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2e437378 | 1 | /* $OpenBSD: moduli.c,v 1.19 2006/11/06 21:25:28 markus Exp $ */ |
70791e56 | 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" | |
2e437378 | 41 | |
42 | #include <sys/types.h> | |
70791e56 | 43 | |
44 | #include <openssl/bn.h> | |
45 | ||
2e437378 | 46 | #include <stdio.h> |
47 | #include <stdlib.h> | |
48 | #include <string.h> | |
49 | #include <stdarg.h> | |
50 | #include <time.h> | |
51 | ||
52 | #include "xmalloc.h" | |
53 | #include "log.h" | |
54 | ||
70791e56 | 55 | /* |
56 | * File output defines | |
57 | */ | |
58 | ||
59 | /* need line long enough for largest moduli plus headers */ | |
1b56ff3d | 60 | #define QLINESIZE (100+8192) |
70791e56 | 61 | |
62 | /* Type: decimal. | |
63 | * Specifies the internal structure of the prime modulus. | |
64 | */ | |
1b56ff3d | 65 | #define QTYPE_UNKNOWN (0) |
66 | #define QTYPE_UNSTRUCTURED (1) | |
67 | #define QTYPE_SAFE (2) | |
34fee935 | 68 | #define QTYPE_SCHNORR (3) |
1b56ff3d | 69 | #define QTYPE_SOPHIE_GERMAIN (4) |
70 | #define QTYPE_STRONG (5) | |
70791e56 | 71 | |
72 | /* Tests: decimal (bit field). | |
73 | * Specifies the methods used in checking for primality. | |
74 | * Usually, more than one test is used. | |
75 | */ | |
1b56ff3d | 76 | #define QTEST_UNTESTED (0x00) |
77 | #define QTEST_COMPOSITE (0x01) | |
78 | #define QTEST_SIEVE (0x02) | |
79 | #define QTEST_MILLER_RABIN (0x04) | |
80 | #define QTEST_JACOBI (0x08) | |
81 | #define QTEST_ELLIPTIC (0x10) | |
70791e56 | 82 | |
416fd2a8 | 83 | /* |
84 | * Size: decimal. | |
70791e56 | 85 | * Specifies the number of the most significant bit (0 to M). |
416fd2a8 | 86 | * WARNING: internally, usually 1 to N. |
70791e56 | 87 | */ |
1b56ff3d | 88 | #define QSIZE_MINIMUM (511) |
70791e56 | 89 | |
90 | /* | |
91 | * Prime sieving defines | |
92 | */ | |
93 | ||
94 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
1b56ff3d | 95 | #define SHIFT_BIT (3) |
96 | #define SHIFT_BYTE (2) | |
97 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
98 | #define SHIFT_MEGABYTE (20) | |
99 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
100 | ||
101 | /* | |
102 | * Using virtual memory can cause thrashing. This should be the largest | |
103 | * number that is supported without a large amount of disk activity -- | |
104 | * that would increase the run time from hours to days or weeks! | |
105 | */ | |
106 | #define LARGE_MINIMUM (8UL) /* megabytes */ | |
107 | ||
108 | /* | |
109 | * Do not increase this number beyond the unsigned integer bit size. | |
110 | * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). | |
111 | */ | |
112 | #define LARGE_MAXIMUM (127UL) /* megabytes */ | |
70791e56 | 113 | |
114 | /* | |
115 | * Constant: when used with 32-bit integers, the largest sieve prime | |
116 | * has to be less than 2**32. | |
117 | */ | |
1b56ff3d | 118 | #define SMALL_MAXIMUM (0xffffffffUL) |
70791e56 | 119 | |
120 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
1b56ff3d | 121 | #define TINY_NUMBER (1UL<<16) |
70791e56 | 122 | |
123 | /* Ensure enough bit space for testing 2*q. */ | |
34fee935 | 124 | #define TEST_MAXIMUM (1UL<<16) |
125 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
126 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
127 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
70791e56 | 128 | |
129 | /* bit operations on 32-bit words */ | |
34fee935 | 130 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) |
131 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
132 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
70791e56 | 133 | |
134 | /* | |
135 | * Prime testing defines | |
136 | */ | |
137 | ||
1b56ff3d | 138 | /* Minimum number of primality tests to perform */ |
34fee935 | 139 | #define TRIAL_MINIMUM (4) |
1b56ff3d | 140 | |
70791e56 | 141 | /* |
142 | * Sieving data (XXX - move to struct) | |
143 | */ | |
144 | ||
145 | /* sieve 2**16 */ | |
146 | static u_int32_t *TinySieve, tinybits; | |
147 | ||
148 | /* sieve 2**30 in 2**16 parts */ | |
149 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
150 | ||
151 | /* sieve relative to the initial value */ | |
152 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
153 | static u_int32_t largebits, largememory; /* megabytes */ | |
154 | static BIGNUM *largebase; | |
155 | ||
34fee935 | 156 | int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); |
1b56ff3d | 157 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); |
70791e56 | 158 | |
159 | /* | |
160 | * print moduli out in consistent form, | |
161 | */ | |
162 | static int | |
163 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
164 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
165 | { | |
166 | struct tm *gtm; | |
167 | time_t time_now; | |
168 | int res; | |
169 | ||
170 | time(&time_now); | |
171 | gtm = gmtime(&time_now); | |
416fd2a8 | 172 | |
70791e56 | 173 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", |
174 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
175 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
176 | otype, otests, otries, osize, ogenerator); | |
177 | ||
178 | if (res < 0) | |
179 | return (-1); | |
180 | ||
181 | if (BN_print_fp(ofile, omodulus) < 1) | |
182 | return (-1); | |
183 | ||
184 | res = fprintf(ofile, "\n"); | |
185 | fflush(ofile); | |
186 | ||
187 | return (res > 0 ? 0 : -1); | |
188 | } | |
189 | ||
190 | ||
191 | /* | |
192 | ** Sieve p's and q's with small factors | |
193 | */ | |
194 | static void | |
195 | sieve_large(u_int32_t s) | |
196 | { | |
197 | u_int32_t r, u; | |
198 | ||
416fd2a8 | 199 | debug3("sieve_large %u", s); |
70791e56 | 200 | largetries++; |
201 | /* r = largebase mod s */ | |
202 | r = BN_mod_word(largebase, s); | |
203 | if (r == 0) | |
204 | u = 0; /* s divides into largebase exactly */ | |
205 | else | |
206 | u = s - r; /* largebase+u is first entry divisible by s */ | |
207 | ||
208 | if (u < largebits * 2) { | |
209 | /* | |
210 | * The sieve omits p's and q's divisible by 2, so ensure that | |
211 | * largebase+u is odd. Then, step through the sieve in | |
212 | * increments of 2*s | |
213 | */ | |
214 | if (u & 0x1) | |
215 | u += s; /* Make largebase+u odd, and u even */ | |
216 | ||
217 | /* Mark all multiples of 2*s */ | |
218 | for (u /= 2; u < largebits; u += s) | |
219 | BIT_SET(LargeSieve, u); | |
220 | } | |
221 | ||
222 | /* r = p mod s */ | |
223 | r = (2 * r + 1) % s; | |
224 | if (r == 0) | |
225 | u = 0; /* s divides p exactly */ | |
226 | else | |
227 | u = s - r; /* p+u is first entry divisible by s */ | |
228 | ||
229 | if (u < largebits * 4) { | |
230 | /* | |
231 | * The sieve omits p's divisible by 4, so ensure that | |
232 | * largebase+u is not. Then, step through the sieve in | |
233 | * increments of 4*s | |
234 | */ | |
235 | while (u & 0x3) { | |
236 | if (SMALL_MAXIMUM - u < s) | |
237 | return; | |
238 | u += s; | |
239 | } | |
240 | ||
241 | /* Mark all multiples of 4*s */ | |
242 | for (u /= 4; u < largebits; u += s) | |
243 | BIT_SET(LargeSieve, u); | |
244 | } | |
245 | } | |
246 | ||
247 | /* | |
1b56ff3d | 248 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
70791e56 | 249 | * to standard output. |
250 | * The list is checked against small known primes (less than 2**30). | |
251 | */ | |
252 | int | |
34fee935 | 253 | gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) |
70791e56 | 254 | { |
255 | BIGNUM *q; | |
256 | u_int32_t j, r, s, t; | |
257 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
258 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
259 | time_t time_start, time_stop; | |
34fee935 | 260 | u_int32_t i; |
261 | int ret = 0; | |
70791e56 | 262 | |
263 | largememory = memory; | |
264 | ||
1b56ff3d | 265 | if (memory != 0 && |
34fee935 | 266 | (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { |
1b56ff3d | 267 | error("Invalid memory amount (min %ld, max %ld)", |
268 | LARGE_MINIMUM, LARGE_MAXIMUM); | |
269 | return (-1); | |
270 | } | |
271 | ||
70791e56 | 272 | /* |
416fd2a8 | 273 | * Set power to the length in bits of the prime to be generated. |
274 | * This is changed to 1 less than the desired safe prime moduli p. | |
275 | */ | |
70791e56 | 276 | if (power > TEST_MAXIMUM) { |
277 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
278 | return (-1); | |
279 | } else if (power < TEST_MINIMUM) { | |
280 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
281 | return (-1); | |
282 | } | |
283 | power--; /* decrement before squaring */ | |
284 | ||
285 | /* | |
416fd2a8 | 286 | * The density of ordinary primes is on the order of 1/bits, so the |
287 | * density of safe primes should be about (1/bits)**2. Set test range | |
288 | * to something well above bits**2 to be reasonably sure (but not | |
289 | * guaranteed) of catching at least one safe prime. | |
70791e56 | 290 | */ |
291 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
292 | ||
293 | /* | |
416fd2a8 | 294 | * Need idea of how much memory is available. We don't have to use all |
295 | * of it. | |
70791e56 | 296 | */ |
297 | if (largememory > LARGE_MAXIMUM) { | |
298 | logit("Limited memory: %u MB; limit %lu MB", | |
299 | largememory, LARGE_MAXIMUM); | |
300 | largememory = LARGE_MAXIMUM; | |
301 | } | |
302 | ||
303 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
304 | logit("Increased memory: %u MB; need %u bytes", | |
305 | largememory, (largewords << SHIFT_BYTE)); | |
306 | largewords = (largememory << SHIFT_MEGAWORD); | |
307 | } else if (largememory > 0) { | |
308 | logit("Decreased memory: %u MB; want %u bytes", | |
309 | largememory, (largewords << SHIFT_BYTE)); | |
310 | largewords = (largememory << SHIFT_MEGAWORD); | |
311 | } | |
312 | ||
2e437378 | 313 | TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); |
70791e56 | 314 | tinybits = tinywords << SHIFT_WORD; |
315 | ||
2e437378 | 316 | SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); |
70791e56 | 317 | smallbits = smallwords << SHIFT_WORD; |
318 | ||
319 | /* | |
320 | * dynamically determine available memory | |
321 | */ | |
322 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
323 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
324 | ||
325 | largebits = largewords << SHIFT_WORD; | |
326 | largenumbers = largebits * 2; /* even numbers excluded */ | |
327 | ||
328 | /* validation check: count the number of primes tried */ | |
329 | largetries = 0; | |
2e437378 | 330 | if ((q = BN_new()) == NULL) |
331 | fatal("BN_new failed"); | |
70791e56 | 332 | |
333 | /* | |
416fd2a8 | 334 | * Generate random starting point for subprime search, or use |
335 | * specified parameter. | |
70791e56 | 336 | */ |
2e437378 | 337 | if ((largebase = BN_new()) == NULL) |
338 | fatal("BN_new failed"); | |
339 | if (start == NULL) { | |
340 | if (BN_rand(largebase, power, 1, 1) == 0) | |
341 | fatal("BN_rand failed"); | |
342 | } else { | |
343 | if (BN_copy(largebase, start) == NULL) | |
344 | fatal("BN_copy: failed"); | |
345 | } | |
70791e56 | 346 | |
347 | /* ensure odd */ | |
2e437378 | 348 | if (BN_set_bit(largebase, 0) == 0) |
349 | fatal("BN_set_bit: failed"); | |
70791e56 | 350 | |
351 | time(&time_start); | |
352 | ||
416fd2a8 | 353 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
70791e56 | 354 | largenumbers, power); |
355 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
356 | ||
357 | /* | |
416fd2a8 | 358 | * TinySieve |
359 | */ | |
70791e56 | 360 | for (i = 0; i < tinybits; i++) { |
361 | if (BIT_TEST(TinySieve, i)) | |
362 | continue; /* 2*i+3 is composite */ | |
363 | ||
364 | /* The next tiny prime */ | |
365 | t = 2 * i + 3; | |
366 | ||
367 | /* Mark all multiples of t */ | |
368 | for (j = i + t; j < tinybits; j += t) | |
369 | BIT_SET(TinySieve, j); | |
370 | ||
371 | sieve_large(t); | |
372 | } | |
373 | ||
374 | /* | |
416fd2a8 | 375 | * Start the small block search at the next possible prime. To avoid |
376 | * fencepost errors, the last pass is skipped. | |
377 | */ | |
70791e56 | 378 | for (smallbase = TINY_NUMBER + 3; |
34fee935 | 379 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); |
380 | smallbase += TINY_NUMBER) { | |
70791e56 | 381 | for (i = 0; i < tinybits; i++) { |
382 | if (BIT_TEST(TinySieve, i)) | |
383 | continue; /* 2*i+3 is composite */ | |
384 | ||
385 | /* The next tiny prime */ | |
386 | t = 2 * i + 3; | |
387 | r = smallbase % t; | |
388 | ||
389 | if (r == 0) { | |
390 | s = 0; /* t divides into smallbase exactly */ | |
391 | } else { | |
392 | /* smallbase+s is first entry divisible by t */ | |
393 | s = t - r; | |
394 | } | |
395 | ||
396 | /* | |
397 | * The sieve omits even numbers, so ensure that | |
398 | * smallbase+s is odd. Then, step through the sieve | |
399 | * in increments of 2*t | |
400 | */ | |
401 | if (s & 1) | |
402 | s += t; /* Make smallbase+s odd, and s even */ | |
403 | ||
404 | /* Mark all multiples of 2*t */ | |
405 | for (s /= 2; s < smallbits; s += t) | |
406 | BIT_SET(SmallSieve, s); | |
407 | } | |
408 | ||
409 | /* | |
416fd2a8 | 410 | * SmallSieve |
411 | */ | |
70791e56 | 412 | for (i = 0; i < smallbits; i++) { |
413 | if (BIT_TEST(SmallSieve, i)) | |
414 | continue; /* 2*i+smallbase is composite */ | |
415 | ||
416 | /* The next small prime */ | |
417 | sieve_large((2 * i) + smallbase); | |
418 | } | |
419 | ||
420 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
421 | } | |
422 | ||
423 | time(&time_stop); | |
424 | ||
425 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
426 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
427 | ||
428 | for (j = r = 0; j < largebits; j++) { | |
429 | if (BIT_TEST(LargeSieve, j)) | |
430 | continue; /* Definitely composite, skip */ | |
431 | ||
432 | debug2("test q = largebase+%u", 2 * j); | |
2e437378 | 433 | if (BN_set_word(q, 2 * j) == 0) |
434 | fatal("BN_set_word failed"); | |
435 | if (BN_add(q, q, largebase) == 0) | |
436 | fatal("BN_add failed"); | |
1b56ff3d | 437 | if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
70791e56 | 438 | largetries, (power - 1) /* MSB */, (0), q) == -1) { |
439 | ret = -1; | |
440 | break; | |
441 | } | |
442 | ||
443 | r++; /* count q */ | |
444 | } | |
445 | ||
446 | time(&time_stop); | |
447 | ||
448 | xfree(LargeSieve); | |
449 | xfree(SmallSieve); | |
450 | xfree(TinySieve); | |
451 | ||
452 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
453 | ||
454 | return (ret); | |
455 | } | |
456 | ||
457 | /* | |
458 | * perform a Miller-Rabin primality test | |
459 | * on the list of candidates | |
460 | * (checking both q and p) | |
461 | * The result is a list of so-call "safe" primes | |
462 | */ | |
463 | int | |
1b56ff3d | 464 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
70791e56 | 465 | { |
466 | BIGNUM *q, *p, *a; | |
467 | BN_CTX *ctx; | |
468 | char *cp, *lp; | |
469 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
470 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
471 | time_t time_start, time_stop; | |
472 | int res; | |
473 | ||
1b56ff3d | 474 | if (trials < TRIAL_MINIMUM) { |
475 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
476 | return (-1); | |
477 | } | |
478 | ||
70791e56 | 479 | time(&time_start); |
480 | ||
2e437378 | 481 | if ((p = BN_new()) == NULL) |
482 | fatal("BN_new failed"); | |
483 | if ((q = BN_new()) == NULL) | |
484 | fatal("BN_new failed"); | |
485 | if ((ctx = BN_CTX_new()) == NULL) | |
486 | fatal("BN_CTX_new failed"); | |
70791e56 | 487 | |
488 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
489 | ctime(&time_start), trials, generator_wanted); | |
490 | ||
491 | res = 0; | |
492 | lp = xmalloc(QLINESIZE + 1); | |
493 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
494 | int ll = strlen(lp); | |
495 | ||
496 | count_in++; | |
497 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
498 | debug2("%10u: comment or short line", count_in); | |
499 | continue; | |
500 | } | |
501 | ||
502 | /* XXX - fragile parser */ | |
503 | /* time */ | |
504 | cp = &lp[14]; /* (skip) */ | |
505 | ||
506 | /* type */ | |
507 | in_type = strtoul(cp, &cp, 10); | |
508 | ||
509 | /* tests */ | |
510 | in_tests = strtoul(cp, &cp, 10); | |
511 | ||
512 | if (in_tests & QTEST_COMPOSITE) { | |
513 | debug2("%10u: known composite", count_in); | |
514 | continue; | |
515 | } | |
416fd2a8 | 516 | |
70791e56 | 517 | /* tries */ |
518 | in_tries = strtoul(cp, &cp, 10); | |
519 | ||
520 | /* size (most significant bit) */ | |
521 | in_size = strtoul(cp, &cp, 10); | |
522 | ||
523 | /* generator (hex) */ | |
524 | generator_known = strtoul(cp, &cp, 16); | |
525 | ||
526 | /* Skip white space */ | |
527 | cp += strspn(cp, " "); | |
528 | ||
529 | /* modulus (hex) */ | |
530 | switch (in_type) { | |
1b56ff3d | 531 | case QTYPE_SOPHIE_GERMAIN: |
532 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
70791e56 | 533 | a = q; |
2e437378 | 534 | if (BN_hex2bn(&a, cp) == 0) |
535 | fatal("BN_hex2bn failed"); | |
70791e56 | 536 | /* p = 2*q + 1 */ |
2e437378 | 537 | if (BN_lshift(p, q, 1) == 0) |
538 | fatal("BN_lshift failed"); | |
539 | if (BN_add_word(p, 1) == 0) | |
540 | fatal("BN_add_word failed"); | |
70791e56 | 541 | in_size += 1; |
542 | generator_known = 0; | |
543 | break; | |
416fd2a8 | 544 | case QTYPE_UNSTRUCTURED: |
545 | case QTYPE_SAFE: | |
34fee935 | 546 | case QTYPE_SCHNORR: |
416fd2a8 | 547 | case QTYPE_STRONG: |
548 | case QTYPE_UNKNOWN: | |
70791e56 | 549 | debug2("%10u: (%u)", count_in, in_type); |
550 | a = p; | |
2e437378 | 551 | if (BN_hex2bn(&a, cp) == 0) |
552 | fatal("BN_hex2bn failed"); | |
70791e56 | 553 | /* q = (p-1) / 2 */ |
2e437378 | 554 | if (BN_rshift(q, p, 1) == 0) |
555 | fatal("BN_rshift failed"); | |
70791e56 | 556 | break; |
416fd2a8 | 557 | default: |
558 | debug2("Unknown prime type"); | |
559 | break; | |
70791e56 | 560 | } |
561 | ||
562 | /* | |
563 | * due to earlier inconsistencies in interpretation, check | |
564 | * the proposed bit size. | |
565 | */ | |
34fee935 | 566 | if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { |
70791e56 | 567 | debug2("%10u: bit size %u mismatch", count_in, in_size); |
568 | continue; | |
569 | } | |
570 | if (in_size < QSIZE_MINIMUM) { | |
571 | debug2("%10u: bit size %u too short", count_in, in_size); | |
572 | continue; | |
573 | } | |
574 | ||
575 | if (in_tests & QTEST_MILLER_RABIN) | |
576 | in_tries += trials; | |
577 | else | |
578 | in_tries = trials; | |
416fd2a8 | 579 | |
70791e56 | 580 | /* |
581 | * guess unknown generator | |
582 | */ | |
583 | if (generator_known == 0) { | |
584 | if (BN_mod_word(p, 24) == 11) | |
585 | generator_known = 2; | |
586 | else if (BN_mod_word(p, 12) == 5) | |
587 | generator_known = 3; | |
588 | else { | |
589 | u_int32_t r = BN_mod_word(p, 10); | |
590 | ||
416fd2a8 | 591 | if (r == 3 || r == 7) |
70791e56 | 592 | generator_known = 5; |
70791e56 | 593 | } |
594 | } | |
595 | /* | |
596 | * skip tests when desired generator doesn't match | |
597 | */ | |
598 | if (generator_wanted > 0 && | |
599 | generator_wanted != generator_known) { | |
600 | debug2("%10u: generator %d != %d", | |
601 | count_in, generator_known, generator_wanted); | |
602 | continue; | |
603 | } | |
604 | ||
416fd2a8 | 605 | /* |
606 | * Primes with no known generator are useless for DH, so | |
607 | * skip those. | |
608 | */ | |
609 | if (generator_known == 0) { | |
610 | debug2("%10u: no known generator", count_in); | |
611 | continue; | |
612 | } | |
613 | ||
70791e56 | 614 | count_possible++; |
615 | ||
616 | /* | |
416fd2a8 | 617 | * The (1/4)^N performance bound on Miller-Rabin is |
618 | * extremely pessimistic, so don't spend a lot of time | |
619 | * really verifying that q is prime until after we know | |
620 | * that p is also prime. A single pass will weed out the | |
70791e56 | 621 | * vast majority of composite q's. |
622 | */ | |
623 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
416fd2a8 | 624 | debug("%10u: q failed first possible prime test", |
70791e56 | 625 | count_in); |
626 | continue; | |
627 | } | |
416fd2a8 | 628 | |
70791e56 | 629 | /* |
416fd2a8 | 630 | * q is possibly prime, so go ahead and really make sure |
631 | * that p is prime. If it is, then we can go back and do | |
632 | * the same for q. If p is composite, chances are that | |
70791e56 | 633 | * will show up on the first Rabin-Miller iteration so it |
634 | * doesn't hurt to specify a high iteration count. | |
635 | */ | |
636 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
416fd2a8 | 637 | debug("%10u: p is not prime", count_in); |
70791e56 | 638 | continue; |
639 | } | |
640 | debug("%10u: p is almost certainly prime", count_in); | |
641 | ||
642 | /* recheck q more rigorously */ | |
643 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
644 | debug("%10u: q is not prime", count_in); | |
645 | continue; | |
646 | } | |
647 | debug("%10u: q is almost certainly prime", count_in); | |
648 | ||
416fd2a8 | 649 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
70791e56 | 650 | in_tries, in_size, generator_known, p)) { |
651 | res = -1; | |
652 | break; | |
653 | } | |
654 | ||
655 | count_out++; | |
656 | } | |
657 | ||
658 | time(&time_stop); | |
659 | xfree(lp); | |
660 | BN_free(p); | |
661 | BN_free(q); | |
662 | BN_CTX_free(ctx); | |
663 | ||
664 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
416fd2a8 | 665 | ctime(&time_stop), count_out, count_possible, |
70791e56 | 666 | (long) (time_stop - time_start)); |
667 | ||
668 | return (res); | |
669 | } |