blob: 294ff8fde0fa6098003a4e38fa3535e1fd10a980 [file] [log] [blame]
Darren Tuckera627d422013-06-02 07:31:17 +10001/* $OpenBSD: moduli.c,v 1.27 2013/05/17 00:13:13 djm Exp $ */
Darren Tuckerb2f9d412003-08-02 23:51:38 +10002/*
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"
Damien Miller5598b4f2006-07-24 14:09:40 +100041
Damien Miller91f3eae2011-10-18 16:05:55 +110042#include <sys/param.h>
Damien Miller5598b4f2006-07-24 14:09:40 +100043#include <sys/types.h>
Darren Tuckerb2f9d412003-08-02 23:51:38 +100044
45#include <openssl/bn.h>
Damien Miller2e9cf492008-06-29 22:47:04 +100046#include <openssl/dh.h>
Darren Tuckerb2f9d412003-08-02 23:51:38 +100047
Damien Miller91f3eae2011-10-18 16:05:55 +110048#include <errno.h>
Damien Millera7a73ee2006-08-05 11:37:59 +100049#include <stdio.h>
Damien Millere7a1e5c2006-08-05 11:34:19 +100050#include <stdlib.h>
Damien Millere3476ed2006-07-24 14:13:33 +100051#include <string.h>
Damien Millerd7834352006-08-05 12:39:39 +100052#include <stdarg.h>
Damien Miller5598b4f2006-07-24 14:09:40 +100053#include <time.h>
Damien Miller390d0562011-10-18 16:05:19 +110054#include <unistd.h>
Damien Miller5598b4f2006-07-24 14:09:40 +100055
56#include "xmalloc.h"
Damien Miller2e9cf492008-06-29 22:47:04 +100057#include "dh.h"
Damien Miller5598b4f2006-07-24 14:09:40 +100058#include "log.h"
59
Darren Tuckerebdef762010-12-04 23:20:50 +110060#include "openbsd-compat/openssl-compat.h"
61
Darren Tuckerb2f9d412003-08-02 23:51:38 +100062/*
63 * File output defines
64 */
65
66/* need line long enough for largest moduli plus headers */
Darren Tuckerfc959702004-07-17 16:12:08 +100067#define QLINESIZE (100+8192)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100068
Darren Tucker06930c72003-12-31 11:34:51 +110069/*
70 * Size: decimal.
Darren Tuckerb2f9d412003-08-02 23:51:38 +100071 * Specifies the number of the most significant bit (0 to M).
Darren Tucker06930c72003-12-31 11:34:51 +110072 * WARNING: internally, usually 1 to N.
Darren Tuckerb2f9d412003-08-02 23:51:38 +100073 */
Darren Tuckerfc959702004-07-17 16:12:08 +100074#define QSIZE_MINIMUM (511)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100075
76/*
77 * Prime sieving defines
78 */
79
80/* Constant: assuming 8 bit bytes and 32 bit words */
Darren Tuckerfc959702004-07-17 16:12:08 +100081#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)
Darren Tuckerb2f9d412003-08-02 23:51:38 +100086
87/*
Darren Tucker770fc012004-05-13 16:24:32 +100088 * 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 */
Darren Tuckerfc959702004-07-17 16:12:08 +100092#define LARGE_MINIMUM (8UL) /* megabytes */
Darren Tucker770fc012004-05-13 16:24:32 +100093
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 */
Darren Tuckerfc959702004-07-17 16:12:08 +100098#define LARGE_MAXIMUM (127UL) /* megabytes */
Darren Tucker770fc012004-05-13 16:24:32 +100099
100/*
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000101 * Constant: when used with 32-bit integers, the largest sieve prime
102 * has to be less than 2**32.
103 */
Darren Tuckerfc959702004-07-17 16:12:08 +1000104#define SMALL_MAXIMUM (0xffffffffUL)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000105
106/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */
Darren Tuckerfc959702004-07-17 16:12:08 +1000107#define TINY_NUMBER (1UL<<16)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000108
109/* Ensure enough bit space for testing 2*q. */
Damien Miller0dc1bef2005-07-17 17:22:45 +1000110#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 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000114
115/* bit operations on 32-bit words */
Damien Miller0dc1bef2005-07-17 17:22:45 +1000116#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)))
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000119
120/*
121 * Prime testing defines
122 */
123
Darren Tucker770fc012004-05-13 16:24:32 +1000124/* Minimum number of primality tests to perform */
Damien Miller0dc1bef2005-07-17 17:22:45 +1000125#define TRIAL_MINIMUM (4)
Darren Tucker770fc012004-05-13 16:24:32 +1000126
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000127/*
128 * Sieving data (XXX - move to struct)
129 */
130
131/* sieve 2**16 */
132static u_int32_t *TinySieve, tinybits;
133
134/* sieve 2**30 in 2**16 parts */
135static u_int32_t *SmallSieve, smallbits, smallbase;
136
137/* sieve relative to the initial value */
138static u_int32_t *LargeSieve, largewords, largetries, largenumbers;
139static u_int32_t largebits, largememory; /* megabytes */
140static BIGNUM *largebase;
141
Damien Millerb089fb52005-05-26 12:16:18 +1000142int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *);
Damien Millerdfceafe2012-07-06 13:44:19 +1000143int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long,
144 unsigned long);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000145
146/*
147 * print moduli out in consistent form,
148 */
149static int
150qfileout(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);
Damien Miller787b2ec2003-11-21 23:56:47 +1100159
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000160 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 */
181static void
182sieve_large(u_int32_t s)
183{
184 u_int32_t r, u;
185
Darren Tucker06930c72003-12-31 11:34:51 +1100186 debug3("sieve_large %u", s);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000187 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/*
Darren Tucker47abce42004-05-02 22:09:00 +1000235 * list candidates for Sophie-Germain primes (where q = (p-1)/2)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000236 * to standard output.
237 * The list is checked against small known primes (less than 2**30).
238 */
239int
Damien Millerb089fb52005-05-26 12:16:18 +1000240gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000241{
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;
Damien Millerb089fb52005-05-26 12:16:18 +1000247 u_int32_t i;
248 int ret = 0;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000249
250 largememory = memory;
251
Darren Tucker770fc012004-05-13 16:24:32 +1000252 if (memory != 0 &&
Damien Miller0dc1bef2005-07-17 17:22:45 +1000253 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) {
Darren Tucker770fc012004-05-13 16:24:32 +1000254 error("Invalid memory amount (min %ld, max %ld)",
255 LARGE_MINIMUM, LARGE_MAXIMUM);
256 return (-1);
257 }
258
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000259 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100260 * 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 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000263 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 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100273 * 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.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000277 */
278 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER));
279
280 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100281 * Need idea of how much memory is available. We don't have to use all
282 * of it.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000283 */
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
Damien Miller07d86be2006-03-26 14:19:21 +1100300 TinySieve = xcalloc(tinywords, sizeof(u_int32_t));
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000301 tinybits = tinywords << SHIFT_WORD;
302
Damien Miller07d86be2006-03-26 14:19:21 +1100303 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t));
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000304 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;
Darren Tucker0bc85572006-11-07 23:14:41 +1100317 if ((q = BN_new()) == NULL)
318 fatal("BN_new failed");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000319
320 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100321 * Generate random starting point for subprime search, or use
322 * specified parameter.
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000323 */
Darren Tucker0bc85572006-11-07 23:14:41 +1100324 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 }
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000333
334 /* ensure odd */
Darren Tucker0bc85572006-11-07 23:14:41 +1100335 if (BN_set_bit(largebase, 0) == 0)
336 fatal("BN_set_bit: failed");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000337
338 time(&time_start);
339
Damien Millera8e06ce2003-11-21 23:48:55 +1100340 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start),
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000341 largenumbers, power);
342 debug2("start point: 0x%s", BN_bn2hex(largebase));
343
344 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100345 * TinySieve
346 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000347 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 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100362 * Start the small block search at the next possible prime. To avoid
363 * fencepost errors, the last pass is skipped.
364 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000365 for (smallbase = TINY_NUMBER + 3;
Damien Miller0dc1bef2005-07-17 17:22:45 +1000366 smallbase < (SMALL_MAXIMUM - TINY_NUMBER);
367 smallbase += TINY_NUMBER) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000368 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 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100397 * SmallSieve
398 */
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000399 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);
Darren Tucker0bc85572006-11-07 23:14:41 +1100420 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");
Damien Miller2e9cf492008-06-29 22:47:04 +1000424 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN,
425 MODULI_TESTS_SIEVE, largetries,
426 (power - 1) /* MSB */, (0), q) == -1) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000427 ret = -1;
428 break;
429 }
430
431 r++; /* count q */
432 }
433
434 time(&time_stop);
435
Darren Tuckera627d422013-06-02 07:31:17 +1000436 free(LargeSieve);
437 free(SmallSieve);
438 free(TinySieve);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000439
440 logit("%.24s Found %u candidates", ctime(&time_stop), r);
441
442 return (ret);
443}
444
Damien Miller390d0562011-10-18 16:05:19 +1100445static void
446write_checkpoint(char *cpfile, u_int32_t lineno)
447{
448 FILE *fp;
Darren Tucker9ee09cf2011-11-04 10:52:43 +1100449 char tmp[MAXPATHLEN];
Damien Miller390d0562011-10-18 16:05:19 +1100450 int r;
451
Darren Tucker9ee09cf2011-11-04 10:52:43 +1100452 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile);
Damien Miller390d0562011-10-18 16:05:19 +1100453 if (r == -1 || r >= MAXPATHLEN) {
454 logit("write_checkpoint: temp pathname too long");
455 return;
456 }
Darren Tucker9ee09cf2011-11-04 10:52:43 +1100457 if ((r = mkstemp(tmp)) == -1) {
458 logit("mkstemp(%s): %s", tmp, strerror(errno));
Damien Miller390d0562011-10-18 16:05:19 +1100459 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
Darren Tucker9ee09cf2011-11-04 10:52:43 +1100467 && rename(tmp, cpfile) == 0)
Damien Miller390d0562011-10-18 16:05:19 +1100468 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
475static unsigned long
476read_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
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000491/*
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 */
497int
Damien Miller390d0562011-10-18 16:05:19 +1100498prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted,
Damien Millerdfceafe2012-07-06 13:44:19 +1000499 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000500{
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;
Damien Millerdfceafe2012-07-06 13:44:19 +1000506 unsigned long last_processed = 0, end_lineno;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000507 time_t time_start, time_stop;
508 int res;
509
Darren Tucker770fc012004-05-13 16:24:32 +1000510 if (trials < TRIAL_MINIMUM) {
511 error("Minimum primality trials is %d", TRIAL_MINIMUM);
512 return (-1);
513 }
514
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000515 time(&time_start);
516
Darren Tucker0bc85572006-11-07 23:14:41 +1100517 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");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000523
524 debug2("%.24s Final %u Miller-Rabin trials (%x generator)",
525 ctime(&time_start), trials, generator_wanted);
526
Damien Miller390d0562011-10-18 16:05:19 +1100527 if (checkpoint_file != NULL)
528 last_processed = read_checkpoint(checkpoint_file);
Damien Millerdfceafe2012-07-06 13:44:19 +1000529 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);
Damien Miller390d0562011-10-18 16:05:19 +1100536
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000537 res = 0;
538 lp = xmalloc(QLINESIZE + 1);
Damien Millerdfceafe2012-07-06 13:44:19 +1000539 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000540 count_in++;
Damien Miller390d0562011-10-18 16:05:19 +1100541 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 }
Darren Tucker90aaed42007-02-25 20:38:55 +1100549 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000550 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
Damien Miller2e9cf492008-06-29 22:47:04 +1000564 if (in_tests & MODULI_TESTS_COMPOSITE) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000565 debug2("%10u: known composite", count_in);
566 continue;
567 }
Darren Tucker06930c72003-12-31 11:34:51 +1100568
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000569 /* 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) {
Damien Miller2e9cf492008-06-29 22:47:04 +1000583 case MODULI_TYPE_SOPHIE_GERMAIN:
Darren Tucker47abce42004-05-02 22:09:00 +1000584 debug2("%10u: (%u) Sophie-Germain", count_in, in_type);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000585 a = q;
Darren Tucker0bc85572006-11-07 23:14:41 +1100586 if (BN_hex2bn(&a, cp) == 0)
587 fatal("BN_hex2bn failed");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000588 /* p = 2*q + 1 */
Darren Tucker0bc85572006-11-07 23:14:41 +1100589 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");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000593 in_size += 1;
594 generator_known = 0;
595 break;
Damien Miller2e9cf492008-06-29 22:47:04 +1000596 case MODULI_TYPE_UNSTRUCTURED:
597 case MODULI_TYPE_SAFE:
598 case MODULI_TYPE_SCHNORR:
599 case MODULI_TYPE_STRONG:
600 case MODULI_TYPE_UNKNOWN:
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000601 debug2("%10u: (%u)", count_in, in_type);
602 a = p;
Darren Tucker0bc85572006-11-07 23:14:41 +1100603 if (BN_hex2bn(&a, cp) == 0)
604 fatal("BN_hex2bn failed");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000605 /* q = (p-1) / 2 */
Darren Tucker0bc85572006-11-07 23:14:41 +1100606 if (BN_rshift(q, p, 1) == 0)
607 fatal("BN_rshift failed");
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000608 break;
Darren Tucker06930c72003-12-31 11:34:51 +1100609 default:
610 debug2("Unknown prime type");
611 break;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000612 }
613
614 /*
615 * due to earlier inconsistencies in interpretation, check
616 * the proposed bit size.
617 */
Damien Millerb089fb52005-05-26 12:16:18 +1000618 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000619 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
Damien Miller2e9cf492008-06-29 22:47:04 +1000627 if (in_tests & MODULI_TESTS_MILLER_RABIN)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000628 in_tries += trials;
629 else
630 in_tries = trials;
Darren Tucker06930c72003-12-31 11:34:51 +1100631
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000632 /*
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
Darren Tucker06930c72003-12-31 11:34:51 +1100643 if (r == 3 || r == 7)
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000644 generator_known = 5;
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000645 }
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
Darren Tucker5cd9d442003-12-10 00:54:38 +1100657 /*
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
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000666 count_possible++;
667
668 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100669 * 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
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000673 * vast majority of composite q's.
674 */
Damien Miller4499f4c2010-11-20 15:15:49 +1100675 if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) {
Darren Tucker06930c72003-12-31 11:34:51 +1100676 debug("%10u: q failed first possible prime test",
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000677 count_in);
678 continue;
679 }
Damien Miller787b2ec2003-11-21 23:56:47 +1100680
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000681 /*
Damien Millera8e06ce2003-11-21 23:48:55 +1100682 * 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
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000685 * will show up on the first Rabin-Miller iteration so it
686 * doesn't hurt to specify a high iteration count.
687 */
Damien Miller4499f4c2010-11-20 15:15:49 +1100688 if (!BN_is_prime_ex(p, trials, ctx, NULL)) {
Darren Tucker06930c72003-12-31 11:34:51 +1100689 debug("%10u: p is not prime", count_in);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000690 continue;
691 }
692 debug("%10u: p is almost certainly prime", count_in);
693
694 /* recheck q more rigorously */
Damien Miller4499f4c2010-11-20 15:15:49 +1100695 if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) {
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000696 debug("%10u: q is not prime", count_in);
697 continue;
698 }
699 debug("%10u: q is almost certainly prime", count_in);
700
Damien Miller2e9cf492008-06-29 22:47:04 +1000701 if (qfileout(out, MODULI_TYPE_SAFE,
702 in_tests | MODULI_TESTS_MILLER_RABIN,
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000703 in_tries, in_size, generator_known, p)) {
704 res = -1;
705 break;
706 }
707
708 count_out++;
709 }
710
711 time(&time_stop);
Darren Tuckera627d422013-06-02 07:31:17 +1000712 free(lp);
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000713 BN_free(p);
714 BN_free(q);
715 BN_CTX_free(ctx);
716
Damien Miller390d0562011-10-18 16:05:19 +1100717 if (checkpoint_file != NULL)
718 unlink(checkpoint_file);
719
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000720 logit("%.24s Found %u safe primes of %u candidates in %ld seconds",
Damien Millera8e06ce2003-11-21 23:48:55 +1100721 ctime(&time_stop), count_out, count_possible,
Darren Tuckerb2f9d412003-08-02 23:51:38 +1000722 (long) (time_stop - time_start));
723
724 return (res);
725}