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00146caa | 1 | /* $OpenBSD: moduli.c,v 1.15 2006/07/22 20:48:23 stevesk Exp $ */ |
5ae3dc68 | 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" | |
b0f6943a | 41 | |
42 | #include <sys/types.h> | |
5ae3dc68 | 43 | |
44 | #include <openssl/bn.h> | |
45 | ||
00146caa | 46 | #include <string.h> |
b0f6943a | 47 | #include <time.h> |
48 | ||
49 | #include "xmalloc.h" | |
50 | #include "log.h" | |
51 | ||
5ae3dc68 | 52 | /* |
53 | * File output defines | |
54 | */ | |
55 | ||
56 | /* need line long enough for largest moduli plus headers */ | |
f2107e97 | 57 | #define QLINESIZE (100+8192) |
5ae3dc68 | 58 | |
59 | /* Type: decimal. | |
60 | * Specifies the internal structure of the prime modulus. | |
61 | */ | |
f2107e97 | 62 | #define QTYPE_UNKNOWN (0) |
63 | #define QTYPE_UNSTRUCTURED (1) | |
64 | #define QTYPE_SAFE (2) | |
1d03d1ad | 65 | #define QTYPE_SCHNORR (3) |
f2107e97 | 66 | #define QTYPE_SOPHIE_GERMAIN (4) |
67 | #define QTYPE_STRONG (5) | |
5ae3dc68 | 68 | |
69 | /* Tests: decimal (bit field). | |
70 | * Specifies the methods used in checking for primality. | |
71 | * Usually, more than one test is used. | |
72 | */ | |
f2107e97 | 73 | #define QTEST_UNTESTED (0x00) |
74 | #define QTEST_COMPOSITE (0x01) | |
75 | #define QTEST_SIEVE (0x02) | |
76 | #define QTEST_MILLER_RABIN (0x04) | |
77 | #define QTEST_JACOBI (0x08) | |
78 | #define QTEST_ELLIPTIC (0x10) | |
5ae3dc68 | 79 | |
c6fbc95a | 80 | /* |
81 | * Size: decimal. | |
5ae3dc68 | 82 | * Specifies the number of the most significant bit (0 to M). |
c6fbc95a | 83 | * WARNING: internally, usually 1 to N. |
5ae3dc68 | 84 | */ |
f2107e97 | 85 | #define QSIZE_MINIMUM (511) |
5ae3dc68 | 86 | |
87 | /* | |
88 | * Prime sieving defines | |
89 | */ | |
90 | ||
91 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
f2107e97 | 92 | #define SHIFT_BIT (3) |
93 | #define SHIFT_BYTE (2) | |
94 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
95 | #define SHIFT_MEGABYTE (20) | |
96 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
5ae3dc68 | 97 | |
20eea1d7 | 98 | /* |
99 | * Using virtual memory can cause thrashing. This should be the largest | |
100 | * number that is supported without a large amount of disk activity -- | |
101 | * that would increase the run time from hours to days or weeks! | |
102 | */ | |
f2107e97 | 103 | #define LARGE_MINIMUM (8UL) /* megabytes */ |
20eea1d7 | 104 | |
105 | /* | |
106 | * Do not increase this number beyond the unsigned integer bit size. | |
107 | * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). | |
108 | */ | |
f2107e97 | 109 | #define LARGE_MAXIMUM (127UL) /* megabytes */ |
20eea1d7 | 110 | |
5ae3dc68 | 111 | /* |
112 | * Constant: when used with 32-bit integers, the largest sieve prime | |
113 | * has to be less than 2**32. | |
114 | */ | |
f2107e97 | 115 | #define SMALL_MAXIMUM (0xffffffffUL) |
5ae3dc68 | 116 | |
117 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
f2107e97 | 118 | #define TINY_NUMBER (1UL<<16) |
5ae3dc68 | 119 | |
120 | /* Ensure enough bit space for testing 2*q. */ | |
4e2e5cfd | 121 | #define TEST_MAXIMUM (1UL<<16) |
122 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
123 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
124 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
5ae3dc68 | 125 | |
126 | /* bit operations on 32-bit words */ | |
4e2e5cfd | 127 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) |
128 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
129 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
5ae3dc68 | 130 | |
131 | /* | |
132 | * Prime testing defines | |
133 | */ | |
134 | ||
20eea1d7 | 135 | /* Minimum number of primality tests to perform */ |
4e2e5cfd | 136 | #define TRIAL_MINIMUM (4) |
20eea1d7 | 137 | |
5ae3dc68 | 138 | /* |
139 | * Sieving data (XXX - move to struct) | |
140 | */ | |
141 | ||
142 | /* sieve 2**16 */ | |
143 | static u_int32_t *TinySieve, tinybits; | |
144 | ||
145 | /* sieve 2**30 in 2**16 parts */ | |
146 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
147 | ||
148 | /* sieve relative to the initial value */ | |
149 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
150 | static u_int32_t largebits, largememory; /* megabytes */ | |
151 | static BIGNUM *largebase; | |
152 | ||
c784ae09 | 153 | int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); |
7e9a0e92 | 154 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); |
5ae3dc68 | 155 | |
156 | /* | |
157 | * print moduli out in consistent form, | |
158 | */ | |
159 | static int | |
160 | qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, | |
161 | u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) | |
162 | { | |
163 | struct tm *gtm; | |
164 | time_t time_now; | |
165 | int res; | |
166 | ||
167 | time(&time_now); | |
168 | gtm = gmtime(&time_now); | |
b6453d99 | 169 | |
5ae3dc68 | 170 | res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", |
171 | gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, | |
172 | gtm->tm_hour, gtm->tm_min, gtm->tm_sec, | |
173 | otype, otests, otries, osize, ogenerator); | |
174 | ||
175 | if (res < 0) | |
176 | return (-1); | |
177 | ||
178 | if (BN_print_fp(ofile, omodulus) < 1) | |
179 | return (-1); | |
180 | ||
181 | res = fprintf(ofile, "\n"); | |
182 | fflush(ofile); | |
183 | ||
184 | return (res > 0 ? 0 : -1); | |
185 | } | |
186 | ||
187 | ||
188 | /* | |
189 | ** Sieve p's and q's with small factors | |
190 | */ | |
191 | static void | |
192 | sieve_large(u_int32_t s) | |
193 | { | |
194 | u_int32_t r, u; | |
195 | ||
c6fbc95a | 196 | debug3("sieve_large %u", s); |
5ae3dc68 | 197 | largetries++; |
198 | /* r = largebase mod s */ | |
199 | r = BN_mod_word(largebase, s); | |
200 | if (r == 0) | |
201 | u = 0; /* s divides into largebase exactly */ | |
202 | else | |
203 | u = s - r; /* largebase+u is first entry divisible by s */ | |
204 | ||
205 | if (u < largebits * 2) { | |
206 | /* | |
207 | * The sieve omits p's and q's divisible by 2, so ensure that | |
208 | * largebase+u is odd. Then, step through the sieve in | |
209 | * increments of 2*s | |
210 | */ | |
211 | if (u & 0x1) | |
212 | u += s; /* Make largebase+u odd, and u even */ | |
213 | ||
214 | /* Mark all multiples of 2*s */ | |
215 | for (u /= 2; u < largebits; u += s) | |
216 | BIT_SET(LargeSieve, u); | |
217 | } | |
218 | ||
219 | /* r = p mod s */ | |
220 | r = (2 * r + 1) % s; | |
221 | if (r == 0) | |
222 | u = 0; /* s divides p exactly */ | |
223 | else | |
224 | u = s - r; /* p+u is first entry divisible by s */ | |
225 | ||
226 | if (u < largebits * 4) { | |
227 | /* | |
228 | * The sieve omits p's divisible by 4, so ensure that | |
229 | * largebase+u is not. Then, step through the sieve in | |
230 | * increments of 4*s | |
231 | */ | |
232 | while (u & 0x3) { | |
233 | if (SMALL_MAXIMUM - u < s) | |
234 | return; | |
235 | u += s; | |
236 | } | |
237 | ||
238 | /* Mark all multiples of 4*s */ | |
239 | for (u /= 4; u < largebits; u += s) | |
240 | BIT_SET(LargeSieve, u); | |
241 | } | |
242 | } | |
243 | ||
244 | /* | |
df5a0d7e | 245 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
5ae3dc68 | 246 | * to standard output. |
247 | * The list is checked against small known primes (less than 2**30). | |
248 | */ | |
249 | int | |
c784ae09 | 250 | gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) |
5ae3dc68 | 251 | { |
252 | BIGNUM *q; | |
253 | u_int32_t j, r, s, t; | |
254 | u_int32_t smallwords = TINY_NUMBER >> 6; | |
255 | u_int32_t tinywords = TINY_NUMBER >> 6; | |
256 | time_t time_start, time_stop; | |
c784ae09 | 257 | u_int32_t i; |
258 | int ret = 0; | |
5ae3dc68 | 259 | |
260 | largememory = memory; | |
261 | ||
20eea1d7 | 262 | if (memory != 0 && |
4e2e5cfd | 263 | (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { |
20eea1d7 | 264 | error("Invalid memory amount (min %ld, max %ld)", |
265 | LARGE_MINIMUM, LARGE_MAXIMUM); | |
266 | return (-1); | |
267 | } | |
268 | ||
5ae3dc68 | 269 | /* |
aff51935 | 270 | * Set power to the length in bits of the prime to be generated. |
271 | * This is changed to 1 less than the desired safe prime moduli p. | |
272 | */ | |
5ae3dc68 | 273 | if (power > TEST_MAXIMUM) { |
274 | error("Too many bits: %u > %lu", power, TEST_MAXIMUM); | |
275 | return (-1); | |
276 | } else if (power < TEST_MINIMUM) { | |
277 | error("Too few bits: %u < %u", power, TEST_MINIMUM); | |
278 | return (-1); | |
279 | } | |
280 | power--; /* decrement before squaring */ | |
281 | ||
282 | /* | |
aff51935 | 283 | * The density of ordinary primes is on the order of 1/bits, so the |
284 | * density of safe primes should be about (1/bits)**2. Set test range | |
285 | * to something well above bits**2 to be reasonably sure (but not | |
286 | * guaranteed) of catching at least one safe prime. | |
5ae3dc68 | 287 | */ |
288 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
289 | ||
290 | /* | |
aff51935 | 291 | * Need idea of how much memory is available. We don't have to use all |
292 | * of it. | |
5ae3dc68 | 293 | */ |
294 | if (largememory > LARGE_MAXIMUM) { | |
295 | logit("Limited memory: %u MB; limit %lu MB", | |
296 | largememory, LARGE_MAXIMUM); | |
297 | largememory = LARGE_MAXIMUM; | |
298 | } | |
299 | ||
300 | if (largewords <= (largememory << SHIFT_MEGAWORD)) { | |
301 | logit("Increased memory: %u MB; need %u bytes", | |
302 | largememory, (largewords << SHIFT_BYTE)); | |
303 | largewords = (largememory << SHIFT_MEGAWORD); | |
304 | } else if (largememory > 0) { | |
305 | logit("Decreased memory: %u MB; want %u bytes", | |
306 | largememory, (largewords << SHIFT_BYTE)); | |
307 | largewords = (largememory << SHIFT_MEGAWORD); | |
308 | } | |
309 | ||
52e3daed | 310 | TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); |
5ae3dc68 | 311 | tinybits = tinywords << SHIFT_WORD; |
312 | ||
52e3daed | 313 | SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); |
5ae3dc68 | 314 | smallbits = smallwords << SHIFT_WORD; |
315 | ||
316 | /* | |
317 | * dynamically determine available memory | |
318 | */ | |
319 | while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) | |
320 | largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ | |
321 | ||
322 | largebits = largewords << SHIFT_WORD; | |
323 | largenumbers = largebits * 2; /* even numbers excluded */ | |
324 | ||
325 | /* validation check: count the number of primes tried */ | |
326 | largetries = 0; | |
327 | q = BN_new(); | |
328 | ||
329 | /* | |
aff51935 | 330 | * Generate random starting point for subprime search, or use |
331 | * specified parameter. | |
5ae3dc68 | 332 | */ |
333 | largebase = BN_new(); | |
334 | if (start == NULL) | |
335 | BN_rand(largebase, power, 1, 1); | |
336 | else | |
337 | BN_copy(largebase, start); | |
338 | ||
339 | /* ensure odd */ | |
340 | BN_set_bit(largebase, 0); | |
341 | ||
342 | time(&time_start); | |
343 | ||
aff51935 | 344 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
5ae3dc68 | 345 | largenumbers, power); |
346 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
347 | ||
348 | /* | |
aff51935 | 349 | * TinySieve |
350 | */ | |
5ae3dc68 | 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 | /* | |
aff51935 | 366 | * Start the small block search at the next possible prime. To avoid |
367 | * fencepost errors, the last pass is skipped. | |
368 | */ | |
5ae3dc68 | 369 | for (smallbase = TINY_NUMBER + 3; |
4e2e5cfd | 370 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); |
371 | smallbase += TINY_NUMBER) { | |
5ae3dc68 | 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 | /* | |
aff51935 | 401 | * SmallSieve |
402 | */ | |
5ae3dc68 | 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 | BN_set_word(q, 2 * j); | |
425 | BN_add(q, q, largebase); | |
df5a0d7e | 426 | if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
5ae3dc68 | 427 | largetries, (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 | xfree(LargeSieve); | |
438 | xfree(SmallSieve); | |
439 | xfree(TinySieve); | |
440 | ||
441 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
442 | ||
443 | return (ret); | |
444 | } | |
445 | ||
446 | /* | |
447 | * perform a Miller-Rabin primality test | |
448 | * on the list of candidates | |
449 | * (checking both q and p) | |
450 | * The result is a list of so-call "safe" primes | |
451 | */ | |
452 | int | |
20eea1d7 | 453 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
5ae3dc68 | 454 | { |
455 | BIGNUM *q, *p, *a; | |
456 | BN_CTX *ctx; | |
457 | char *cp, *lp; | |
458 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
459 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
460 | time_t time_start, time_stop; | |
461 | int res; | |
462 | ||
20eea1d7 | 463 | if (trials < TRIAL_MINIMUM) { |
464 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
465 | return (-1); | |
466 | } | |
467 | ||
5ae3dc68 | 468 | time(&time_start); |
469 | ||
470 | p = BN_new(); | |
471 | q = BN_new(); | |
472 | ctx = BN_CTX_new(); | |
473 | ||
474 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
475 | ctime(&time_start), trials, generator_wanted); | |
476 | ||
477 | res = 0; | |
478 | lp = xmalloc(QLINESIZE + 1); | |
479 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
480 | int ll = strlen(lp); | |
481 | ||
482 | count_in++; | |
483 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
484 | debug2("%10u: comment or short line", count_in); | |
485 | continue; | |
486 | } | |
487 | ||
488 | /* XXX - fragile parser */ | |
489 | /* time */ | |
490 | cp = &lp[14]; /* (skip) */ | |
491 | ||
492 | /* type */ | |
493 | in_type = strtoul(cp, &cp, 10); | |
494 | ||
495 | /* tests */ | |
496 | in_tests = strtoul(cp, &cp, 10); | |
497 | ||
498 | if (in_tests & QTEST_COMPOSITE) { | |
499 | debug2("%10u: known composite", count_in); | |
500 | continue; | |
501 | } | |
c6fbc95a | 502 | |
5ae3dc68 | 503 | /* tries */ |
504 | in_tries = strtoul(cp, &cp, 10); | |
505 | ||
506 | /* size (most significant bit) */ | |
507 | in_size = strtoul(cp, &cp, 10); | |
508 | ||
509 | /* generator (hex) */ | |
510 | generator_known = strtoul(cp, &cp, 16); | |
511 | ||
512 | /* Skip white space */ | |
513 | cp += strspn(cp, " "); | |
514 | ||
515 | /* modulus (hex) */ | |
516 | switch (in_type) { | |
df5a0d7e | 517 | case QTYPE_SOPHIE_GERMAIN: |
518 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
5ae3dc68 | 519 | a = q; |
520 | BN_hex2bn(&a, cp); | |
521 | /* p = 2*q + 1 */ | |
522 | BN_lshift(p, q, 1); | |
523 | BN_add_word(p, 1); | |
524 | in_size += 1; | |
525 | generator_known = 0; | |
526 | break; | |
c6fbc95a | 527 | case QTYPE_UNSTRUCTURED: |
528 | case QTYPE_SAFE: | |
1d03d1ad | 529 | case QTYPE_SCHNORR: |
c6fbc95a | 530 | case QTYPE_STRONG: |
531 | case QTYPE_UNKNOWN: | |
5ae3dc68 | 532 | debug2("%10u: (%u)", count_in, in_type); |
533 | a = p; | |
534 | BN_hex2bn(&a, cp); | |
535 | /* q = (p-1) / 2 */ | |
536 | BN_rshift(q, p, 1); | |
537 | break; | |
c6fbc95a | 538 | default: |
539 | debug2("Unknown prime type"); | |
540 | break; | |
5ae3dc68 | 541 | } |
542 | ||
543 | /* | |
544 | * due to earlier inconsistencies in interpretation, check | |
545 | * the proposed bit size. | |
546 | */ | |
c784ae09 | 547 | if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { |
5ae3dc68 | 548 | debug2("%10u: bit size %u mismatch", count_in, in_size); |
549 | continue; | |
550 | } | |
551 | if (in_size < QSIZE_MINIMUM) { | |
552 | debug2("%10u: bit size %u too short", count_in, in_size); | |
553 | continue; | |
554 | } | |
555 | ||
556 | if (in_tests & QTEST_MILLER_RABIN) | |
557 | in_tries += trials; | |
558 | else | |
559 | in_tries = trials; | |
c6fbc95a | 560 | |
5ae3dc68 | 561 | /* |
562 | * guess unknown generator | |
563 | */ | |
564 | if (generator_known == 0) { | |
565 | if (BN_mod_word(p, 24) == 11) | |
566 | generator_known = 2; | |
567 | else if (BN_mod_word(p, 12) == 5) | |
568 | generator_known = 3; | |
569 | else { | |
570 | u_int32_t r = BN_mod_word(p, 10); | |
571 | ||
c6fbc95a | 572 | if (r == 3 || r == 7) |
5ae3dc68 | 573 | generator_known = 5; |
5ae3dc68 | 574 | } |
575 | } | |
576 | /* | |
577 | * skip tests when desired generator doesn't match | |
578 | */ | |
579 | if (generator_wanted > 0 && | |
580 | generator_wanted != generator_known) { | |
581 | debug2("%10u: generator %d != %d", | |
582 | count_in, generator_known, generator_wanted); | |
583 | continue; | |
584 | } | |
585 | ||
eb7a33b8 | 586 | /* |
587 | * Primes with no known generator are useless for DH, so | |
588 | * skip those. | |
589 | */ | |
590 | if (generator_known == 0) { | |
591 | debug2("%10u: no known generator", count_in); | |
592 | continue; | |
593 | } | |
594 | ||
5ae3dc68 | 595 | count_possible++; |
596 | ||
597 | /* | |
aff51935 | 598 | * The (1/4)^N performance bound on Miller-Rabin is |
599 | * extremely pessimistic, so don't spend a lot of time | |
600 | * really verifying that q is prime until after we know | |
601 | * that p is also prime. A single pass will weed out the | |
5ae3dc68 | 602 | * vast majority of composite q's. |
603 | */ | |
604 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
c6fbc95a | 605 | debug("%10u: q failed first possible prime test", |
5ae3dc68 | 606 | count_in); |
607 | continue; | |
608 | } | |
b6453d99 | 609 | |
5ae3dc68 | 610 | /* |
aff51935 | 611 | * q is possibly prime, so go ahead and really make sure |
612 | * that p is prime. If it is, then we can go back and do | |
613 | * the same for q. If p is composite, chances are that | |
5ae3dc68 | 614 | * will show up on the first Rabin-Miller iteration so it |
615 | * doesn't hurt to specify a high iteration count. | |
616 | */ | |
617 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
c6fbc95a | 618 | debug("%10u: p is not prime", count_in); |
5ae3dc68 | 619 | continue; |
620 | } | |
621 | debug("%10u: p is almost certainly prime", count_in); | |
622 | ||
623 | /* recheck q more rigorously */ | |
624 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
625 | debug("%10u: q is not prime", count_in); | |
626 | continue; | |
627 | } | |
628 | debug("%10u: q is almost certainly prime", count_in); | |
629 | ||
aff51935 | 630 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
5ae3dc68 | 631 | in_tries, in_size, generator_known, p)) { |
632 | res = -1; | |
633 | break; | |
634 | } | |
635 | ||
636 | count_out++; | |
637 | } | |
638 | ||
639 | time(&time_stop); | |
640 | xfree(lp); | |
641 | BN_free(p); | |
642 | BN_free(q); | |
643 | BN_CTX_free(ctx); | |
644 | ||
645 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
aff51935 | 646 | ctime(&time_stop), count_out, count_possible, |
5ae3dc68 | 647 | (long) (time_stop - time_start)); |
648 | ||
649 | return (res); | |
650 | } |