1 /* $NetBSD: moduli.c,v 1.19 2026/04/08 18:58:40 christos Exp $ */ 2 /* $OpenBSD: moduli.c,v 1.41 2026/03/03 09:57:25 dtucker Exp $ */ 3 4 /* 5 * Copyright 1994 Phil Karn <karn (at) qualcomm.com> 6 * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson (at) greendragon.com> 7 * Copyright 2000 Niels Provos <provos (at) citi.umich.edu> 8 * All rights reserved. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 19 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR 20 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES 21 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. 22 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, 23 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT 24 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 25 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 26 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 27 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF 28 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 29 */ 30 31 /* 32 * Two-step process to generate safe primes for DHGEX 33 * 34 * Sieve candidates for "safe" primes, 35 * suitable for use as Diffie-Hellman moduli; 36 * that is, where q = (p-1)/2 is also prime. 37 * 38 * First step: generate candidate primes (memory intensive) 39 * Second step: test primes' safety (processor intensive) 40 */ 41 #include "includes.h" 42 __RCSID("$NetBSD: moduli.c,v 1.19 2026/04/08 18:58:40 christos Exp $"); 43 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 * Do not increase this number beyond the unsigned integer bit size. 90 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 91 */ 92 #define LARGE_MAXIMUM (127UL) /* megabytes */ 93 94 /* 95 * Constant: when used with 32-bit integers, the largest sieve prime 96 * has to be less than 2**32. 97 */ 98 #define SMALL_MAXIMUM (0xffffffffUL) 99 100 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 101 #define TINY_NUMBER (1UL<<16) 102 103 /* Ensure enough bit space for testing 2*q. */ 104 #define TEST_MAXIMUM (1UL<<16) 105 #define TEST_MINIMUM (QSIZE_MINIMUM + 1) 106 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 107 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 108 109 /* bit operations on 32-bit words */ 110 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 111 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 112 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 113 114 /* 115 * Prime testing defines 116 */ 117 118 /* Minimum number of primality tests to perform */ 119 #define TRIAL_MINIMUM (4) 120 121 /* 122 * Sieving data (XXX - move to struct) 123 */ 124 125 /* sieve 2**16 */ 126 static uint32_t *TinySieve, tinybits; 127 128 /* sieve 2**30 in 2**16 parts */ 129 static uint32_t *SmallSieve, smallbits, smallbase; 130 131 /* sieve relative to the initial value */ 132 static uint32_t *LargeSieve, largewords, largetries, largenumbers; 133 static uint32_t largebits, largememory; /* megabytes */ 134 static BIGNUM *largebase; 135 136 int gen_candidates(FILE *, uint32_t, BIGNUM *); 137 int prime_test(FILE *, FILE *, uint32_t, uint32_t, char *, unsigned long, 138 unsigned long); 139 140 /* 141 * print moduli out in consistent form, 142 */ 143 static int 144 qfileout(FILE * ofile, uint32_t otype, uint32_t otests, uint32_t otries, 145 uint32_t osize, uint32_t ogenerator, BIGNUM * omodulus) 146 { 147 struct tm *gtm; 148 time_t time_now; 149 int res; 150 151 time(&time_now); 152 gtm = gmtime(&time_now); 153 if (gtm == NULL) 154 return -1; 155 156 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 157 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 158 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 159 otype, otests, otries, osize, ogenerator); 160 161 if (res < 0) 162 return (-1); 163 164 if (BN_print_fp(ofile, omodulus) < 1) 165 return (-1); 166 167 res = fprintf(ofile, "\n"); 168 fflush(ofile); 169 170 return (res > 0 ? 0 : -1); 171 } 172 173 174 /* 175 ** Sieve p's and q's with small factors 176 */ 177 static void 178 sieve_large(uint32_t s32) 179 { 180 uint64_t r, u, s = s32; 181 182 debug3("sieve_large %u", s32); 183 largetries++; 184 /* r = largebase mod s */ 185 r = BN_mod_word(largebase, s32); 186 if (r == 0) 187 u = 0; /* s divides into largebase exactly */ 188 else 189 u = s - r; /* largebase+u is first entry divisible by s */ 190 191 if (u < largebits * 2ULL) { 192 /* 193 * The sieve omits p's and q's divisible by 2, so ensure that 194 * largebase+u is odd. Then, step through the sieve in 195 * increments of 2*s 196 */ 197 if (u & 0x1) 198 u += s; /* Make largebase+u odd, and u even */ 199 200 /* Mark all multiples of 2*s */ 201 for (u /= 2; u < largebits; u += s) 202 BIT_SET(LargeSieve, u); 203 } 204 205 /* r = p mod s */ 206 r = (2 * r + 1) % s; 207 if (r == 0) 208 u = 0; /* s divides p exactly */ 209 else 210 u = s - r; /* p+u is first entry divisible by s */ 211 212 if (u < largebits * 4ULL) { 213 /* 214 * The sieve omits p's divisible by 4, so ensure that 215 * largebase+u is not. Then, step through the sieve in 216 * increments of 4*s 217 */ 218 while (u & 0x3) { 219 if (SMALL_MAXIMUM - u < s) 220 return; 221 u += s; 222 } 223 224 /* Mark all multiples of 4*s */ 225 for (u /= 4; u < largebits; u += s) 226 BIT_SET(LargeSieve, u); 227 } 228 } 229 230 /* 231 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 232 * to standard output. 233 * The list is checked against small known primes (less than 2**30). 234 */ 235 int 236 gen_candidates(FILE *out, uint32_t power, BIGNUM *start) 237 { 238 BIGNUM *q; 239 uint32_t j, r, s, t; 240 uint32_t smallwords = TINY_NUMBER >> 6; 241 uint32_t tinywords = TINY_NUMBER >> 6; 242 time_t time_start, time_stop; 243 uint32_t i; 244 int ret = 0; 245 246 /* 247 * Set power to the length in bits of the prime to be generated. 248 * This is changed to 1 less than the desired safe prime moduli p. 249 */ 250 if (power > TEST_MAXIMUM) { 251 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 252 return (-1); 253 } else if (power < TEST_MINIMUM) { 254 error("Too few bits: %u < %u", power, TEST_MINIMUM); 255 return (-1); 256 } 257 power--; /* decrement before squaring */ 258 259 /* Always use the maximum amount of memory supported by the algorithm. */ 260 largememory = LARGE_MAXIMUM; 261 largewords = (largememory << SHIFT_MEGAWORD); 262 263 TinySieve = xcalloc(tinywords, sizeof(uint32_t)); 264 tinybits = tinywords << SHIFT_WORD; 265 266 SmallSieve = xcalloc(smallwords, sizeof(uint32_t)); 267 smallbits = smallwords << SHIFT_WORD; 268 269 LargeSieve = xcalloc(largewords, sizeof(uint32_t)); 270 largebits = largewords << SHIFT_WORD; 271 largenumbers = largebits * 2; /* even numbers excluded */ 272 273 /* validation check: count the number of primes tried */ 274 largetries = 0; 275 if ((q = BN_new()) == NULL) 276 fatal("BN_new failed"); 277 278 /* 279 * Generate random starting point for subprime search, or use 280 * specified parameter. 281 */ 282 if ((largebase = BN_new()) == NULL) 283 fatal("BN_new failed"); 284 if (start == NULL) { 285 if (BN_rand(largebase, power, 1, 1) == 0) 286 fatal("BN_rand failed"); 287 } else { 288 if (BN_copy(largebase, start) == NULL) 289 fatal("BN_copy: failed"); 290 } 291 292 /* ensure odd */ 293 if (BN_set_bit(largebase, 0) == 0) 294 fatal("BN_set_bit: failed"); 295 296 time(&time_start); 297 298 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 299 largenumbers, power); 300 debug2("start point: 0x%s", BN_bn2hex(largebase)); 301 302 /* 303 * TinySieve 304 */ 305 for (i = 0; i < tinybits; i++) { 306 if (BIT_TEST(TinySieve, i)) 307 continue; /* 2*i+3 is composite */ 308 309 /* The next tiny prime */ 310 t = 2 * i + 3; 311 312 /* Mark all multiples of t */ 313 for (j = i + t; j < tinybits; j += t) 314 BIT_SET(TinySieve, j); 315 316 sieve_large(t); 317 } 318 319 /* 320 * Start the small block search at the next possible prime. To avoid 321 * fencepost errors, the last pass is skipped. 322 */ 323 for (smallbase = TINY_NUMBER + 3; 324 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 325 smallbase += TINY_NUMBER) { 326 for (i = 0; i < tinybits; i++) { 327 if (BIT_TEST(TinySieve, i)) 328 continue; /* 2*i+3 is composite */ 329 330 /* The next tiny prime */ 331 t = 2 * i + 3; 332 r = smallbase % t; 333 334 if (r == 0) { 335 s = 0; /* t divides into smallbase exactly */ 336 } else { 337 /* smallbase+s is first entry divisible by t */ 338 s = t - r; 339 } 340 341 /* 342 * The sieve omits even numbers, so ensure that 343 * smallbase+s is odd. Then, step through the sieve 344 * in increments of 2*t 345 */ 346 if (s & 1) 347 s += t; /* Make smallbase+s odd, and s even */ 348 349 /* Mark all multiples of 2*t */ 350 for (s /= 2; s < smallbits; s += t) 351 BIT_SET(SmallSieve, s); 352 } 353 354 /* 355 * SmallSieve 356 */ 357 for (i = 0; i < smallbits; i++) { 358 if (BIT_TEST(SmallSieve, i)) 359 continue; /* 2*i+smallbase is composite */ 360 361 /* The next small prime */ 362 sieve_large((2 * i) + smallbase); 363 } 364 365 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 366 } 367 368 time(&time_stop); 369 370 logit("%.24s Sieved with %u small primes in %lld seconds", 371 ctime(&time_stop), largetries, (long long)(time_stop - time_start)); 372 373 for (j = r = 0; j < largebits; j++) { 374 if (BIT_TEST(LargeSieve, j)) 375 continue; /* Definitely composite, skip */ 376 377 debug2("test q = largebase+%u", 2 * j); 378 if (BN_set_word(q, 2 * j) == 0) 379 fatal("BN_set_word failed"); 380 if (BN_add(q, q, largebase) == 0) 381 fatal("BN_add failed"); 382 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 383 MODULI_TESTS_SIEVE, largetries, 384 (power - 1) /* MSB */, (0), q) == -1) { 385 ret = -1; 386 break; 387 } 388 389 r++; /* count q */ 390 } 391 392 time(&time_stop); 393 394 free(LargeSieve); 395 free(SmallSieve); 396 free(TinySieve); 397 398 logit("%.24s Found %u candidates", ctime(&time_stop), r); 399 400 return (ret); 401 } 402 403 static void 404 write_checkpoint(char *cpfile, uint32_t lineno) 405 { 406 FILE *fp; 407 char tmp[PATH_MAX]; 408 int r, writeok, closeok; 409 410 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 411 if (r < 0 || r >= PATH_MAX) { 412 logit("write_checkpoint: temp pathname too long"); 413 return; 414 } 415 if ((r = mkstemp(tmp)) == -1) { 416 logit("mkstemp(%s): %s", tmp, strerror(errno)); 417 return; 418 } 419 if ((fp = fdopen(r, "w")) == NULL) { 420 logit("write_checkpoint: fdopen: %s", strerror(errno)); 421 unlink(tmp); 422 close(r); 423 return; 424 } 425 writeok = (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0); 426 closeok = (fclose(fp) == 0); 427 if (writeok && closeok && rename(tmp, cpfile) == 0) { 428 debug3("wrote checkpoint line %lu to '%s'", 429 (unsigned long)lineno, cpfile); 430 } else { 431 logit("failed to write to checkpoint file '%s': %s", cpfile, 432 strerror(errno)); 433 (void)unlink(tmp); 434 } 435 } 436 437 static unsigned long 438 read_checkpoint(char *cpfile) 439 { 440 FILE *fp; 441 unsigned long lineno = 0; 442 443 if ((fp = fopen(cpfile, "r")) == NULL) 444 return 0; 445 if (fscanf(fp, "%lu\n", &lineno) < 1) 446 logit("Failed to load checkpoint from '%s'", cpfile); 447 else 448 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 449 fclose(fp); 450 return lineno; 451 } 452 453 static unsigned long 454 count_lines(FILE *f) 455 { 456 unsigned long count = 0; 457 char lp[QLINESIZE + 1]; 458 459 if (fseek(f, 0, SEEK_SET) != 0) { 460 debug("input file is not seekable"); 461 return ULONG_MAX; 462 } 463 while (fgets(lp, QLINESIZE + 1, f) != NULL) 464 count++; 465 rewind(f); 466 debug("input file has %lu lines", count); 467 return count; 468 } 469 470 static char * 471 fmt_time(time_t seconds) 472 { 473 int day, hr, min; 474 static char buf[128]; 475 476 min = (seconds / 60) % 60; 477 hr = (seconds / 60 / 60) % 24; 478 day = seconds / 60 / 60 / 24; 479 if (day > 0) 480 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 481 else 482 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 483 return buf; 484 } 485 486 static void 487 print_progress(unsigned long start_lineno, unsigned long current_lineno, 488 unsigned long end_lineno) 489 { 490 static time_t time_start, time_prev; 491 time_t time_now, elapsed; 492 unsigned long num_to_process, processed, remaining, percent, eta; 493 double time_per_line; 494 char *eta_str; 495 496 time_now = monotime(); 497 if (time_start == 0) { 498 time_start = time_prev = time_now; 499 return; 500 } 501 /* print progress after 1m then once per 5m */ 502 if (time_now - time_prev < 5 * 60) 503 return; 504 time_prev = time_now; 505 elapsed = time_now - time_start; 506 processed = current_lineno - start_lineno; 507 remaining = end_lineno - current_lineno; 508 num_to_process = end_lineno - start_lineno; 509 time_per_line = (double)elapsed / processed; 510 /* if we don't know how many we're processing just report count+time */ 511 time(&time_now); 512 if (end_lineno == ULONG_MAX) { 513 logit("%.24s processed %lu in %s", ctime(&time_now), 514 processed, fmt_time(elapsed)); 515 return; 516 } 517 percent = 100 * processed / num_to_process; 518 eta = time_per_line * remaining; 519 eta_str = xstrdup(fmt_time(eta)); 520 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 521 ctime(&time_now), processed, num_to_process, percent, 522 fmt_time(elapsed), eta_str); 523 free(eta_str); 524 } 525 526 /* 527 * perform a Miller-Rabin primality test 528 * on the list of candidates 529 * (checking both q and p) 530 * The result is a list of so-call "safe" primes 531 */ 532 int 533 prime_test(FILE *in, FILE *out, uint32_t trials, uint32_t generator_wanted, 534 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 535 { 536 BIGNUM *q, *p, *a; 537 char *cp, *lp; 538 uint32_t count_in = 0, count_out = 0, count_possible = 0; 539 uint32_t generator_known, in_tests, in_tries, in_type, in_size; 540 unsigned long last_processed = 0, end_lineno; 541 time_t time_start, time_stop; 542 int res, is_prime; 543 544 if (trials < TRIAL_MINIMUM) { 545 error("Minimum primality trials is %d", TRIAL_MINIMUM); 546 return (-1); 547 } 548 549 if (num_lines == 0) 550 end_lineno = count_lines(in); 551 else 552 end_lineno = start_lineno + num_lines; 553 554 time(&time_start); 555 556 if ((p = BN_new()) == NULL) 557 fatal("BN_new failed"); 558 if ((q = BN_new()) == NULL) 559 fatal("BN_new failed"); 560 561 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 562 ctime(&time_start), trials, generator_wanted); 563 564 if (checkpoint_file != NULL) 565 last_processed = read_checkpoint(checkpoint_file); 566 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); 567 if (end_lineno == ULONG_MAX) 568 debug("process from line %lu from pipe", last_processed); 569 else 570 debug("process from line %lu to line %lu", last_processed, 571 end_lineno); 572 573 res = 0; 574 lp = xmalloc(QLINESIZE + 1); 575 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 576 count_in++; 577 if (count_in <= last_processed) { 578 debug3("skipping line %u, before checkpoint or " 579 "specified start line", count_in); 580 continue; 581 } 582 if (checkpoint_file != NULL) 583 write_checkpoint(checkpoint_file, count_in); 584 print_progress(start_lineno, count_in, end_lineno); 585 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 586 debug2("%10u: comment or short line", count_in); 587 continue; 588 } 589 590 /* XXX - fragile parser */ 591 /* time */ 592 cp = &lp[14]; /* (skip) */ 593 594 /* type */ 595 in_type = strtoul(cp, &cp, 10); 596 597 /* tests */ 598 in_tests = strtoul(cp, &cp, 10); 599 600 if (in_tests & MODULI_TESTS_COMPOSITE) { 601 debug2("%10u: known composite", count_in); 602 continue; 603 } 604 605 /* tries */ 606 in_tries = strtoul(cp, &cp, 10); 607 608 /* size (most significant bit) */ 609 in_size = strtoul(cp, &cp, 10); 610 611 /* generator (hex) */ 612 generator_known = strtoul(cp, &cp, 16); 613 614 /* Skip white space */ 615 cp += strspn(cp, " "); 616 617 /* modulus (hex) */ 618 switch (in_type) { 619 case MODULI_TYPE_SOPHIE_GERMAIN: 620 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 621 a = q; 622 if (BN_hex2bn(&a, cp) == 0) 623 fatal("BN_hex2bn failed"); 624 /* p = 2*q + 1 */ 625 if (BN_lshift(p, q, 1) == 0) 626 fatal("BN_lshift failed"); 627 if (BN_add_word(p, 1) == 0) 628 fatal("BN_add_word failed"); 629 in_size += 1; 630 generator_known = 0; 631 break; 632 case MODULI_TYPE_UNSTRUCTURED: 633 case MODULI_TYPE_SAFE: 634 case MODULI_TYPE_SCHNORR: 635 case MODULI_TYPE_STRONG: 636 case MODULI_TYPE_UNKNOWN: 637 debug2("%10u: (%u)", count_in, in_type); 638 a = p; 639 if (BN_hex2bn(&a, cp) == 0) 640 fatal("BN_hex2bn failed"); 641 /* q = (p-1) / 2 */ 642 if (BN_rshift(q, p, 1) == 0) 643 fatal("BN_rshift failed"); 644 break; 645 default: 646 debug2("Unknown prime type"); 647 break; 648 } 649 650 /* 651 * due to earlier inconsistencies in interpretation, check 652 * the proposed bit size. 653 */ 654 if ((uint32_t)BN_num_bits(p) != (in_size + 1)) { 655 debug2("%10u: bit size %u mismatch", count_in, in_size); 656 continue; 657 } 658 if (in_size < QSIZE_MINIMUM) { 659 debug2("%10u: bit size %u too short", count_in, in_size); 660 continue; 661 } 662 663 if (in_tests & MODULI_TESTS_MILLER_RABIN) 664 in_tries += trials; 665 else 666 in_tries = trials; 667 668 /* 669 * guess unknown generator 670 */ 671 if (generator_known == 0) { 672 if (BN_mod_word(p, 24) == 11) 673 generator_known = 2; 674 else { 675 uint32_t r = BN_mod_word(p, 10); 676 677 if (r == 3 || r == 7) 678 generator_known = 5; 679 } 680 } 681 /* 682 * skip tests when desired generator doesn't match 683 */ 684 if (generator_wanted > 0 && 685 generator_wanted != generator_known) { 686 debug2("%10u: generator %d != %d", 687 count_in, generator_known, generator_wanted); 688 continue; 689 } 690 691 /* 692 * Primes with no known generator are useless for DH, so 693 * skip those. 694 */ 695 if (generator_known == 0) { 696 debug2("%10u: no known generator", count_in); 697 continue; 698 } 699 700 count_possible++; 701 702 /* 703 * The (1/4)^N performance bound on Miller-Rabin is 704 * extremely pessimistic, so don't spend a lot of time 705 * really verifying that q is prime until after we know 706 * that p is also prime. A single pass will weed out the 707 * vast majority of composite q's. 708 */ 709 is_prime = BN_is_prime_ex(q, 1, NULL, NULL); 710 if (is_prime < 0) 711 fatal("BN_is_prime_ex failed"); 712 if (is_prime == 0) { 713 debug("%10u: q failed first possible prime test", 714 count_in); 715 continue; 716 } 717 718 /* 719 * q is possibly prime, so go ahead and really make sure 720 * that p is prime. If it is, then we can go back and do 721 * the same for q. If p is composite, chances are that 722 * will show up on the first Rabin-Miller iteration so it 723 * doesn't hurt to specify a high iteration count. 724 */ 725 is_prime = BN_is_prime_ex(p, trials, NULL, NULL); 726 if (is_prime < 0) 727 fatal("BN_is_prime_ex failed"); 728 if (is_prime == 0) { 729 debug("%10u: p is not prime", count_in); 730 continue; 731 } 732 debug("%10u: p is almost certainly prime", count_in); 733 734 /* recheck q more rigorously */ 735 is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL); 736 if (is_prime < 0) 737 fatal("BN_is_prime_ex failed"); 738 if (is_prime == 0) { 739 debug("%10u: q is not prime", count_in); 740 continue; 741 } 742 debug("%10u: q is almost certainly prime", count_in); 743 744 if (qfileout(out, MODULI_TYPE_SAFE, 745 in_tests | MODULI_TESTS_MILLER_RABIN, 746 in_tries, in_size, generator_known, p)) { 747 res = -1; 748 break; 749 } 750 751 count_out++; 752 } 753 754 time(&time_stop); 755 free(lp); 756 BN_free(p); 757 BN_free(q); 758 759 if (checkpoint_file != NULL) 760 unlink(checkpoint_file); 761 762 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 763 ctime(&time_stop), count_out, count_possible, 764 (long) (time_stop - time_start)); 765 766 return (res); 767 } 768
Indexes created Tue Aug 18 00:25:06 UTC 2026