1 /* $OpenBSD: moduli.c,v 1.39 2023/03/02 06:41:56 dtucker Exp $ */ 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" 41 42 #ifdef WITH_OPENSSL 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 #include "openbsd-compat/openssl-compat.h" 64 65 /* 66 * File output defines 67 */ 68 69 /* need line long enough for largest moduli plus headers */ 70 #define QLINESIZE (100+8192) 71 72 /* 73 * Size: decimal. 74 * Specifies the number of the most significant bit (0 to M). 75 * WARNING: internally, usually 1 to N. 76 */ 77 #define QSIZE_MINIMUM (511) 78 79 /* 80 * Prime sieving defines 81 */ 82 83 /* Constant: assuming 8 bit bytes and 32 bit words */ 84 #define SHIFT_BIT (3) 85 #define SHIFT_BYTE (2) 86 #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) 87 #define SHIFT_MEGABYTE (20) 88 #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) 89 90 /* 91 * Using virtual memory can cause thrashing. This should be the largest 92 * number that is supported without a large amount of disk activity -- 93 * that would increase the run time from hours to days or weeks! 94 */ 95 #define LARGE_MINIMUM (8UL) /* megabytes */ 96 97 /* 98 * Do not increase this number beyond the unsigned integer bit size. 99 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 100 */ 101 #define LARGE_MAXIMUM (127UL) /* megabytes */ 102 103 /* 104 * Constant: when used with 32-bit integers, the largest sieve prime 105 * has to be less than 2**32. 106 */ 107 #define SMALL_MAXIMUM (0xffffffffUL) 108 109 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 110 #define TINY_NUMBER (1UL<<16) 111 112 /* Ensure enough bit space for testing 2*q. */ 113 #define TEST_MAXIMUM (1UL<<16) 114 #define TEST_MINIMUM (QSIZE_MINIMUM + 1) 115 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 116 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 117 118 /* bit operations on 32-bit words */ 119 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 120 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 121 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 122 123 /* 124 * Prime testing defines 125 */ 126 127 /* Minimum number of primality tests to perform */ 128 #define TRIAL_MINIMUM (4) 129 130 /* 131 * Sieving data (XXX - move to struct) 132 */ 133 134 /* sieve 2**16 */ 135 static u_int32_t *TinySieve, tinybits; 136 137 /* sieve 2**30 in 2**16 parts */ 138 static u_int32_t *SmallSieve, smallbits, smallbase; 139 140 /* sieve relative to the initial value */ 141 static u_int32_t *LargeSieve, largewords, largetries, largenumbers; 142 static u_int32_t largebits, largememory; /* megabytes */ 143 static BIGNUM *largebase; 144 145 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); 146 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, 147 unsigned long); 148 149 /* 150 * print moduli out in consistent form, 151 */ 152 static int 153 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, 154 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) 155 { 156 struct tm *gtm; 157 time_t time_now; 158 int res; 159 160 time(&time_now); 161 gtm = gmtime(&time_now); 162 if (gtm == NULL) 163 return -1; 164 165 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 166 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 167 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 168 otype, otests, otries, osize, ogenerator); 169 170 if (res < 0) 171 return (-1); 172 173 if (BN_print_fp(ofile, omodulus) < 1) 174 return (-1); 175 176 res = fprintf(ofile, "\n"); 177 fflush(ofile); 178 179 return (res > 0 ? 0 : -1); 180 } 181 182 183 /* 184 ** Sieve p's and q's with small factors 185 */ 186 static void 187 sieve_large(u_int32_t s32) 188 { 189 u_int64_t r, u, s = s32; 190 191 debug3("sieve_large %u", s32); 192 largetries++; 193 /* r = largebase mod s */ 194 r = BN_mod_word(largebase, s32); 195 if (r == 0) 196 u = 0; /* s divides into largebase exactly */ 197 else 198 u = s - r; /* largebase+u is first entry divisible by s */ 199 200 if (u < largebits * 2ULL) { 201 /* 202 * The sieve omits p's and q's divisible by 2, so ensure that 203 * largebase+u is odd. Then, step through the sieve in 204 * increments of 2*s 205 */ 206 if (u & 0x1) 207 u += s; /* Make largebase+u odd, and u even */ 208 209 /* Mark all multiples of 2*s */ 210 for (u /= 2; u < largebits; u += s) 211 BIT_SET(LargeSieve, u); 212 } 213 214 /* r = p mod s */ 215 r = (2 * r + 1) % s; 216 if (r == 0) 217 u = 0; /* s divides p exactly */ 218 else 219 u = s - r; /* p+u is first entry divisible by s */ 220 221 if (u < largebits * 4ULL) { 222 /* 223 * The sieve omits p's divisible by 4, so ensure that 224 * largebase+u is not. Then, step through the sieve in 225 * increments of 4*s 226 */ 227 while (u & 0x3) { 228 if (SMALL_MAXIMUM - u < s) 229 return; 230 u += s; 231 } 232 233 /* Mark all multiples of 4*s */ 234 for (u /= 4; u < largebits; u += s) 235 BIT_SET(LargeSieve, u); 236 } 237 } 238 239 /* 240 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 241 * to standard output. 242 * The list is checked against small known primes (less than 2**30). 243 */ 244 int 245 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) 246 { 247 BIGNUM *q; 248 u_int32_t j, r, s, t; 249 u_int32_t smallwords = TINY_NUMBER >> 6; 250 u_int32_t tinywords = TINY_NUMBER >> 6; 251 time_t time_start, time_stop; 252 u_int32_t i; 253 int ret = 0; 254 255 largememory = memory; 256 257 if (memory != 0 && 258 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { 259 error("Invalid memory amount (min %ld, max %ld)", 260 LARGE_MINIMUM, LARGE_MAXIMUM); 261 return (-1); 262 } 263 264 /* 265 * Set power to the length in bits of the prime to be generated. 266 * This is changed to 1 less than the desired safe prime moduli p. 267 */ 268 if (power > TEST_MAXIMUM) { 269 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 270 return (-1); 271 } else if (power < TEST_MINIMUM) { 272 error("Too few bits: %u < %u", power, TEST_MINIMUM); 273 return (-1); 274 } 275 power--; /* decrement before squaring */ 276 277 /* 278 * The density of ordinary primes is on the order of 1/bits, so the 279 * density of safe primes should be about (1/bits)**2. Set test range 280 * to something well above bits**2 to be reasonably sure (but not 281 * guaranteed) of catching at least one safe prime. 282 */ 283 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); 284 285 /* 286 * Need idea of how much memory is available. We don't have to use all 287 * of it. 288 */ 289 if (largememory > LARGE_MAXIMUM) { 290 logit("Limited memory: %u MB; limit %lu MB", 291 largememory, LARGE_MAXIMUM); 292 largememory = LARGE_MAXIMUM; 293 } 294 295 if (largewords <= (largememory << SHIFT_MEGAWORD)) { 296 logit("Increased memory: %u MB; need %u bytes", 297 largememory, (largewords << SHIFT_BYTE)); 298 largewords = (largememory << SHIFT_MEGAWORD); 299 } else if (largememory > 0) { 300 logit("Decreased memory: %u MB; want %u bytes", 301 largememory, (largewords << SHIFT_BYTE)); 302 largewords = (largememory << SHIFT_MEGAWORD); 303 } 304 305 TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); 306 tinybits = tinywords << SHIFT_WORD; 307 308 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); 309 smallbits = smallwords << SHIFT_WORD; 310 311 /* 312 * dynamically determine available memory 313 */ 314 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) 315 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ 316 317 largebits = largewords << SHIFT_WORD; 318 largenumbers = largebits * 2; /* even numbers excluded */ 319 320 /* validation check: count the number of primes tried */ 321 largetries = 0; 322 if ((q = BN_new()) == NULL) 323 fatal("BN_new failed"); 324 325 /* 326 * Generate random starting point for subprime search, or use 327 * specified parameter. 328 */ 329 if ((largebase = BN_new()) == NULL) 330 fatal("BN_new failed"); 331 if (start == NULL) { 332 if (BN_rand(largebase, power, 1, 1) == 0) 333 fatal("BN_rand failed"); 334 } else { 335 if (BN_copy(largebase, start) == NULL) 336 fatal("BN_copy: failed"); 337 } 338 339 /* ensure odd */ 340 if (BN_set_bit(largebase, 0) == 0) 341 fatal("BN_set_bit: failed"); 342 343 time(&time_start); 344 345 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 346 largenumbers, power); 347 debug2("start point: 0x%s", BN_bn2hex(largebase)); 348 349 /* 350 * TinySieve 351 */ 352 for (i = 0; i < tinybits; i++) { 353 if (BIT_TEST(TinySieve, i)) 354 continue; /* 2*i+3 is composite */ 355 356 /* The next tiny prime */ 357 t = 2 * i + 3; 358 359 /* Mark all multiples of t */ 360 for (j = i + t; j < tinybits; j += t) 361 BIT_SET(TinySieve, j); 362 363 sieve_large(t); 364 } 365 366 /* 367 * Start the small block search at the next possible prime. To avoid 368 * fencepost errors, the last pass is skipped. 369 */ 370 for (smallbase = TINY_NUMBER + 3; 371 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 372 smallbase += TINY_NUMBER) { 373 for (i = 0; i < tinybits; i++) { 374 if (BIT_TEST(TinySieve, i)) 375 continue; /* 2*i+3 is composite */ 376 377 /* The next tiny prime */ 378 t = 2 * i + 3; 379 r = smallbase % t; 380 381 if (r == 0) { 382 s = 0; /* t divides into smallbase exactly */ 383 } else { 384 /* smallbase+s is first entry divisible by t */ 385 s = t - r; 386 } 387 388 /* 389 * The sieve omits even numbers, so ensure that 390 * smallbase+s is odd. Then, step through the sieve 391 * in increments of 2*t 392 */ 393 if (s & 1) 394 s += t; /* Make smallbase+s odd, and s even */ 395 396 /* Mark all multiples of 2*t */ 397 for (s /= 2; s < smallbits; s += t) 398 BIT_SET(SmallSieve, s); 399 } 400 401 /* 402 * SmallSieve 403 */ 404 for (i = 0; i < smallbits; i++) { 405 if (BIT_TEST(SmallSieve, i)) 406 continue; /* 2*i+smallbase is composite */ 407 408 /* The next small prime */ 409 sieve_large((2 * i) + smallbase); 410 } 411 412 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 413 } 414 415 time(&time_stop); 416 417 logit("%.24s Sieved with %u small primes in %lld seconds", 418 ctime(&time_stop), largetries, (long long)(time_stop - time_start)); 419 420 for (j = r = 0; j < largebits; j++) { 421 if (BIT_TEST(LargeSieve, j)) 422 continue; /* Definitely composite, skip */ 423 424 debug2("test q = largebase+%u", 2 * j); 425 if (BN_set_word(q, 2 * j) == 0) 426 fatal("BN_set_word failed"); 427 if (BN_add(q, q, largebase) == 0) 428 fatal("BN_add failed"); 429 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 430 MODULI_TESTS_SIEVE, largetries, 431 (power - 1) /* MSB */, (0), q) == -1) { 432 ret = -1; 433 break; 434 } 435 436 r++; /* count q */ 437 } 438 439 time(&time_stop); 440 441 free(LargeSieve); 442 free(SmallSieve); 443 free(TinySieve); 444 445 logit("%.24s Found %u candidates", ctime(&time_stop), r); 446 447 return (ret); 448 } 449 450 static void 451 write_checkpoint(char *cpfile, u_int32_t lineno) 452 { 453 FILE *fp; 454 char tmp[PATH_MAX]; 455 int r, writeok, closeok; 456 457 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 458 if (r < 0 || r >= PATH_MAX) { 459 logit("write_checkpoint: temp pathname too long"); 460 return; 461 } 462 if ((r = mkstemp(tmp)) == -1) { 463 logit("mkstemp(%s): %s", tmp, strerror(errno)); 464 return; 465 } 466 if ((fp = fdopen(r, "w")) == NULL) { 467 logit("write_checkpoint: fdopen: %s", strerror(errno)); 468 unlink(tmp); 469 close(r); 470 return; 471 } 472 writeok = (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0); 473 closeok = (fclose(fp) == 0); 474 if (writeok && closeok && rename(tmp, cpfile) == 0) { 475 debug3("wrote checkpoint line %lu to '%s'", 476 (unsigned long)lineno, cpfile); 477 } else { 478 logit("failed to write to checkpoint file '%s': %s", cpfile, 479 strerror(errno)); 480 (void)unlink(tmp); 481 } 482 } 483 484 static unsigned long 485 read_checkpoint(char *cpfile) 486 { 487 FILE *fp; 488 unsigned long lineno = 0; 489 490 if ((fp = fopen(cpfile, "r")) == NULL) 491 return 0; 492 if (fscanf(fp, "%lu\n", &lineno) < 1) 493 logit("Failed to load checkpoint from '%s'", cpfile); 494 else 495 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 496 fclose(fp); 497 return lineno; 498 } 499 500 static unsigned long 501 count_lines(FILE *f) 502 { 503 unsigned long count = 0; 504 char lp[QLINESIZE + 1]; 505 506 if (fseek(f, 0, SEEK_SET) != 0) { 507 debug("input file is not seekable"); 508 return ULONG_MAX; 509 } 510 while (fgets(lp, QLINESIZE + 1, f) != NULL) 511 count++; 512 rewind(f); 513 debug("input file has %lu lines", count); 514 return count; 515 } 516 517 static char * 518 fmt_time(time_t seconds) 519 { 520 int day, hr, min; 521 static char buf[128]; 522 523 min = (seconds / 60) % 60; 524 hr = (seconds / 60 / 60) % 24; 525 day = seconds / 60 / 60 / 24; 526 if (day > 0) 527 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 528 else 529 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 530 return buf; 531 } 532 533 static void 534 print_progress(unsigned long start_lineno, unsigned long current_lineno, 535 unsigned long end_lineno) 536 { 537 static time_t time_start, time_prev; 538 time_t time_now, elapsed; 539 unsigned long num_to_process, processed, remaining, percent, eta; 540 double time_per_line; 541 char *eta_str; 542 543 time_now = monotime(); 544 if (time_start == 0) { 545 time_start = time_prev = time_now; 546 return; 547 } 548 /* print progress after 1m then once per 5m */ 549 if (time_now - time_prev < 5 * 60) 550 return; 551 time_prev = time_now; 552 elapsed = time_now - time_start; 553 processed = current_lineno - start_lineno; 554 remaining = end_lineno - current_lineno; 555 num_to_process = end_lineno - start_lineno; 556 time_per_line = (double)elapsed / processed; 557 /* if we don't know how many we're processing just report count+time */ 558 time(&time_now); 559 if (end_lineno == ULONG_MAX) { 560 logit("%.24s processed %lu in %s", ctime(&time_now), 561 processed, fmt_time(elapsed)); 562 return; 563 } 564 percent = 100 * processed / num_to_process; 565 eta = time_per_line * remaining; 566 eta_str = xstrdup(fmt_time(eta)); 567 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 568 ctime(&time_now), processed, num_to_process, percent, 569 fmt_time(elapsed), eta_str); 570 free(eta_str); 571 } 572 573 /* 574 * perform a Miller-Rabin primality test 575 * on the list of candidates 576 * (checking both q and p) 577 * The result is a list of so-call "safe" primes 578 */ 579 int 580 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, 581 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 582 { 583 BIGNUM *q, *p, *a; 584 char *cp, *lp; 585 u_int32_t count_in = 0, count_out = 0, count_possible = 0; 586 u_int32_t generator_known, in_tests, in_tries, in_type, in_size; 587 unsigned long last_processed = 0, end_lineno; 588 time_t time_start, time_stop; 589 int res, is_prime; 590 591 if (trials < TRIAL_MINIMUM) { 592 error("Minimum primality trials is %d", TRIAL_MINIMUM); 593 return (-1); 594 } 595 596 if (num_lines == 0) 597 end_lineno = count_lines(in); 598 else 599 end_lineno = start_lineno + num_lines; 600 601 time(&time_start); 602 603 if ((p = BN_new()) == NULL) 604 fatal("BN_new failed"); 605 if ((q = BN_new()) == NULL) 606 fatal("BN_new failed"); 607 608 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 609 ctime(&time_start), trials, generator_wanted); 610 611 if (checkpoint_file != NULL) 612 last_processed = read_checkpoint(checkpoint_file); 613 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); 614 if (end_lineno == ULONG_MAX) 615 debug("process from line %lu from pipe", last_processed); 616 else 617 debug("process from line %lu to line %lu", last_processed, 618 end_lineno); 619 620 res = 0; 621 lp = xmalloc(QLINESIZE + 1); 622 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 623 count_in++; 624 if (count_in <= last_processed) { 625 debug3("skipping line %u, before checkpoint or " 626 "specified start line", count_in); 627 continue; 628 } 629 if (checkpoint_file != NULL) 630 write_checkpoint(checkpoint_file, count_in); 631 print_progress(start_lineno, count_in, end_lineno); 632 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 633 debug2("%10u: comment or short line", count_in); 634 continue; 635 } 636 637 /* XXX - fragile parser */ 638 /* time */ 639 cp = &lp[14]; /* (skip) */ 640 641 /* type */ 642 in_type = strtoul(cp, &cp, 10); 643 644 /* tests */ 645 in_tests = strtoul(cp, &cp, 10); 646 647 if (in_tests & MODULI_TESTS_COMPOSITE) { 648 debug2("%10u: known composite", count_in); 649 continue; 650 } 651 652 /* tries */ 653 in_tries = strtoul(cp, &cp, 10); 654 655 /* size (most significant bit) */ 656 in_size = strtoul(cp, &cp, 10); 657 658 /* generator (hex) */ 659 generator_known = strtoul(cp, &cp, 16); 660 661 /* Skip white space */ 662 cp += strspn(cp, " "); 663 664 /* modulus (hex) */ 665 switch (in_type) { 666 case MODULI_TYPE_SOPHIE_GERMAIN: 667 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 668 a = q; 669 if (BN_hex2bn(&a, cp) == 0) 670 fatal("BN_hex2bn failed"); 671 /* p = 2*q + 1 */ 672 if (BN_lshift(p, q, 1) == 0) 673 fatal("BN_lshift failed"); 674 if (BN_add_word(p, 1) == 0) 675 fatal("BN_add_word failed"); 676 in_size += 1; 677 generator_known = 0; 678 break; 679 case MODULI_TYPE_UNSTRUCTURED: 680 case MODULI_TYPE_SAFE: 681 case MODULI_TYPE_SCHNORR: 682 case MODULI_TYPE_STRONG: 683 case MODULI_TYPE_UNKNOWN: 684 debug2("%10u: (%u)", count_in, in_type); 685 a = p; 686 if (BN_hex2bn(&a, cp) == 0) 687 fatal("BN_hex2bn failed"); 688 /* q = (p-1) / 2 */ 689 if (BN_rshift(q, p, 1) == 0) 690 fatal("BN_rshift failed"); 691 break; 692 default: 693 debug2("Unknown prime type"); 694 break; 695 } 696 697 /* 698 * due to earlier inconsistencies in interpretation, check 699 * the proposed bit size. 700 */ 701 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { 702 debug2("%10u: bit size %u mismatch", count_in, in_size); 703 continue; 704 } 705 if (in_size < QSIZE_MINIMUM) { 706 debug2("%10u: bit size %u too short", count_in, in_size); 707 continue; 708 } 709 710 if (in_tests & MODULI_TESTS_MILLER_RABIN) 711 in_tries += trials; 712 else 713 in_tries = trials; 714 715 /* 716 * guess unknown generator 717 */ 718 if (generator_known == 0) { 719 if (BN_mod_word(p, 24) == 11) 720 generator_known = 2; 721 else { 722 u_int32_t r = BN_mod_word(p, 10); 723 724 if (r == 3 || r == 7) 725 generator_known = 5; 726 } 727 } 728 /* 729 * skip tests when desired generator doesn't match 730 */ 731 if (generator_wanted > 0 && 732 generator_wanted != generator_known) { 733 debug2("%10u: generator %d != %d", 734 count_in, generator_known, generator_wanted); 735 continue; 736 } 737 738 /* 739 * Primes with no known generator are useless for DH, so 740 * skip those. 741 */ 742 if (generator_known == 0) { 743 debug2("%10u: no known generator", count_in); 744 continue; 745 } 746 747 count_possible++; 748 749 /* 750 * The (1/4)^N performance bound on Miller-Rabin is 751 * extremely pessimistic, so don't spend a lot of time 752 * really verifying that q is prime until after we know 753 * that p is also prime. A single pass will weed out the 754 * vast majority of composite q's. 755 */ 756 is_prime = BN_is_prime_ex(q, 1, NULL, NULL); 757 if (is_prime < 0) 758 fatal("BN_is_prime_ex failed"); 759 if (is_prime == 0) { 760 debug("%10u: q failed first possible prime test", 761 count_in); 762 continue; 763 } 764 765 /* 766 * q is possibly prime, so go ahead and really make sure 767 * that p is prime. If it is, then we can go back and do 768 * the same for q. If p is composite, chances are that 769 * will show up on the first Rabin-Miller iteration so it 770 * doesn't hurt to specify a high iteration count. 771 */ 772 is_prime = BN_is_prime_ex(p, trials, NULL, NULL); 773 if (is_prime < 0) 774 fatal("BN_is_prime_ex failed"); 775 if (is_prime == 0) { 776 debug("%10u: p is not prime", count_in); 777 continue; 778 } 779 debug("%10u: p is almost certainly prime", count_in); 780 781 /* recheck q more rigorously */ 782 is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL); 783 if (is_prime < 0) 784 fatal("BN_is_prime_ex failed"); 785 if (is_prime == 0) { 786 debug("%10u: q is not prime", count_in); 787 continue; 788 } 789 debug("%10u: q is almost certainly prime", count_in); 790 791 if (qfileout(out, MODULI_TYPE_SAFE, 792 in_tests | MODULI_TESTS_MILLER_RABIN, 793 in_tries, in_size, generator_known, p)) { 794 res = -1; 795 break; 796 } 797 798 count_out++; 799 } 800 801 time(&time_stop); 802 free(lp); 803 BN_free(p); 804 BN_free(q); 805 806 if (checkpoint_file != NULL) 807 unlink(checkpoint_file); 808 809 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 810 ctime(&time_stop), count_out, count_possible, 811 (long) (time_stop - time_start)); 812 813 return (res); 814 } 815 816 #endif /* WITH_OPENSSL */ 817