1/* $NetBSD: moduli.c,v 1.17 2023/07/26 17:58:15 christos Exp $ */ 2/* $OpenBSD: moduli.c,v 1.39 2023/03/02 06:41:56 dtucker 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 1.17 2023/07/26 17:58:15 christos Exp $"); 42 43#include <sys/types.h> 44 45#include <openssl/bn.h> 46#include <openssl/dh.h> 47 48#include <errno.h> 49#include <stdio.h> 50#include <stdlib.h> 51#include <string.h> 52#include <stdarg.h> 53#include <time.h> 54#include <unistd.h> 55#include <limits.h> 56 57#include "xmalloc.h" 58#include "dh.h" 59#include "log.h" 60#include "misc.h" 61 62/* 63 * File output defines 64 */ 65 66/* need line long enough for largest moduli plus headers */ 67#define QLINESIZE (100+8192) 68 69/* 70 * Size: decimal. 71 * Specifies the number of the most significant bit (0 to M). 72 * WARNING: internally, usually 1 to N. 73 */ 74#define QSIZE_MINIMUM (511) 75 76/* 77 * Prime sieving defines 78 */ 79 80/* Constant: assuming 8 bit bytes and 32 bit words */ 81#define SHIFT_BIT (3) 82#define SHIFT_BYTE (2) 83#define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) 84#define SHIFT_MEGABYTE (20) 85#define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) 86 87/* 88 * Using virtual memory can cause thrashing. This should be the largest 89 * number that is supported without a large amount of disk activity -- 90 * that would increase the run time from hours to days or weeks! 91 */ 92#define LARGE_MINIMUM (8UL) /* megabytes */ 93 94/* 95 * Do not increase this number beyond the unsigned integer bit size. 96 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 97 */ 98#define LARGE_MAXIMUM (127UL) /* megabytes */ 99 100/* 101 * Constant: when used with 32-bit integers, the largest sieve prime 102 * has to be less than 2**32. 103 */ 104#define SMALL_MAXIMUM (0xffffffffUL) 105 106/* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 107#define TINY_NUMBER (1UL<<16) 108 109/* Ensure enough bit space for testing 2*q. */ 110#define TEST_MAXIMUM (1UL<<16) 111#define TEST_MINIMUM (QSIZE_MINIMUM + 1) 112/* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 113#define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 114 115/* bit operations on 32-bit words */ 116#define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 117#define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 118#define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 119 120/* 121 * Prime testing defines 122 */ 123 124/* Minimum number of primality tests to perform */ 125#define TRIAL_MINIMUM (4) 126 127/* 128 * Sieving data (XXX - move to struct) 129 */ 130 131/* sieve 2**16 */ 132static u_int32_t *TinySieve, tinybits; 133 134/* sieve 2**30 in 2**16 parts */ 135static u_int32_t *SmallSieve, smallbits, smallbase; 136 137/* sieve relative to the initial value */ 138static u_int32_t *LargeSieve, largewords, largetries, largenumbers; 139static u_int32_t largebits, largememory; /* megabytes */ 140static BIGNUM *largebase; 141 142int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); 143int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, 144 unsigned long); 145 146/* 147 * print moduli out in consistent form, 148 */ 149static int 150qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, 151 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) 152{ 153 struct tm *gtm; 154 time_t time_now; 155 int res; 156 157 time(&time_now); 158 gtm = gmtime(&time_now); 159 if (gtm == NULL) 160 return -1; 161 162 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 163 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 164 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 165 otype, otests, otries, osize, ogenerator); 166 167 if (res < 0) 168 return (-1); 169 170 if (BN_print_fp(ofile, omodulus) < 1) 171 return (-1); 172 173 res = fprintf(ofile, "\n"); 174 fflush(ofile); 175 176 return (res > 0 ? 0 : -1); 177} 178 179 180/* 181 ** Sieve p's and q's with small factors 182 */ 183static void 184sieve_large(u_int32_t s32) 185{ 186 u_int64_t r, u, s = s32; 187 188 debug3("sieve_large %u", s32); 189 largetries++; 190 /* r = largebase mod s */ 191 r = BN_mod_word(largebase, s32); 192 if (r == 0) 193 u = 0; /* s divides into largebase exactly */ 194 else 195 u = s - r; /* largebase+u is first entry divisible by s */ 196 197 if (u < largebits * 2ULL) { 198 /* 199 * The sieve omits p's and q's divisible by 2, so ensure that 200 * largebase+u is odd. Then, step through the sieve in 201 * increments of 2*s 202 */ 203 if (u & 0x1) 204 u += s; /* Make largebase+u odd, and u even */ 205 206 /* Mark all multiples of 2*s */ 207 for (u /= 2; u < largebits; u += s) 208 BIT_SET(LargeSieve, u); 209 } 210 211 /* r = p mod s */ 212 r = (2 * r + 1) % s; 213 if (r == 0) 214 u = 0; /* s divides p exactly */ 215 else 216 u = s - r; /* p+u is first entry divisible by s */ 217 218 if (u < largebits * 4ULL) { 219 /* 220 * The sieve omits p's divisible by 4, so ensure that 221 * largebase+u is not. Then, step through the sieve in 222 * increments of 4*s 223 */ 224 while (u & 0x3) { 225 if (SMALL_MAXIMUM - u < s) 226 return; 227 u += s; 228 } 229 230 /* Mark all multiples of 4*s */ 231 for (u /= 4; u < largebits; u += s) 232 BIT_SET(LargeSieve, u); 233 } 234} 235 236/* 237 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 238 * to standard output. 239 * The list is checked against small known primes (less than 2**30). 240 */ 241int 242gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) 243{ 244 BIGNUM *q; 245 u_int32_t j, r, s, t; 246 u_int32_t smallwords = TINY_NUMBER >> 6; 247 u_int32_t tinywords = TINY_NUMBER >> 6; 248 time_t time_start, time_stop; 249 u_int32_t i; 250 int ret = 0; 251 252 largememory = memory; 253 254 if (memory != 0 && 255 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { 256 error("Invalid memory amount (min %ld, max %ld)", 257 LARGE_MINIMUM, LARGE_MAXIMUM); 258 return (-1); 259 } 260 261 /* 262 * Set power to the length in bits of the prime to be generated. 263 * This is changed to 1 less than the desired safe prime moduli p. 264 */ 265 if (power > TEST_MAXIMUM) { 266 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 267 return (-1); 268 } else if (power < TEST_MINIMUM) { 269 error("Too few bits: %u < %u", power, TEST_MINIMUM); 270 return (-1); 271 } 272 power--; /* decrement before squaring */ 273 274 /* 275 * The density of ordinary primes is on the order of 1/bits, so the 276 * density of safe primes should be about (1/bits)**2. Set test range 277 * to something well above bits**2 to be reasonably sure (but not 278 * guaranteed) of catching at least one safe prime. 279 */ 280 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); 281 282 /* 283 * Need idea of how much memory is available. We don't have to use all 284 * of it. 285 */ 286 if (largememory > LARGE_MAXIMUM) { 287 logit("Limited memory: %u MB; limit %lu MB", 288 largememory, LARGE_MAXIMUM); 289 largememory = LARGE_MAXIMUM; 290 } 291 292 if (largewords <= (largememory << SHIFT_MEGAWORD)) { 293 logit("Increased memory: %u MB; need %u bytes", 294 largememory, (largewords << SHIFT_BYTE)); 295 largewords = (largememory << SHIFT_MEGAWORD); 296 } else if (largememory > 0) { 297 logit("Decreased memory: %u MB; want %u bytes", 298 largememory, (largewords << SHIFT_BYTE)); 299 largewords = (largememory << SHIFT_MEGAWORD); 300 } 301 302 TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); 303 tinybits = tinywords << SHIFT_WORD; 304 305 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); 306 smallbits = smallwords << SHIFT_WORD; 307 308 /* 309 * dynamically determine available memory 310 */ 311 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) 312 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ 313 314 largebits = largewords << SHIFT_WORD; 315 largenumbers = largebits * 2; /* even numbers excluded */ 316 317 /* validation check: count the number of primes tried */ 318 largetries = 0; 319 if ((q = BN_new()) == NULL) 320 fatal("BN_new failed"); 321 322 /* 323 * Generate random starting point for subprime search, or use 324 * specified parameter. 325 */ 326 if ((largebase = BN_new()) == NULL) 327 fatal("BN_new failed"); 328 if (start == NULL) { 329 if (BN_rand(largebase, power, 1, 1) == 0) 330 fatal("BN_rand failed"); 331 } else { 332 if (BN_copy(largebase, start) == NULL) 333 fatal("BN_copy: failed"); 334 } 335 336 /* ensure odd */ 337 if (BN_set_bit(largebase, 0) == 0) 338 fatal("BN_set_bit: failed"); 339 340 time(&time_start); 341 342 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 343 largenumbers, power); 344 debug2("start point: 0x%s", BN_bn2hex(largebase)); 345 346 /* 347 * TinySieve 348 */ 349 for (i = 0; i < tinybits; i++) { 350 if (BIT_TEST(TinySieve, i)) 351 continue; /* 2*i+3 is composite */ 352 353 /* The next tiny prime */ 354 t = 2 * i + 3; 355 356 /* Mark all multiples of t */ 357 for (j = i + t; j < tinybits; j += t) 358 BIT_SET(TinySieve, j); 359 360 sieve_large(t); 361 } 362 363 /* 364 * Start the small block search at the next possible prime. To avoid 365 * fencepost errors, the last pass is skipped. 366 */ 367 for (smallbase = TINY_NUMBER + 3; 368 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 369 smallbase += TINY_NUMBER) { 370 for (i = 0; i < tinybits; i++) { 371 if (BIT_TEST(TinySieve, i)) 372 continue; /* 2*i+3 is composite */ 373 374 /* The next tiny prime */ 375 t = 2 * i + 3; 376 r = smallbase % t; 377 378 if (r == 0) { 379 s = 0; /* t divides into smallbase exactly */ 380 } else { 381 /* smallbase+s is first entry divisible by t */ 382 s = t - r; 383 } 384 385 /* 386 * The sieve omits even numbers, so ensure that 387 * smallbase+s is odd. Then, step through the sieve 388 * in increments of 2*t 389 */ 390 if (s & 1) 391 s += t; /* Make smallbase+s odd, and s even */ 392 393 /* Mark all multiples of 2*t */ 394 for (s /= 2; s < smallbits; s += t) 395 BIT_SET(SmallSieve, s); 396 } 397 398 /* 399 * SmallSieve 400 */ 401 for (i = 0; i < smallbits; i++) { 402 if (BIT_TEST(SmallSieve, i)) 403 continue; /* 2*i+smallbase is composite */ 404 405 /* The next small prime */ 406 sieve_large((2 * i) + smallbase); 407 } 408 409 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 410 } 411 412 time(&time_stop); 413 414 logit("%.24s Sieved with %u small primes in %lld seconds", 415 ctime(&time_stop), largetries, (long long)(time_stop - time_start)); 416 417 for (j = r = 0; j < largebits; j++) { 418 if (BIT_TEST(LargeSieve, j)) 419 continue; /* Definitely composite, skip */ 420 421 debug2("test q = largebase+%u", 2 * j); 422 if (BN_set_word(q, 2 * j) == 0) 423 fatal("BN_set_word failed"); 424 if (BN_add(q, q, largebase) == 0) 425 fatal("BN_add failed"); 426 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 427 MODULI_TESTS_SIEVE, largetries, 428 (power - 1) /* MSB */, (0), q) == -1) { 429 ret = -1; 430 break; 431 } 432 433 r++; /* count q */ 434 } 435 436 time(&time_stop); 437 438 free(LargeSieve); 439 free(SmallSieve); 440 free(TinySieve); 441 442 logit("%.24s Found %u candidates", ctime(&time_stop), r); 443 444 return (ret); 445} 446 447static void 448write_checkpoint(char *cpfile, u_int32_t lineno) 449{ 450 FILE *fp; 451 char tmp[PATH_MAX]; 452 int r, writeok, closeok; 453 454 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 455 if (r < 0 || r >= PATH_MAX) { 456 logit("write_checkpoint: temp pathname too long"); 457 return; 458 } 459 if ((r = mkstemp(tmp)) == -1) { 460 logit("mkstemp(%s): %s", tmp, strerror(errno)); 461 return; 462 } 463 if ((fp = fdopen(r, "w")) == NULL) { 464 logit("write_checkpoint: fdopen: %s", strerror(errno)); 465 unlink(tmp); 466 close(r); 467 return; 468 } 469 writeok = (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0); 470 closeok = (fclose(fp) == 0); 471 if (writeok && closeok && rename(tmp, cpfile) == 0) { 472 debug3("wrote checkpoint line %lu to '%s'", 473 (unsigned long)lineno, cpfile); 474 } else { 475 logit("failed to write to checkpoint file '%s': %s", cpfile, 476 strerror(errno)); 477 (void)unlink(tmp); 478 } 479} 480 481static unsigned long 482read_checkpoint(char *cpfile) 483{ 484 FILE *fp; 485 unsigned long lineno = 0; 486 487 if ((fp = fopen(cpfile, "r")) == NULL) 488 return 0; 489 if (fscanf(fp, "%lu\n", &lineno) < 1) 490 logit("Failed to load checkpoint from '%s'", cpfile); 491 else 492 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 493 fclose(fp); 494 return lineno; 495} 496 497static unsigned long 498count_lines(FILE *f) 499{ 500 unsigned long count = 0; 501 char lp[QLINESIZE + 1]; 502 503 if (fseek(f, 0, SEEK_SET) != 0) { 504 debug("input file is not seekable"); 505 return ULONG_MAX; 506 } 507 while (fgets(lp, QLINESIZE + 1, f) != NULL) 508 count++; 509 rewind(f); 510 debug("input file has %lu lines", count); 511 return count; 512} 513 514static char * 515fmt_time(time_t seconds) 516{ 517 int day, hr, min; 518 static char buf[128]; 519 520 min = (seconds / 60) % 60; 521 hr = (seconds / 60 / 60) % 24; 522 day = seconds / 60 / 60 / 24; 523 if (day > 0) 524 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 525 else 526 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 527 return buf; 528} 529 530static void 531print_progress(unsigned long start_lineno, unsigned long current_lineno, 532 unsigned long end_lineno) 533{ 534 static time_t time_start, time_prev; 535 time_t time_now, elapsed; 536 unsigned long num_to_process, processed, remaining, percent, eta; 537 double time_per_line; 538 char *eta_str; 539 540 time_now = monotime(); 541 if (time_start == 0) { 542 time_start = time_prev = time_now; 543 return; 544 } 545 /* print progress after 1m then once per 5m */ 546 if (time_now - time_prev < 5 * 60) 547 return; 548 time_prev = time_now; 549 elapsed = time_now - time_start; 550 processed = current_lineno - start_lineno; 551 remaining = end_lineno - current_lineno; 552 num_to_process = end_lineno - start_lineno; 553 time_per_line = (double)elapsed / processed; 554 /* if we don't know how many we're processing just report count+time */ 555 time(&time_now); 556 if (end_lineno == ULONG_MAX) { 557 logit("%.24s processed %lu in %s", ctime(&time_now), 558 processed, fmt_time(elapsed)); 559 return; 560 } 561 percent = 100 * processed / num_to_process; 562 eta = time_per_line * remaining; 563 eta_str = xstrdup(fmt_time(eta)); 564 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 565 ctime(&time_now), processed, num_to_process, percent, 566 fmt_time(elapsed), eta_str); 567 free(eta_str); 568} 569 570/* 571 * perform a Miller-Rabin primality test 572 * on the list of candidates 573 * (checking both q and p) 574 * The result is a list of so-call "safe" primes 575 */ 576int 577prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, 578 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 579{ 580 BIGNUM *q, *p, *a; 581 char *cp, *lp; 582 u_int32_t count_in = 0, count_out = 0, count_possible = 0; 583 u_int32_t generator_known, in_tests, in_tries, in_type, in_size; 584 unsigned long last_processed = 0, end_lineno; 585 time_t time_start, time_stop; 586 int res, is_prime; 587 588 if (trials < TRIAL_MINIMUM) { 589 error("Minimum primality trials is %d", TRIAL_MINIMUM); 590 return (-1); 591 } 592 593 if (num_lines == 0) 594 end_lineno = count_lines(in); 595 else 596 end_lineno = start_lineno + num_lines; 597 598 time(&time_start); 599 600 if ((p = BN_new()) == NULL) 601 fatal("BN_new failed"); 602 if ((q = BN_new()) == NULL) 603 fatal("BN_new failed"); 604 605 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 606 ctime(&time_start), trials, generator_wanted); 607 608 if (checkpoint_file != NULL) 609 last_processed = read_checkpoint(checkpoint_file); 610 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); 611 if (end_lineno == ULONG_MAX) 612 debug("process from line %lu from pipe", last_processed); 613 else 614 debug("process from line %lu to line %lu", last_processed, 615 end_lineno); 616 617 res = 0; 618 lp = xmalloc(QLINESIZE + 1); 619 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 620 count_in++; 621 if (count_in <= last_processed) { 622 debug3("skipping line %u, before checkpoint or " 623 "specified start line", count_in); 624 continue; 625 } 626 if (checkpoint_file != NULL) 627 write_checkpoint(checkpoint_file, count_in); 628 print_progress(start_lineno, count_in, end_lineno); 629 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 630 debug2("%10u: comment or short line", count_in); 631 continue; 632 } 633 634 /* XXX - fragile parser */ 635 /* time */ 636 cp = &lp[14]; /* (skip) */ 637 638 /* type */ 639 in_type = strtoul(cp, &cp, 10); 640 641 /* tests */ 642 in_tests = strtoul(cp, &cp, 10); 643 644 if (in_tests & MODULI_TESTS_COMPOSITE) { 645 debug2("%10u: known composite", count_in); 646 continue; 647 } 648 649 /* tries */ 650 in_tries = strtoul(cp, &cp, 10); 651 652 /* size (most significant bit) */ 653 in_size = strtoul(cp, &cp, 10); 654 655 /* generator (hex) */ 656 generator_known = strtoul(cp, &cp, 16); 657 658 /* Skip white space */ 659 cp += strspn(cp, " "); 660 661 /* modulus (hex) */ 662 switch (in_type) { 663 case MODULI_TYPE_SOPHIE_GERMAIN: 664 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 665 a = q; 666 if (BN_hex2bn(&a, cp) == 0) 667 fatal("BN_hex2bn failed"); 668 /* p = 2*q + 1 */ 669 if (BN_lshift(p, q, 1) == 0) 670 fatal("BN_lshift failed"); 671 if (BN_add_word(p, 1) == 0) 672 fatal("BN_add_word failed"); 673 in_size += 1; 674 generator_known = 0; 675 break; 676 case MODULI_TYPE_UNSTRUCTURED: 677 case MODULI_TYPE_SAFE: 678 case MODULI_TYPE_SCHNORR: 679 case MODULI_TYPE_STRONG: 680 case MODULI_TYPE_UNKNOWN: 681 debug2("%10u: (%u)", count_in, in_type); 682 a = p; 683 if (BN_hex2bn(&a, cp) == 0) 684 fatal("BN_hex2bn failed"); 685 /* q = (p-1) / 2 */ 686 if (BN_rshift(q, p, 1) == 0) 687 fatal("BN_rshift failed"); 688 break; 689 default: 690 debug2("Unknown prime type"); 691 break; 692 } 693 694 /* 695 * due to earlier inconsistencies in interpretation, check 696 * the proposed bit size. 697 */ 698 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { 699 debug2("%10u: bit size %u mismatch", count_in, in_size); 700 continue; 701 } 702 if (in_size < QSIZE_MINIMUM) { 703 debug2("%10u: bit size %u too short", count_in, in_size); 704 continue; 705 } 706 707 if (in_tests & MODULI_TESTS_MILLER_RABIN) 708 in_tries += trials; 709 else 710 in_tries = trials; 711 712 /* 713 * guess unknown generator 714 */ 715 if (generator_known == 0) { 716 if (BN_mod_word(p, 24) == 11) 717 generator_known = 2; 718 else { 719 u_int32_t r = BN_mod_word(p, 10); 720 721 if (r == 3 || r == 7) 722 generator_known = 5; 723 } 724 } 725 /* 726 * skip tests when desired generator doesn't match 727 */ 728 if (generator_wanted > 0 && 729 generator_wanted != generator_known) { 730 debug2("%10u: generator %d != %d", 731 count_in, generator_known, generator_wanted); 732 continue; 733 } 734 735 /* 736 * Primes with no known generator are useless for DH, so 737 * skip those. 738 */ 739 if (generator_known == 0) { 740 debug2("%10u: no known generator", count_in); 741 continue; 742 } 743 744 count_possible++; 745 746 /* 747 * The (1/4)^N performance bound on Miller-Rabin is 748 * extremely pessimistic, so don't spend a lot of time 749 * really verifying that q is prime until after we know 750 * that p is also prime. A single pass will weed out the 751 * vast majority of composite q's. 752 */ 753 is_prime = BN_is_prime_ex(q, 1, NULL, NULL); 754 if (is_prime < 0) 755 fatal("BN_is_prime_ex failed"); 756 if (is_prime == 0) { 757 debug("%10u: q failed first possible prime test", 758 count_in); 759 continue; 760 } 761 762 /* 763 * q is possibly prime, so go ahead and really make sure 764 * that p is prime. If it is, then we can go back and do 765 * the same for q. If p is composite, chances are that 766 * will show up on the first Rabin-Miller iteration so it 767 * doesn't hurt to specify a high iteration count. 768 */ 769 is_prime = BN_is_prime_ex(p, trials, NULL, NULL); 770 if (is_prime < 0) 771 fatal("BN_is_prime_ex failed"); 772 if (is_prime == 0) { 773 debug("%10u: p is not prime", count_in); 774 continue; 775 } 776 debug("%10u: p is almost certainly prime", count_in); 777 778 /* recheck q more rigorously */ 779 is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL); 780 if (is_prime < 0) 781 fatal("BN_is_prime_ex failed"); 782 if (is_prime == 0) { 783 debug("%10u: q is not prime", count_in); 784 continue; 785 } 786 debug("%10u: q is almost certainly prime", count_in); 787 788 if (qfileout(out, MODULI_TYPE_SAFE, 789 in_tests | MODULI_TESTS_MILLER_RABIN, 790 in_tries, in_size, generator_known, p)) { 791 res = -1; 792 break; 793 } 794 795 count_out++; 796 } 797 798 time(&time_stop); 799 free(lp); 800 BN_free(p); 801 BN_free(q); 802 803 if (checkpoint_file != NULL) 804 unlink(checkpoint_file); 805 806 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 807 ctime(&time_stop), count_out, count_possible, 808 (long) (time_stop - time_start)); 809 810 return (res); 811} 812