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52e3daed | 1 | /* $OpenBSD: moduli.c,v 1.13 2006/03/25 00:05:41 djm 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" | |
5ae3dc68 | 41 | #include "xmalloc.h" |
42 | #include "log.h" | |
43 | ||
44 | #include <openssl/bn.h> | |
45 | ||
5ae3dc68 | 46 | /* |
47 | * File output defines | |
48 | */ | |
49 | ||
50 | /* need line long enough for largest moduli plus headers */ | |
f2107e97 | 51 | #define QLINESIZE (100+8192) |
5ae3dc68 | 52 | |
53 | /* Type: decimal. | |
54 | * Specifies the internal structure of the prime modulus. | |
55 | */ | |
f2107e97 | 56 | #define QTYPE_UNKNOWN (0) |
57 | #define QTYPE_UNSTRUCTURED (1) | |
58 | #define QTYPE_SAFE (2) | |
1d03d1ad | 59 | #define QTYPE_SCHNORR (3) |
f2107e97 | 60 | #define QTYPE_SOPHIE_GERMAIN (4) |
61 | #define QTYPE_STRONG (5) | |
5ae3dc68 | 62 | |
63 | /* Tests: decimal (bit field). | |
64 | * Specifies the methods used in checking for primality. | |
65 | * Usually, more than one test is used. | |
66 | */ | |
f2107e97 | 67 | #define QTEST_UNTESTED (0x00) |
68 | #define QTEST_COMPOSITE (0x01) | |
69 | #define QTEST_SIEVE (0x02) | |
70 | #define QTEST_MILLER_RABIN (0x04) | |
71 | #define QTEST_JACOBI (0x08) | |
72 | #define QTEST_ELLIPTIC (0x10) | |
5ae3dc68 | 73 | |
c6fbc95a | 74 | /* |
75 | * Size: decimal. | |
5ae3dc68 | 76 | * Specifies the number of the most significant bit (0 to M). |
c6fbc95a | 77 | * WARNING: internally, usually 1 to N. |
5ae3dc68 | 78 | */ |
f2107e97 | 79 | #define QSIZE_MINIMUM (511) |
5ae3dc68 | 80 | |
81 | /* | |
82 | * Prime sieving defines | |
83 | */ | |
84 | ||
85 | /* Constant: assuming 8 bit bytes and 32 bit words */ | |
f2107e97 | 86 | #define SHIFT_BIT (3) |
87 | #define SHIFT_BYTE (2) | |
88 | #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) | |
89 | #define SHIFT_MEGABYTE (20) | |
90 | #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) | |
5ae3dc68 | 91 | |
20eea1d7 | 92 | /* |
93 | * Using virtual memory can cause thrashing. This should be the largest | |
94 | * number that is supported without a large amount of disk activity -- | |
95 | * that would increase the run time from hours to days or weeks! | |
96 | */ | |
f2107e97 | 97 | #define LARGE_MINIMUM (8UL) /* megabytes */ |
20eea1d7 | 98 | |
99 | /* | |
100 | * Do not increase this number beyond the unsigned integer bit size. | |
101 | * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). | |
102 | */ | |
f2107e97 | 103 | #define LARGE_MAXIMUM (127UL) /* megabytes */ |
20eea1d7 | 104 | |
5ae3dc68 | 105 | /* |
106 | * Constant: when used with 32-bit integers, the largest sieve prime | |
107 | * has to be less than 2**32. | |
108 | */ | |
f2107e97 | 109 | #define SMALL_MAXIMUM (0xffffffffUL) |
5ae3dc68 | 110 | |
111 | /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ | |
f2107e97 | 112 | #define TINY_NUMBER (1UL<<16) |
5ae3dc68 | 113 | |
114 | /* Ensure enough bit space for testing 2*q. */ | |
4e2e5cfd | 115 | #define TEST_MAXIMUM (1UL<<16) |
116 | #define TEST_MINIMUM (QSIZE_MINIMUM + 1) | |
117 | /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ | |
118 | #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ | |
5ae3dc68 | 119 | |
120 | /* bit operations on 32-bit words */ | |
4e2e5cfd | 121 | #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) |
122 | #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) | |
123 | #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) | |
5ae3dc68 | 124 | |
125 | /* | |
126 | * Prime testing defines | |
127 | */ | |
128 | ||
20eea1d7 | 129 | /* Minimum number of primality tests to perform */ |
4e2e5cfd | 130 | #define TRIAL_MINIMUM (4) |
20eea1d7 | 131 | |
5ae3dc68 | 132 | /* |
133 | * Sieving data (XXX - move to struct) | |
134 | */ | |
135 | ||
136 | /* sieve 2**16 */ | |
137 | static u_int32_t *TinySieve, tinybits; | |
138 | ||
139 | /* sieve 2**30 in 2**16 parts */ | |
140 | static u_int32_t *SmallSieve, smallbits, smallbase; | |
141 | ||
142 | /* sieve relative to the initial value */ | |
143 | static u_int32_t *LargeSieve, largewords, largetries, largenumbers; | |
144 | static u_int32_t largebits, largememory; /* megabytes */ | |
145 | static BIGNUM *largebase; | |
146 | ||
c784ae09 | 147 | int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); |
7e9a0e92 | 148 | int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); |
5ae3dc68 | 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); | |
b6453d99 | 163 | |
5ae3dc68 | 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 | ||
c6fbc95a | 190 | debug3("sieve_large %u", s); |
5ae3dc68 | 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 | /* | |
df5a0d7e | 239 | * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
5ae3dc68 | 240 | * to standard output. |
241 | * The list is checked against small known primes (less than 2**30). | |
242 | */ | |
243 | int | |
c784ae09 | 244 | gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) |
5ae3dc68 | 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; | |
c784ae09 | 251 | u_int32_t i; |
252 | int ret = 0; | |
5ae3dc68 | 253 | |
254 | largememory = memory; | |
255 | ||
20eea1d7 | 256 | if (memory != 0 && |
4e2e5cfd | 257 | (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { |
20eea1d7 | 258 | error("Invalid memory amount (min %ld, max %ld)", |
259 | LARGE_MINIMUM, LARGE_MAXIMUM); | |
260 | return (-1); | |
261 | } | |
262 | ||
5ae3dc68 | 263 | /* |
aff51935 | 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 | */ | |
5ae3dc68 | 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 | /* | |
aff51935 | 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. | |
5ae3dc68 | 281 | */ |
282 | largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); | |
283 | ||
284 | /* | |
aff51935 | 285 | * Need idea of how much memory is available. We don't have to use all |
286 | * of it. | |
5ae3dc68 | 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 | ||
52e3daed | 304 | TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); |
5ae3dc68 | 305 | tinybits = tinywords << SHIFT_WORD; |
306 | ||
52e3daed | 307 | SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); |
5ae3dc68 | 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 | q = BN_new(); | |
322 | ||
323 | /* | |
aff51935 | 324 | * Generate random starting point for subprime search, or use |
325 | * specified parameter. | |
5ae3dc68 | 326 | */ |
327 | largebase = BN_new(); | |
328 | if (start == NULL) | |
329 | BN_rand(largebase, power, 1, 1); | |
330 | else | |
331 | BN_copy(largebase, start); | |
332 | ||
333 | /* ensure odd */ | |
334 | BN_set_bit(largebase, 0); | |
335 | ||
336 | time(&time_start); | |
337 | ||
aff51935 | 338 | logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
5ae3dc68 | 339 | largenumbers, power); |
340 | debug2("start point: 0x%s", BN_bn2hex(largebase)); | |
341 | ||
342 | /* | |
aff51935 | 343 | * TinySieve |
344 | */ | |
5ae3dc68 | 345 | for (i = 0; i < tinybits; i++) { |
346 | if (BIT_TEST(TinySieve, i)) | |
347 | continue; /* 2*i+3 is composite */ | |
348 | ||
349 | /* The next tiny prime */ | |
350 | t = 2 * i + 3; | |
351 | ||
352 | /* Mark all multiples of t */ | |
353 | for (j = i + t; j < tinybits; j += t) | |
354 | BIT_SET(TinySieve, j); | |
355 | ||
356 | sieve_large(t); | |
357 | } | |
358 | ||
359 | /* | |
aff51935 | 360 | * Start the small block search at the next possible prime. To avoid |
361 | * fencepost errors, the last pass is skipped. | |
362 | */ | |
5ae3dc68 | 363 | for (smallbase = TINY_NUMBER + 3; |
4e2e5cfd | 364 | smallbase < (SMALL_MAXIMUM - TINY_NUMBER); |
365 | smallbase += TINY_NUMBER) { | |
5ae3dc68 | 366 | for (i = 0; i < tinybits; i++) { |
367 | if (BIT_TEST(TinySieve, i)) | |
368 | continue; /* 2*i+3 is composite */ | |
369 | ||
370 | /* The next tiny prime */ | |
371 | t = 2 * i + 3; | |
372 | r = smallbase % t; | |
373 | ||
374 | if (r == 0) { | |
375 | s = 0; /* t divides into smallbase exactly */ | |
376 | } else { | |
377 | /* smallbase+s is first entry divisible by t */ | |
378 | s = t - r; | |
379 | } | |
380 | ||
381 | /* | |
382 | * The sieve omits even numbers, so ensure that | |
383 | * smallbase+s is odd. Then, step through the sieve | |
384 | * in increments of 2*t | |
385 | */ | |
386 | if (s & 1) | |
387 | s += t; /* Make smallbase+s odd, and s even */ | |
388 | ||
389 | /* Mark all multiples of 2*t */ | |
390 | for (s /= 2; s < smallbits; s += t) | |
391 | BIT_SET(SmallSieve, s); | |
392 | } | |
393 | ||
394 | /* | |
aff51935 | 395 | * SmallSieve |
396 | */ | |
5ae3dc68 | 397 | for (i = 0; i < smallbits; i++) { |
398 | if (BIT_TEST(SmallSieve, i)) | |
399 | continue; /* 2*i+smallbase is composite */ | |
400 | ||
401 | /* The next small prime */ | |
402 | sieve_large((2 * i) + smallbase); | |
403 | } | |
404 | ||
405 | memset(SmallSieve, 0, smallwords << SHIFT_BYTE); | |
406 | } | |
407 | ||
408 | time(&time_stop); | |
409 | ||
410 | logit("%.24s Sieved with %u small primes in %ld seconds", | |
411 | ctime(&time_stop), largetries, (long) (time_stop - time_start)); | |
412 | ||
413 | for (j = r = 0; j < largebits; j++) { | |
414 | if (BIT_TEST(LargeSieve, j)) | |
415 | continue; /* Definitely composite, skip */ | |
416 | ||
417 | debug2("test q = largebase+%u", 2 * j); | |
418 | BN_set_word(q, 2 * j); | |
419 | BN_add(q, q, largebase); | |
df5a0d7e | 420 | if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
5ae3dc68 | 421 | largetries, (power - 1) /* MSB */, (0), q) == -1) { |
422 | ret = -1; | |
423 | break; | |
424 | } | |
425 | ||
426 | r++; /* count q */ | |
427 | } | |
428 | ||
429 | time(&time_stop); | |
430 | ||
431 | xfree(LargeSieve); | |
432 | xfree(SmallSieve); | |
433 | xfree(TinySieve); | |
434 | ||
435 | logit("%.24s Found %u candidates", ctime(&time_stop), r); | |
436 | ||
437 | return (ret); | |
438 | } | |
439 | ||
440 | /* | |
441 | * perform a Miller-Rabin primality test | |
442 | * on the list of candidates | |
443 | * (checking both q and p) | |
444 | * The result is a list of so-call "safe" primes | |
445 | */ | |
446 | int | |
20eea1d7 | 447 | prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
5ae3dc68 | 448 | { |
449 | BIGNUM *q, *p, *a; | |
450 | BN_CTX *ctx; | |
451 | char *cp, *lp; | |
452 | u_int32_t count_in = 0, count_out = 0, count_possible = 0; | |
453 | u_int32_t generator_known, in_tests, in_tries, in_type, in_size; | |
454 | time_t time_start, time_stop; | |
455 | int res; | |
456 | ||
20eea1d7 | 457 | if (trials < TRIAL_MINIMUM) { |
458 | error("Minimum primality trials is %d", TRIAL_MINIMUM); | |
459 | return (-1); | |
460 | } | |
461 | ||
5ae3dc68 | 462 | time(&time_start); |
463 | ||
464 | p = BN_new(); | |
465 | q = BN_new(); | |
466 | ctx = BN_CTX_new(); | |
467 | ||
468 | debug2("%.24s Final %u Miller-Rabin trials (%x generator)", | |
469 | ctime(&time_start), trials, generator_wanted); | |
470 | ||
471 | res = 0; | |
472 | lp = xmalloc(QLINESIZE + 1); | |
473 | while (fgets(lp, QLINESIZE, in) != NULL) { | |
474 | int ll = strlen(lp); | |
475 | ||
476 | count_in++; | |
477 | if (ll < 14 || *lp == '!' || *lp == '#') { | |
478 | debug2("%10u: comment or short line", count_in); | |
479 | continue; | |
480 | } | |
481 | ||
482 | /* XXX - fragile parser */ | |
483 | /* time */ | |
484 | cp = &lp[14]; /* (skip) */ | |
485 | ||
486 | /* type */ | |
487 | in_type = strtoul(cp, &cp, 10); | |
488 | ||
489 | /* tests */ | |
490 | in_tests = strtoul(cp, &cp, 10); | |
491 | ||
492 | if (in_tests & QTEST_COMPOSITE) { | |
493 | debug2("%10u: known composite", count_in); | |
494 | continue; | |
495 | } | |
c6fbc95a | 496 | |
5ae3dc68 | 497 | /* tries */ |
498 | in_tries = strtoul(cp, &cp, 10); | |
499 | ||
500 | /* size (most significant bit) */ | |
501 | in_size = strtoul(cp, &cp, 10); | |
502 | ||
503 | /* generator (hex) */ | |
504 | generator_known = strtoul(cp, &cp, 16); | |
505 | ||
506 | /* Skip white space */ | |
507 | cp += strspn(cp, " "); | |
508 | ||
509 | /* modulus (hex) */ | |
510 | switch (in_type) { | |
df5a0d7e | 511 | case QTYPE_SOPHIE_GERMAIN: |
512 | debug2("%10u: (%u) Sophie-Germain", count_in, in_type); | |
5ae3dc68 | 513 | a = q; |
514 | BN_hex2bn(&a, cp); | |
515 | /* p = 2*q + 1 */ | |
516 | BN_lshift(p, q, 1); | |
517 | BN_add_word(p, 1); | |
518 | in_size += 1; | |
519 | generator_known = 0; | |
520 | break; | |
c6fbc95a | 521 | case QTYPE_UNSTRUCTURED: |
522 | case QTYPE_SAFE: | |
1d03d1ad | 523 | case QTYPE_SCHNORR: |
c6fbc95a | 524 | case QTYPE_STRONG: |
525 | case QTYPE_UNKNOWN: | |
5ae3dc68 | 526 | debug2("%10u: (%u)", count_in, in_type); |
527 | a = p; | |
528 | BN_hex2bn(&a, cp); | |
529 | /* q = (p-1) / 2 */ | |
530 | BN_rshift(q, p, 1); | |
531 | break; | |
c6fbc95a | 532 | default: |
533 | debug2("Unknown prime type"); | |
534 | break; | |
5ae3dc68 | 535 | } |
536 | ||
537 | /* | |
538 | * due to earlier inconsistencies in interpretation, check | |
539 | * the proposed bit size. | |
540 | */ | |
c784ae09 | 541 | if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { |
5ae3dc68 | 542 | debug2("%10u: bit size %u mismatch", count_in, in_size); |
543 | continue; | |
544 | } | |
545 | if (in_size < QSIZE_MINIMUM) { | |
546 | debug2("%10u: bit size %u too short", count_in, in_size); | |
547 | continue; | |
548 | } | |
549 | ||
550 | if (in_tests & QTEST_MILLER_RABIN) | |
551 | in_tries += trials; | |
552 | else | |
553 | in_tries = trials; | |
c6fbc95a | 554 | |
5ae3dc68 | 555 | /* |
556 | * guess unknown generator | |
557 | */ | |
558 | if (generator_known == 0) { | |
559 | if (BN_mod_word(p, 24) == 11) | |
560 | generator_known = 2; | |
561 | else if (BN_mod_word(p, 12) == 5) | |
562 | generator_known = 3; | |
563 | else { | |
564 | u_int32_t r = BN_mod_word(p, 10); | |
565 | ||
c6fbc95a | 566 | if (r == 3 || r == 7) |
5ae3dc68 | 567 | generator_known = 5; |
5ae3dc68 | 568 | } |
569 | } | |
570 | /* | |
571 | * skip tests when desired generator doesn't match | |
572 | */ | |
573 | if (generator_wanted > 0 && | |
574 | generator_wanted != generator_known) { | |
575 | debug2("%10u: generator %d != %d", | |
576 | count_in, generator_known, generator_wanted); | |
577 | continue; | |
578 | } | |
579 | ||
eb7a33b8 | 580 | /* |
581 | * Primes with no known generator are useless for DH, so | |
582 | * skip those. | |
583 | */ | |
584 | if (generator_known == 0) { | |
585 | debug2("%10u: no known generator", count_in); | |
586 | continue; | |
587 | } | |
588 | ||
5ae3dc68 | 589 | count_possible++; |
590 | ||
591 | /* | |
aff51935 | 592 | * The (1/4)^N performance bound on Miller-Rabin is |
593 | * extremely pessimistic, so don't spend a lot of time | |
594 | * really verifying that q is prime until after we know | |
595 | * that p is also prime. A single pass will weed out the | |
5ae3dc68 | 596 | * vast majority of composite q's. |
597 | */ | |
598 | if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { | |
c6fbc95a | 599 | debug("%10u: q failed first possible prime test", |
5ae3dc68 | 600 | count_in); |
601 | continue; | |
602 | } | |
b6453d99 | 603 | |
5ae3dc68 | 604 | /* |
aff51935 | 605 | * q is possibly prime, so go ahead and really make sure |
606 | * that p is prime. If it is, then we can go back and do | |
607 | * the same for q. If p is composite, chances are that | |
5ae3dc68 | 608 | * will show up on the first Rabin-Miller iteration so it |
609 | * doesn't hurt to specify a high iteration count. | |
610 | */ | |
611 | if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { | |
c6fbc95a | 612 | debug("%10u: p is not prime", count_in); |
5ae3dc68 | 613 | continue; |
614 | } | |
615 | debug("%10u: p is almost certainly prime", count_in); | |
616 | ||
617 | /* recheck q more rigorously */ | |
618 | if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { | |
619 | debug("%10u: q is not prime", count_in); | |
620 | continue; | |
621 | } | |
622 | debug("%10u: q is almost certainly prime", count_in); | |
623 | ||
aff51935 | 624 | if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
5ae3dc68 | 625 | in_tries, in_size, generator_known, p)) { |
626 | res = -1; | |
627 | break; | |
628 | } | |
629 | ||
630 | count_out++; | |
631 | } | |
632 | ||
633 | time(&time_stop); | |
634 | xfree(lp); | |
635 | BN_free(p); | |
636 | BN_free(q); | |
637 | BN_CTX_free(ctx); | |
638 | ||
639 | logit("%.24s Found %u safe primes of %u candidates in %ld seconds", | |
aff51935 | 640 | ctime(&time_stop), count_out, count_possible, |
5ae3dc68 | 641 | (long) (time_stop - time_start)); |
642 | ||
643 | return (res); | |
644 | } |