1 /* $NetBSD: moduli.c,v 1.8 2015/04/03 23:58:19 christos Exp $ */ 2 /* $OpenBSD: moduli.c,v 1.30 2015/01/20 23:14:00 deraadt Exp $ */ 3 /* 4 * Copyright 1994 Phil Karn <karn@qualcomm.com> 5 * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> 6 * Copyright 2000 Niels Provos <provos@citi.umich.edu> 7 * All rights reserved. 8 * 9 * Redistribution and use in source and binary forms, with or without 10 * modification, are permitted provided that the following conditions 11 * are met: 12 * 1. Redistributions of source code must retain the above copyright 13 * notice, this list of conditions and the following disclaimer. 14 * 2. Redistributions in binary form must reproduce the above copyright 15 * notice, this list of conditions and the following disclaimer in the 16 * documentation and/or other materials provided with the distribution. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 19 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 20 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 21 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 22 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 23 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 24 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 25 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 26 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 27 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 28 */ 29 30 /* 31 * Two-step process to generate safe primes for DHGEX 32 * 33 * Sieve candidates for "safe" primes, 34 * suitable for use as Diffie-Hellman moduli; 35 * that is, where q = (p-1)/2 is also prime. 36 * 37 * First step: generate candidate primes (memory intensive) 38 * Second step: test primes' safety (processor intensive) 39 */ 40 #include "includes.h" 41 __RCSID("$NetBSD: moduli.c,v 1.8 2015/04/03 23:58:19 christos Exp $"); 42 43 #include <sys/param.h> /* MAX */ 44 #include <sys/types.h> 45 46 #include <openssl/bn.h> 47 #include <openssl/dh.h> 48 49 #include <errno.h> 50 #include <stdio.h> 51 #include <stdlib.h> 52 #include <string.h> 53 #include <stdarg.h> 54 #include <time.h> 55 #include <unistd.h> 56 #include <limits.h> 57 58 #include "xmalloc.h" 59 #include "dh.h" 60 #include "log.h" 61 #include "misc.h" 62 63 /* 64 * File output defines 65 */ 66 67 /* need line long enough for largest moduli plus headers */ 68 #define QLINESIZE (100+8192) 69 70 /* 71 * Size: decimal. 72 * Specifies the number of the most significant bit (0 to M). 73 * WARNING: internally, usually 1 to N. 74 */ 75 #define QSIZE_MINIMUM (511) 76 77 /* 78 * Prime sieving defines 79 */ 80 81 /* Constant: assuming 8 bit bytes and 32 bit words */ 82 #define SHIFT_BIT (3) 83 #define SHIFT_BYTE (2) 84 #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) 85 #define SHIFT_MEGABYTE (20) 86 #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) 87 88 /* 89 * Using virtual memory can cause thrashing. This should be the largest 90 * number that is supported without a large amount of disk activity -- 91 * that would increase the run time from hours to days or weeks! 92 */ 93 #define LARGE_MINIMUM (8UL) /* megabytes */ 94 95 /* 96 * Do not increase this number beyond the unsigned integer bit size. 97 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 98 */ 99 #define LARGE_MAXIMUM (127UL) /* megabytes */ 100 101 /* 102 * Constant: when used with 32-bit integers, the largest sieve prime 103 * has to be less than 2**32. 104 */ 105 #define SMALL_MAXIMUM (0xffffffffUL) 106 107 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 108 #define TINY_NUMBER (1UL<<16) 109 110 /* Ensure enough bit space for testing 2*q. */ 111 #define TEST_MAXIMUM (1UL<<16) 112 #define TEST_MINIMUM (QSIZE_MINIMUM + 1) 113 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 114 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 115 116 /* bit operations on 32-bit words */ 117 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 118 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 119 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 120 121 /* 122 * Prime testing defines 123 */ 124 125 /* Minimum number of primality tests to perform */ 126 #define TRIAL_MINIMUM (4) 127 128 /* 129 * Sieving data (XXX - move to struct) 130 */ 131 132 /* sieve 2**16 */ 133 static u_int32_t *TinySieve, tinybits; 134 135 /* sieve 2**30 in 2**16 parts */ 136 static u_int32_t *SmallSieve, smallbits, smallbase; 137 138 /* sieve relative to the initial value */ 139 static u_int32_t *LargeSieve, largewords, largetries, largenumbers; 140 static u_int32_t largebits, largememory; /* megabytes */ 141 static BIGNUM *largebase; 142 143 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); 144 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, 145 unsigned long); 146 147 /* 148 * print moduli out in consistent form, 149 */ 150 static int 151 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, 152 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) 153 { 154 struct tm *gtm; 155 time_t time_now; 156 int res; 157 158 time(&time_now); 159 gtm = gmtime(&time_now); 160 161 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 162 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 163 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 164 otype, otests, otries, osize, ogenerator); 165 166 if (res < 0) 167 return (-1); 168 169 if (BN_print_fp(ofile, omodulus) < 1) 170 return (-1); 171 172 res = fprintf(ofile, "\n"); 173 fflush(ofile); 174 175 return (res > 0 ? 0 : -1); 176 } 177 178 179 /* 180 ** Sieve p's and q's with small factors 181 */ 182 static void 183 sieve_large(u_int32_t s) 184 { 185 u_int32_t r, u; 186 187 debug3("sieve_large %u", s); 188 largetries++; 189 /* r = largebase mod s */ 190 r = BN_mod_word(largebase, s); 191 if (r == 0) 192 u = 0; /* s divides into largebase exactly */ 193 else 194 u = s - r; /* largebase+u is first entry divisible by s */ 195 196 if (u < largebits * 2) { 197 /* 198 * The sieve omits p's and q's divisible by 2, so ensure that 199 * largebase+u is odd. Then, step through the sieve in 200 * increments of 2*s 201 */ 202 if (u & 0x1) 203 u += s; /* Make largebase+u odd, and u even */ 204 205 /* Mark all multiples of 2*s */ 206 for (u /= 2; u < largebits; u += s) 207 BIT_SET(LargeSieve, u); 208 } 209 210 /* r = p mod s */ 211 r = (2 * r + 1) % s; 212 if (r == 0) 213 u = 0; /* s divides p exactly */ 214 else 215 u = s - r; /* p+u is first entry divisible by s */ 216 217 if (u < largebits * 4) { 218 /* 219 * The sieve omits p's divisible by 4, so ensure that 220 * largebase+u is not. Then, step through the sieve in 221 * increments of 4*s 222 */ 223 while (u & 0x3) { 224 if (SMALL_MAXIMUM - u < s) 225 return; 226 u += s; 227 } 228 229 /* Mark all multiples of 4*s */ 230 for (u /= 4; u < largebits; u += s) 231 BIT_SET(LargeSieve, u); 232 } 233 } 234 235 /* 236 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 237 * to standard output. 238 * The list is checked against small known primes (less than 2**30). 239 */ 240 int 241 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) 242 { 243 BIGNUM *q; 244 u_int32_t j, r, s, t; 245 u_int32_t smallwords = TINY_NUMBER >> 6; 246 u_int32_t tinywords = TINY_NUMBER >> 6; 247 time_t time_start, time_stop; 248 u_int32_t i; 249 int ret = 0; 250 251 largememory = memory; 252 253 if (memory != 0 && 254 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { 255 error("Invalid memory amount (min %ld, max %ld)", 256 LARGE_MINIMUM, LARGE_MAXIMUM); 257 return (-1); 258 } 259 260 /* 261 * Set power to the length in bits of the prime to be generated. 262 * This is changed to 1 less than the desired safe prime moduli p. 263 */ 264 if (power > TEST_MAXIMUM) { 265 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 266 return (-1); 267 } else if (power < TEST_MINIMUM) { 268 error("Too few bits: %u < %u", power, TEST_MINIMUM); 269 return (-1); 270 } 271 power--; /* decrement before squaring */ 272 273 /* 274 * The density of ordinary primes is on the order of 1/bits, so the 275 * density of safe primes should be about (1/bits)**2. Set test range 276 * to something well above bits**2 to be reasonably sure (but not 277 * guaranteed) of catching at least one safe prime. 278 */ 279 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); 280 281 /* 282 * Need idea of how much memory is available. We don't have to use all 283 * of it. 284 */ 285 if (largememory > LARGE_MAXIMUM) { 286 logit("Limited memory: %u MB; limit %lu MB", 287 largememory, LARGE_MAXIMUM); 288 largememory = LARGE_MAXIMUM; 289 } 290 291 if (largewords <= (largememory << SHIFT_MEGAWORD)) { 292 logit("Increased memory: %u MB; need %u bytes", 293 largememory, (largewords << SHIFT_BYTE)); 294 largewords = (largememory << SHIFT_MEGAWORD); 295 } else if (largememory > 0) { 296 logit("Decreased memory: %u MB; want %u bytes", 297 largememory, (largewords << SHIFT_BYTE)); 298 largewords = (largememory << SHIFT_MEGAWORD); 299 } 300 301 TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); 302 tinybits = tinywords << SHIFT_WORD; 303 304 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); 305 smallbits = smallwords << SHIFT_WORD; 306 307 /* 308 * dynamically determine available memory 309 */ 310 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) 311 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ 312 313 largebits = largewords << SHIFT_WORD; 314 largenumbers = largebits * 2; /* even numbers excluded */ 315 316 /* validation check: count the number of primes tried */ 317 largetries = 0; 318 if ((q = BN_new()) == NULL) 319 fatal("BN_new failed"); 320 321 /* 322 * Generate random starting point for subprime search, or use 323 * specified parameter. 324 */ 325 if ((largebase = BN_new()) == NULL) 326 fatal("BN_new failed"); 327 if (start == NULL) { 328 if (BN_rand(largebase, power, 1, 1) == 0) 329 fatal("BN_rand failed"); 330 } else { 331 if (BN_copy(largebase, start) == NULL) 332 fatal("BN_copy: failed"); 333 } 334 335 /* ensure odd */ 336 if (BN_set_bit(largebase, 0) == 0) 337 fatal("BN_set_bit: failed"); 338 339 time(&time_start); 340 341 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 342 largenumbers, power); 343 debug2("start point: 0x%s", BN_bn2hex(largebase)); 344 345 /* 346 * TinySieve 347 */ 348 for (i = 0; i < tinybits; i++) { 349 if (BIT_TEST(TinySieve, i)) 350 continue; /* 2*i+3 is composite */ 351 352 /* The next tiny prime */ 353 t = 2 * i + 3; 354 355 /* Mark all multiples of t */ 356 for (j = i + t; j < tinybits; j += t) 357 BIT_SET(TinySieve, j); 358 359 sieve_large(t); 360 } 361 362 /* 363 * Start the small block search at the next possible prime. To avoid 364 * fencepost errors, the last pass is skipped. 365 */ 366 for (smallbase = TINY_NUMBER + 3; 367 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 368 smallbase += TINY_NUMBER) { 369 for (i = 0; i < tinybits; i++) { 370 if (BIT_TEST(TinySieve, i)) 371 continue; /* 2*i+3 is composite */ 372 373 /* The next tiny prime */ 374 t = 2 * i + 3; 375 r = smallbase % t; 376 377 if (r == 0) { 378 s = 0; /* t divides into smallbase exactly */ 379 } else { 380 /* smallbase+s is first entry divisible by t */ 381 s = t - r; 382 } 383 384 /* 385 * The sieve omits even numbers, so ensure that 386 * smallbase+s is odd. Then, step through the sieve 387 * in increments of 2*t 388 */ 389 if (s & 1) 390 s += t; /* Make smallbase+s odd, and s even */ 391 392 /* Mark all multiples of 2*t */ 393 for (s /= 2; s < smallbits; s += t) 394 BIT_SET(SmallSieve, s); 395 } 396 397 /* 398 * SmallSieve 399 */ 400 for (i = 0; i < smallbits; i++) { 401 if (BIT_TEST(SmallSieve, i)) 402 continue; /* 2*i+smallbase is composite */ 403 404 /* The next small prime */ 405 sieve_large((2 * i) + smallbase); 406 } 407 408 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 409 } 410 411 time(&time_stop); 412 413 logit("%.24s Sieved with %u small primes in %ld seconds", 414 ctime(&time_stop), largetries, (long) (time_stop - time_start)); 415 416 for (j = r = 0; j < largebits; j++) { 417 if (BIT_TEST(LargeSieve, j)) 418 continue; /* Definitely composite, skip */ 419 420 debug2("test q = largebase+%u", 2 * j); 421 if (BN_set_word(q, 2 * j) == 0) 422 fatal("BN_set_word failed"); 423 if (BN_add(q, q, largebase) == 0) 424 fatal("BN_add failed"); 425 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 426 MODULI_TESTS_SIEVE, largetries, 427 (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 free(LargeSieve); 438 free(SmallSieve); 439 free(TinySieve); 440 441 logit("%.24s Found %u candidates", ctime(&time_stop), r); 442 443 return (ret); 444 } 445 446 static void 447 write_checkpoint(char *cpfile, u_int32_t lineno) 448 { 449 FILE *fp; 450 char tmp[PATH_MAX]; 451 int r; 452 453 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 454 if (r == -1 || r >= PATH_MAX) { 455 logit("write_checkpoint: temp pathname too long"); 456 return; 457 } 458 if ((r = mkstemp(tmp)) == -1) { 459 logit("mkstemp(%s): %s", tmp, strerror(errno)); 460 return; 461 } 462 if ((fp = fdopen(r, "w")) == NULL) { 463 logit("write_checkpoint: fdopen: %s", strerror(errno)); 464 unlink(tmp); 465 close(r); 466 return; 467 } 468 if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0 469 && rename(tmp, cpfile) == 0) 470 debug3("wrote checkpoint line %lu to '%s'", 471 (unsigned long)lineno, cpfile); 472 else 473 logit("failed to write to checkpoint file '%s': %s", cpfile, 474 strerror(errno)); 475 } 476 477 static unsigned long 478 read_checkpoint(char *cpfile) 479 { 480 FILE *fp; 481 unsigned long lineno = 0; 482 483 if ((fp = fopen(cpfile, "r")) == NULL) 484 return 0; 485 if (fscanf(fp, "%lu\n", &lineno) < 1) 486 logit("Failed to load checkpoint from '%s'", cpfile); 487 else 488 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 489 fclose(fp); 490 return lineno; 491 } 492 493 static unsigned long 494 count_lines(FILE *f) 495 { 496 unsigned long count = 0; 497 char lp[QLINESIZE + 1]; 498 499 if (fseek(f, 0, SEEK_SET) != 0) { 500 debug("input file is not seekable"); 501 return ULONG_MAX; 502 } 503 while (fgets(lp, QLINESIZE + 1, f) != NULL) 504 count++; 505 rewind(f); 506 debug("input file has %lu lines", count); 507 return count; 508 } 509 510 static char * 511 fmt_time(time_t seconds) 512 { 513 int day, hr, min; 514 static char buf[128]; 515 516 min = (seconds / 60) % 60; 517 hr = (seconds / 60 / 60) % 24; 518 day = seconds / 60 / 60 / 24; 519 if (day > 0) 520 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 521 else 522 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 523 return buf; 524 } 525 526 static void 527 print_progress(unsigned long start_lineno, unsigned long current_lineno, 528 unsigned long end_lineno) 529 { 530 static time_t time_start, time_prev; 531 time_t time_now, elapsed; 532 unsigned long num_to_process, processed, remaining, percent, eta; 533 double time_per_line; 534 char *eta_str; 535 536 time_now = monotime(); 537 if (time_start == 0) { 538 time_start = time_prev = time_now; 539 return; 540 } 541 /* print progress after 1m then once per 5m */ 542 if (time_now - time_prev < 5 * 60) 543 return; 544 time_prev = time_now; 545 elapsed = time_now - time_start; 546 processed = current_lineno - start_lineno; 547 remaining = end_lineno - current_lineno; 548 num_to_process = end_lineno - start_lineno; 549 time_per_line = (double)elapsed / processed; 550 /* if we don't know how many we're processing just report count+time */ 551 time(&time_now); 552 if (end_lineno == ULONG_MAX) { 553 logit("%.24s processed %lu in %s", ctime(&time_now), 554 processed, fmt_time(elapsed)); 555 return; 556 } 557 percent = 100 * processed / num_to_process; 558 eta = time_per_line * remaining; 559 eta_str = xstrdup(fmt_time(eta)); 560 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 561 ctime(&time_now), processed, num_to_process, percent, 562 fmt_time(elapsed), eta_str); 563 free(eta_str); 564 } 565 566 /* 567 * perform a Miller-Rabin primality test 568 * on the list of candidates 569 * (checking both q and p) 570 * The result is a list of so-call "safe" primes 571 */ 572 int 573 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, 574 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 575 { 576 BIGNUM *q, *p, *a; 577 BN_CTX *ctx; 578 char *cp, *lp; 579 u_int32_t count_in = 0, count_out = 0, count_possible = 0; 580 u_int32_t generator_known, in_tests, in_tries, in_type, in_size; 581 unsigned long last_processed = 0, end_lineno; 582 time_t time_start, time_stop; 583 int res; 584 585 if (trials < TRIAL_MINIMUM) { 586 error("Minimum primality trials is %d", TRIAL_MINIMUM); 587 return (-1); 588 } 589 590 if (num_lines == 0) 591 end_lineno = count_lines(in); 592 else 593 end_lineno = start_lineno + num_lines; 594 595 time(&time_start); 596 597 if ((p = BN_new()) == NULL) 598 fatal("BN_new failed"); 599 if ((q = BN_new()) == NULL) 600 fatal("BN_new failed"); 601 if ((ctx = BN_CTX_new()) == NULL) 602 fatal("BN_CTX_new failed"); 603 604 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 605 ctime(&time_start), trials, generator_wanted); 606 607 if (checkpoint_file != NULL) 608 last_processed = read_checkpoint(checkpoint_file); 609 last_processed = start_lineno = MAX(last_processed, start_lineno); 610 if (end_lineno == ULONG_MAX) 611 debug("process from line %lu from pipe", last_processed); 612 else 613 debug("process from line %lu to line %lu", last_processed, 614 end_lineno); 615 616 res = 0; 617 lp = xmalloc(QLINESIZE + 1); 618 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 619 count_in++; 620 if (count_in <= last_processed) { 621 debug3("skipping line %u, before checkpoint or " 622 "specified start line", count_in); 623 continue; 624 } 625 if (checkpoint_file != NULL) 626 write_checkpoint(checkpoint_file, count_in); 627 print_progress(start_lineno, count_in, end_lineno); 628 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 629 debug2("%10u: comment or short line", count_in); 630 continue; 631 } 632 633 /* XXX - fragile parser */ 634 /* time */ 635 cp = &lp[14]; /* (skip) */ 636 637 /* type */ 638 in_type = strtoul(cp, &cp, 10); 639 640 /* tests */ 641 in_tests = strtoul(cp, &cp, 10); 642 643 if (in_tests & MODULI_TESTS_COMPOSITE) { 644 debug2("%10u: known composite", count_in); 645 continue; 646 } 647 648 /* tries */ 649 in_tries = strtoul(cp, &cp, 10); 650 651 /* size (most significant bit) */ 652 in_size = strtoul(cp, &cp, 10); 653 654 /* generator (hex) */ 655 generator_known = strtoul(cp, &cp, 16); 656 657 /* Skip white space */ 658 cp += strspn(cp, " "); 659 660 /* modulus (hex) */ 661 switch (in_type) { 662 case MODULI_TYPE_SOPHIE_GERMAIN: 663 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 664 a = q; 665 if (BN_hex2bn(&a, cp) == 0) 666 fatal("BN_hex2bn failed"); 667 /* p = 2*q + 1 */ 668 if (BN_lshift(p, q, 1) == 0) 669 fatal("BN_lshift failed"); 670 if (BN_add_word(p, 1) == 0) 671 fatal("BN_add_word failed"); 672 in_size += 1; 673 generator_known = 0; 674 break; 675 case MODULI_TYPE_UNSTRUCTURED: 676 case MODULI_TYPE_SAFE: 677 case MODULI_TYPE_SCHNORR: 678 case MODULI_TYPE_STRONG: 679 case MODULI_TYPE_UNKNOWN: 680 debug2("%10u: (%u)", count_in, in_type); 681 a = p; 682 if (BN_hex2bn(&a, cp) == 0) 683 fatal("BN_hex2bn failed"); 684 /* q = (p-1) / 2 */ 685 if (BN_rshift(q, p, 1) == 0) 686 fatal("BN_rshift failed"); 687 break; 688 default: 689 debug2("Unknown prime type"); 690 break; 691 } 692 693 /* 694 * due to earlier inconsistencies in interpretation, check 695 * the proposed bit size. 696 */ 697 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { 698 debug2("%10u: bit size %u mismatch", count_in, in_size); 699 continue; 700 } 701 if (in_size < QSIZE_MINIMUM) { 702 debug2("%10u: bit size %u too short", count_in, in_size); 703 continue; 704 } 705 706 if (in_tests & MODULI_TESTS_MILLER_RABIN) 707 in_tries += trials; 708 else 709 in_tries = trials; 710 711 /* 712 * guess unknown generator 713 */ 714 if (generator_known == 0) { 715 if (BN_mod_word(p, 24) == 11) 716 generator_known = 2; 717 else if (BN_mod_word(p, 12) == 5) 718 generator_known = 3; 719 else { 720 u_int32_t r = BN_mod_word(p, 10); 721 722 if (r == 3 || r == 7) 723 generator_known = 5; 724 } 725 } 726 /* 727 * skip tests when desired generator doesn't match 728 */ 729 if (generator_wanted > 0 && 730 generator_wanted != generator_known) { 731 debug2("%10u: generator %d != %d", 732 count_in, generator_known, generator_wanted); 733 continue; 734 } 735 736 /* 737 * Primes with no known generator are useless for DH, so 738 * skip those. 739 */ 740 if (generator_known == 0) { 741 debug2("%10u: no known generator", count_in); 742 continue; 743 } 744 745 count_possible++; 746 747 /* 748 * The (1/4)^N performance bound on Miller-Rabin is 749 * extremely pessimistic, so don't spend a lot of time 750 * really verifying that q is prime until after we know 751 * that p is also prime. A single pass will weed out the 752 * vast majority of composite q's. 753 */ 754 if (BN_is_prime_ex(q, 1, ctx, NULL) <= 0) { 755 debug("%10u: q failed first possible prime test", 756 count_in); 757 continue; 758 } 759 760 /* 761 * q is possibly prime, so go ahead and really make sure 762 * that p is prime. If it is, then we can go back and do 763 * the same for q. If p is composite, chances are that 764 * will show up on the first Rabin-Miller iteration so it 765 * doesn't hurt to specify a high iteration count. 766 */ 767 if (!BN_is_prime_ex(p, trials, ctx, NULL)) { 768 debug("%10u: p is not prime", count_in); 769 continue; 770 } 771 debug("%10u: p is almost certainly prime", count_in); 772 773 /* recheck q more rigorously */ 774 if (!BN_is_prime_ex(q, trials - 1, ctx, NULL)) { 775 debug("%10u: q is not prime", count_in); 776 continue; 777 } 778 debug("%10u: q is almost certainly prime", count_in); 779 780 if (qfileout(out, MODULI_TYPE_SAFE, 781 in_tests | MODULI_TESTS_MILLER_RABIN, 782 in_tries, in_size, generator_known, p)) { 783 res = -1; 784 break; 785 } 786 787 count_out++; 788 } 789 790 time(&time_stop); 791 free(lp); 792 BN_free(p); 793 BN_free(q); 794 BN_CTX_free(ctx); 795 796 if (checkpoint_file != NULL) 797 unlink(checkpoint_file); 798 799 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 800 ctime(&time_stop), count_out, count_possible, 801 (long) (time_stop - time_start)); 802 803 return (res); 804 } 805