%s': %s", cpfile,
477 		    strerror(errno));
478 }
479 
480 static unsigned long
481 read_checkpoint(char *cpfile)
482 {
483 	FILE *fp;
484 	unsigned long lineno = 0;
485 
486 	if ((fp = fopen(cpfile, "r")) == NULL)
487 		return 0;
488 	if (fscanf(fp, "%lu\n", &lineno) < 1)
489 		logit("Failed to load checkpoint from '%s'", cpfile);
490 	else
491 		logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno);
492 	fclose(fp);
493 	return lineno;
494 }
495 
496 static unsigned long
497 count_lines(FILE *f)
498 {
499 	unsigned long count = 0;
500 	char lp[QLINESIZE + 1];
501 
502 	if (fseek(f, 0, SEEK_SET) != 0) {
503 		debug("input file is not seekable");
504 		return ULONG_MAX;
505 	}
506 	while (fgets(lp, QLINESIZE + 1, f) != NULL)
507 		count++;
508 	rewind(f);
509 	debug("input file has %lu lines", count);
510 	return count;
511 }
512 
513 static char *
514 fmt_time(time_t seconds)
515 {
516 	int day, hr, min;
517 	static char buf[128];
518 
519 	min = (seconds / 60) % 60;
520 	hr = (seconds / 60 / 60) % 24;
521 	day = seconds / 60 / 60 / 24;
522 	if (day > 0)
523 		snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min);
524 	else
525 		snprintf(buf, sizeof buf, "%d:%02d", hr, min);
526 	return buf;
527 }
528 
529 static void
530 print_progress(unsigned long start_lineno, unsigned long current_lineno,
531     unsigned long end_lineno)
532 {
533 	static time_t time_start, time_prev;
534 	time_t time_now, elapsed;
535 	unsigned long num_to_process, processed, remaining, percent, eta;
536 	double time_per_line;
537 	char *eta_str;
538 
539 	time_now = monotime();
540 	if (time_start == 0) {
541 		time_start = time_prev = time_now;
542 		return;
543 	}
544 	/* print progress after 1m then once per 5m */
545 	if (time_now - time_prev < 5 * 60)
546 		return;
547 	time_prev = time_now;
548 	elapsed = time_now - time_start;
549 	processed = current_lineno - start_lineno;
550 	remaining = end_lineno - current_lineno;
551 	num_to_process = end_lineno - start_lineno;
552 	time_per_line = (double)elapsed / processed;
553 	/* if we don't know how many we're processing just report count+time */
554 	time(&time_now);
555 	if (end_lineno == ULONG_MAX) {
556 		logit("%.24s processed %lu in %s", ctime(&time_now),
557 		    processed, fmt_time(elapsed));
558 		return;
559 	}
560 	percent = 100 * processed / num_to_process;
561 	eta = time_per_line * remaining;
562 	eta_str = xstrdup(fmt_time(eta));
563 	logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s",
564 	    ctime(&time_now), processed, num_to_process, percent,
565 	    fmt_time(elapsed), eta_str);
566 	free(eta_str);
567 }
568 
569 /*
570  * perform a Miller-Rabin primality test
571  * on the list of candidates
572  * (checking both q and p)
573  * The result is a list of so-call "safe" primes
574  */
575 int
576 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
577     char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
578 {
579 	BIGNUM *q, *p, *a;
580 	BN_CTX *ctx;
581 	char *cp, *lp;
582 	u_int32_t count_in = 0, count_out = 0, count_possible = 0;
583 	u_int32_t generator_known, in_tests, in_tries, in_type, in_size;
584 	unsigned long last_processed = 0, end_lineno;
585 	time_t time_start, time_stop;
586 	int res;
587 
588 	if (trials < TRIAL_MINIMUM) {
589 		error("Minimum primality trials is %d", TRIAL_MINIMUM);
590 		return (-1);
591 	}
592 
593 	if (num_lines == 0)
594 		end_lineno = count_lines(in);
595 	else
596 		end_lineno = start_lineno + num_lines;
597 
598 	time(&time_start);
599 
600 	if ((p = BN_new()) == NULL)
601 		fatal("BN_new failed");
602 	if ((q = BN_new()) == NULL)
603 		fatal("BN_new failed");
604 	if ((ctx = BN_CTX_new()) == NULL)
605 		fatal("BN_CTX_new failed");
606 
607 	debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
608 	    ctime(&time_start), trials, generator_wanted);
609 
610 	if (checkpoint_file != NULL)
611 		last_processed = read_checkpoint(checkpoint_file);
612 	last_processed = start_lineno = MAX(last_processed, start_lineno);
613 	if (end_lineno == ULONG_MAX)
614 		debug("process from line %lu from pipe", last_processed);
615 	else
616 		debug("process from line %lu to line %lu", last_processed,
617 		    end_lineno);
618 
619 	res = 0;
620 	lp = xmalloc(QLINESIZE + 1);
621 	while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
622 		count_in++;
623 		if (count_in <= last_processed) {
624 			debug3("skipping line %u, before checkpoint or "
625 			    "specified start line", count_in);
626 			continue;
627 		}
628 		if (checkpoint_file != NULL)
629 			write_checkpoint(checkpoint_file, count_in);
630 		print_progress(start_lineno, count_in, end_lineno);
631 		if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
632 			debug2("%10u: comment or short line", count_in);
633 			continue;
634 		}
635 
636 		/* XXX - fragile parser */
637 		/* time */
638 		cp = &lp[14];	/* (skip) */
639 
640 		/* type */
641 		in_type = strtoul(cp, &cp, 10);
642 
643 		/* tests */
644 		in_tests = strtoul(cp, &cp, 10);
645 
646 		if (in_tests & MODULI_TESTS_COMPOSITE) {
647 			debug2("%10u: known composite", count_in);
648 			continue;
649 		}
650 
651 		/* tries */
652 		in_tries = strtoul(cp, &cp, 10);
653 
654 		/* size (most significant bit) */
655 		in_size = strtoul(cp, &cp, 10);
656 
657 		/* generator (hex) */
658 		generator_known = strtoul(cp, &cp, 16);
659 
660 		/* Skip white space */
661 		cp += strspn(cp, " ");
662 
663 		/* modulus (hex) */
664 		switch (in_type) {
665 		case MODULI_TYPE_SOPHIE_GERMAIN:
666 			debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
667 			a = q;
668 			if (BN_hex2bn(&a, cp) == 0)
669 				fatal("BN_hex2bn failed");
670 			/* p = 2*q + 1 */
671 			if (BN_lshift(p, q, 1) == 0)
672 				fatal("BN_lshift failed");
673 			if (BN_add_word(p, 1) == 0)
674 				fatal("BN_add_word failed");
675 			in_size += 1;
676 			generator_known = 0;
677 			break;
678 		case MODULI_TYPE_UNSTRUCTURED:
679 		case MODULI_TYPE_SAFE:
680 		case MODULI_TYPE_SCHNORR:
681 		case MODULI_TYPE_STRONG:
682 		case MODULI_TYPE_UNKNOWN:
683 			debug2("%10u: (%u)", count_in, in_type);
684 			a = p;
685 			if (BN_hex2bn(&a, cp) == 0)
686 				fatal("BN_hex2bn failed");
687 			/* q = (p-1) / 2 */
688 			if (BN_rshift(q, p, 1) == 0)
689 				fatal("BN_rshift failed");
690 			break;
691 		default:
692 			debug2("Unknown prime type");
693 			break;
694 		}
695 
696 		/*
697 		 * due to earlier inconsistencies in interpretation, check
698 		 * the proposed bit size.
699 		 */
700 		if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
701 			debug2("%10u: bit size %u mismatch", count_in, in_size);
702 			continue;
703 		}
704 		if (in_size < QSIZE_MINIMUM) {
705 			debug2("%10u: bit size %u too short", count_in, in_size);
706 			continue;
707 		}
708 
709 		if (in_tests & MODULI_TESTS_MILLER_RABIN)
710 			in_tries += trials;
711 		else
712 			in_tries = trials;
713 
714 		/*
715 		 * guess unknown generator
716 		 */
717 		if (generator_known == 0) {
718 			if (BN_mod_word(p, 24) == 11)
719 				generator_known = 2;
720 			else if (BN_mod_word(p, 12) == 5)
721 				generator_known = 3;
722 			else {
723 				u_int32_t r = BN_mod_word(p, 10);
724 
725 				if (r == 3 || r == 7)
726 					generator_known = 5;
727 			}
728 		}
729 		/*
730 		 * skip tests when desired generator doesn't match
731 		 */
732 		if (generator_wanted > 0 &&
733 		    generator_wanted != generator_known) {
734 			debug2("%10u: generator %d != %d",
735 			    count_in, generator_known, generator_wanted);
736 			continue;
737 		}
738 
739 		/*
740 		 * Primes with no known generator are useless for DH, so
741 		 * skip those.
742 		 */
743 		if (generator_known == 0) {
744 			debug2("%10u: no known generator", count_in);
745 			continue;
746 		}
747 
748 		count_possible++;
749 
750 		/*
751 		 * The (1/4)^N performance bound on Miller-Rabin is
752 		 * extremely pessimistic, so don't spend a lot of time
753 		 * really verifying that q is prime until after we know
754 		 * that p is also prime. A single pass will weed out the
755 		 * vast majority of composite q's.
756 		 */
757 		if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
758 			debug("%10u: q failed first possible prime test",
759 			    count_in);
760 			continue;
761 		}
762 
763 		/*
764 		 * q is possibly prime, so go ahead and really make sure
765 		 * that p is prime. If it is, then we can go back and do
766 		 * the same for q. If p is composite, chances are that
767 		 * will show up on the first Rabin-Miller iteration so it
768 		 * doesn't hurt to specify a high iteration count.
769 		 */
770 		if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
771 			debug("%10u: p is not prime", count_in);
772 			continue;
773 		}
774 		debug("%10u: p is almost certainly prime", count_in);
775 
776 		/* recheck q more rigorously */
777 		if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
778 			debug("%10u: q is not prime", count_in);
779 			continue;
780 		}
781 		debug("%10u: q is almost certainly prime", count_in);
782 
783 		if (qfileout(out, MODULI_TYPE_SAFE,
784 		    in_tests | MODULI_TESTS_MILLER_RABIN,
785 		    in_tries, in_size, generator_known, p)) {
786 			res = -1;
787 			break;
788 		}
789 
790 		count_out++;
791 	}
792 
793 	time(&time_stop);
794 	free(lp);
795 	BN_free(p);
796 	BN_free(q);
797 	BN_CTX_free(ctx);
798 
799 	if (checkpoint_file != NULL)
800 		unlink(checkpoint_file);
801 
802 	logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
803 	    ctime(&time_stop), count_out, count_possible,
804 	    (long) (time_stop - time_start));
805 
806 	return (res);
807 }
808 
809 #endif /* WITH_OPENSSL */
810