1 /* $OpenBSD: moduli.c,v 1.37 2019/11/15 06:00:20 djm 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 <sys/types.h> 41 42 #include <openssl/bn.h> 43 #include <openssl/dh.h> 44 45 #include <errno.h> 46 #include <stdio.h> 47 #include <stdlib.h> 48 #include <string.h> 49 #include <stdarg.h> 50 #include <time.h> 51 #include <unistd.h> 52 #include <limits.h> 53 54 #include "xmalloc.h" 55 #include "dh.h" 56 #include "log.h" 57 #include "misc.h" 58 59 /* 60 * File output defines 61 */ 62 63 /* need line long enough for largest moduli plus headers */ 64 #define QLINESIZE (100+8192) 65 66 /* 67 * Size: decimal. 68 * Specifies the number of the most significant bit (0 to M). 69 * WARNING: internally, usually 1 to N. 70 */ 71 #define QSIZE_MINIMUM (511) 72 73 /* 74 * Prime sieving defines 75 */ 76 77 /* Constant: assuming 8 bit bytes and 32 bit words */ 78 #define SHIFT_BIT (3) 79 #define SHIFT_BYTE (2) 80 #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) 81 #define SHIFT_MEGABYTE (20) 82 #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) 83 84 /* 85 * Using virtual memory can cause thrashing. This should be the largest 86 * number that is supported without a large amount of disk activity -- 87 * that would increase the run time from hours to days or weeks! 88 */ 89 #define LARGE_MINIMUM (8UL) /* megabytes */ 90 91 /* 92 * Do not increase this number beyond the unsigned integer bit size. 93 * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). 94 */ 95 #define LARGE_MAXIMUM (127UL) /* megabytes */ 96 97 /* 98 * Constant: when used with 32-bit integers, the largest sieve prime 99 * has to be less than 2**32. 100 */ 101 #define SMALL_MAXIMUM (0xffffffffUL) 102 103 /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ 104 #define TINY_NUMBER (1UL<<16) 105 106 /* Ensure enough bit space for testing 2*q. */ 107 #define TEST_MAXIMUM (1UL<<16) 108 #define TEST_MINIMUM (QSIZE_MINIMUM + 1) 109 /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ 110 #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ 111 112 /* bit operations on 32-bit words */ 113 #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) 114 #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) 115 #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) 116 117 /* 118 * Prime testing defines 119 */ 120 121 /* Minimum number of primality tests to perform */ 122 #define TRIAL_MINIMUM (4) 123 124 /* 125 * Sieving data (XXX - move to struct) 126 */ 127 128 /* sieve 2**16 */ 129 static u_int32_t *TinySieve, tinybits; 130 131 /* sieve 2**30 in 2**16 parts */ 132 static u_int32_t *SmallSieve, smallbits, smallbase; 133 134 /* sieve relative to the initial value */ 135 static u_int32_t *LargeSieve, largewords, largetries, largenumbers; 136 static u_int32_t largebits, largememory; /* megabytes */ 137 static BIGNUM *largebase; 138 139 int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); 140 int prime_test(FILE *, FILE *, u_int32_t, u_int32_t, char *, unsigned long, 141 unsigned long); 142 143 /* 144 * print moduli out in consistent form, 145 */ 146 static int 147 qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, 148 u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) 149 { 150 struct tm *gtm; 151 time_t time_now; 152 int res; 153 154 time(&time_now); 155 gtm = gmtime(&time_now); 156 if (gtm == NULL) 157 return -1; 158 159 res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", 160 gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, 161 gtm->tm_hour, gtm->tm_min, gtm->tm_sec, 162 otype, otests, otries, osize, ogenerator); 163 164 if (res < 0) 165 return (-1); 166 167 if (BN_print_fp(ofile, omodulus) < 1) 168 return (-1); 169 170 res = fprintf(ofile, "\n"); 171 fflush(ofile); 172 173 return (res > 0 ? 0 : -1); 174 } 175 176 177 /* 178 ** Sieve p's and q's with small factors 179 */ 180 static void 181 sieve_large(u_int32_t s) 182 { 183 u_int32_t r, u; 184 185 debug3("sieve_large %u", s); 186 largetries++; 187 /* r = largebase mod s */ 188 r = BN_mod_word(largebase, s); 189 if (r == 0) 190 u = 0; /* s divides into largebase exactly */ 191 else 192 u = s - r; /* largebase+u is first entry divisible by s */ 193 194 if (u < largebits * 2) { 195 /* 196 * The sieve omits p's and q's divisible by 2, so ensure that 197 * largebase+u is odd. Then, step through the sieve in 198 * increments of 2*s 199 */ 200 if (u & 0x1) 201 u += s; /* Make largebase+u odd, and u even */ 202 203 /* Mark all multiples of 2*s */ 204 for (u /= 2; u < largebits; u += s) 205 BIT_SET(LargeSieve, u); 206 } 207 208 /* r = p mod s */ 209 r = (2 * r + 1) % s; 210 if (r == 0) 211 u = 0; /* s divides p exactly */ 212 else 213 u = s - r; /* p+u is first entry divisible by s */ 214 215 if (u < largebits * 4) { 216 /* 217 * The sieve omits p's divisible by 4, so ensure that 218 * largebase+u is not. Then, step through the sieve in 219 * increments of 4*s 220 */ 221 while (u & 0x3) { 222 if (SMALL_MAXIMUM - u < s) 223 return; 224 u += s; 225 } 226 227 /* Mark all multiples of 4*s */ 228 for (u /= 4; u < largebits; u += s) 229 BIT_SET(LargeSieve, u); 230 } 231 } 232 233 /* 234 * list candidates for Sophie-Germain primes (where q = (p-1)/2) 235 * to standard output. 236 * The list is checked against small known primes (less than 2**30). 237 */ 238 int 239 gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) 240 { 241 BIGNUM *q; 242 u_int32_t j, r, s, t; 243 u_int32_t smallwords = TINY_NUMBER >> 6; 244 u_int32_t tinywords = TINY_NUMBER >> 6; 245 time_t time_start, time_stop; 246 u_int32_t i; 247 int ret = 0; 248 249 largememory = memory; 250 251 if (memory != 0 && 252 (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { 253 error("Invalid memory amount (min %ld, max %ld)", 254 LARGE_MINIMUM, LARGE_MAXIMUM); 255 return (-1); 256 } 257 258 /* 259 * Set power to the length in bits of the prime to be generated. 260 * This is changed to 1 less than the desired safe prime moduli p. 261 */ 262 if (power > TEST_MAXIMUM) { 263 error("Too many bits: %u > %lu", power, TEST_MAXIMUM); 264 return (-1); 265 } else if (power < TEST_MINIMUM) { 266 error("Too few bits: %u < %u", power, TEST_MINIMUM); 267 return (-1); 268 } 269 power--; /* decrement before squaring */ 270 271 /* 272 * The density of ordinary primes is on the order of 1/bits, so the 273 * density of safe primes should be about (1/bits)**2. Set test range 274 * to something well above bits**2 to be reasonably sure (but not 275 * guaranteed) of catching at least one safe prime. 276 */ 277 largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); 278 279 /* 280 * Need idea of how much memory is available. We don't have to use all 281 * of it. 282 */ 283 if (largememory > LARGE_MAXIMUM) { 284 logit("Limited memory: %u MB; limit %lu MB", 285 largememory, LARGE_MAXIMUM); 286 largememory = LARGE_MAXIMUM; 287 } 288 289 if (largewords <= (largememory << SHIFT_MEGAWORD)) { 290 logit("Increased memory: %u MB; need %u bytes", 291 largememory, (largewords << SHIFT_BYTE)); 292 largewords = (largememory << SHIFT_MEGAWORD); 293 } else if (largememory > 0) { 294 logit("Decreased memory: %u MB; want %u bytes", 295 largememory, (largewords << SHIFT_BYTE)); 296 largewords = (largememory << SHIFT_MEGAWORD); 297 } 298 299 TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); 300 tinybits = tinywords << SHIFT_WORD; 301 302 SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); 303 smallbits = smallwords << SHIFT_WORD; 304 305 /* 306 * dynamically determine available memory 307 */ 308 while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) 309 largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ 310 311 largebits = largewords << SHIFT_WORD; 312 largenumbers = largebits * 2; /* even numbers excluded */ 313 314 /* validation check: count the number of primes tried */ 315 largetries = 0; 316 if ((q = BN_new()) == NULL) 317 fatal("BN_new failed"); 318 319 /* 320 * Generate random starting point for subprime search, or use 321 * specified parameter. 322 */ 323 if ((largebase = BN_new()) == NULL) 324 fatal("BN_new failed"); 325 if (start == NULL) { 326 if (BN_rand(largebase, power, 1, 1) == 0) 327 fatal("BN_rand failed"); 328 } else { 329 if (BN_copy(largebase, start) == NULL) 330 fatal("BN_copy: failed"); 331 } 332 333 /* ensure odd */ 334 if (BN_set_bit(largebase, 0) == 0) 335 fatal("BN_set_bit: failed"); 336 337 time(&time_start); 338 339 logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), 340 largenumbers, power); 341 debug2("start point: 0x%s", BN_bn2hex(largebase)); 342 343 /* 344 * TinySieve 345 */ 346 for (i = 0; i < tinybits; i++) { 347 if (BIT_TEST(TinySieve, i)) 348 continue; /* 2*i+3 is composite */ 349 350 /* The next tiny prime */ 351 t = 2 * i + 3; 352 353 /* Mark all multiples of t */ 354 for (j = i + t; j < tinybits; j += t) 355 BIT_SET(TinySieve, j); 356 357 sieve_large(t); 358 } 359 360 /* 361 * Start the small block search at the next possible prime. To avoid 362 * fencepost errors, the last pass is skipped. 363 */ 364 for (smallbase = TINY_NUMBER + 3; 365 smallbase < (SMALL_MAXIMUM - TINY_NUMBER); 366 smallbase += TINY_NUMBER) { 367 for (i = 0; i < tinybits; i++) { 368 if (BIT_TEST(TinySieve, i)) 369 continue; /* 2*i+3 is composite */ 370 371 /* The next tiny prime */ 372 t = 2 * i + 3; 373 r = smallbase % t; 374 375 if (r == 0) { 376 s = 0; /* t divides into smallbase exactly */ 377 } else { 378 /* smallbase+s is first entry divisible by t */ 379 s = t - r; 380 } 381 382 /* 383 * The sieve omits even numbers, so ensure that 384 * smallbase+s is odd. Then, step through the sieve 385 * in increments of 2*t 386 */ 387 if (s & 1) 388 s += t; /* Make smallbase+s odd, and s even */ 389 390 /* Mark all multiples of 2*t */ 391 for (s /= 2; s < smallbits; s += t) 392 BIT_SET(SmallSieve, s); 393 } 394 395 /* 396 * SmallSieve 397 */ 398 for (i = 0; i < smallbits; i++) { 399 if (BIT_TEST(SmallSieve, i)) 400 continue; /* 2*i+smallbase is composite */ 401 402 /* The next small prime */ 403 sieve_large((2 * i) + smallbase); 404 } 405 406 memset(SmallSieve, 0, smallwords << SHIFT_BYTE); 407 } 408 409 time(&time_stop); 410 411 logit("%.24s Sieved with %u small primes in %lld seconds", 412 ctime(&time_stop), largetries, (long long)(time_stop - time_start)); 413 414 for (j = r = 0; j < largebits; j++) { 415 if (BIT_TEST(LargeSieve, j)) 416 continue; /* Definitely composite, skip */ 417 418 debug2("test q = largebase+%u", 2 * j); 419 if (BN_set_word(q, 2 * j) == 0) 420 fatal("BN_set_word failed"); 421 if (BN_add(q, q, largebase) == 0) 422 fatal("BN_add failed"); 423 if (qfileout(out, MODULI_TYPE_SOPHIE_GERMAIN, 424 MODULI_TESTS_SIEVE, largetries, 425 (power - 1) /* MSB */, (0), q) == -1) { 426 ret = -1; 427 break; 428 } 429 430 r++; /* count q */ 431 } 432 433 time(&time_stop); 434 435 free(LargeSieve); 436 free(SmallSieve); 437 free(TinySieve); 438 439 logit("%.24s Found %u candidates", ctime(&time_stop), r); 440 441 return (ret); 442 } 443 444 static void 445 write_checkpoint(char *cpfile, u_int32_t lineno) 446 { 447 FILE *fp; 448 char tmp[PATH_MAX]; 449 int r; 450 451 r = snprintf(tmp, sizeof(tmp), "%s.XXXXXXXXXX", cpfile); 452 if (r < 0 || r >= PATH_MAX) { 453 logit("write_checkpoint: temp pathname too long"); 454 return; 455 } 456 if ((r = mkstemp(tmp)) == -1) { 457 logit("mkstemp(%s): %s", tmp, strerror(errno)); 458 return; 459 } 460 if ((fp = fdopen(r, "w")) == NULL) { 461 logit("write_checkpoint: fdopen: %s", strerror(errno)); 462 unlink(tmp); 463 close(r); 464 return; 465 } 466 if (fprintf(fp, "%lu\n", (unsigned long)lineno) > 0 && fclose(fp) == 0 467 && rename(tmp, cpfile) == 0) 468 debug3("wrote checkpoint line %lu to '%s'", 469 (unsigned long)lineno, cpfile); 470 else 471 logit("failed to write to checkpoint file '%s': %s", cpfile, 472 strerror(errno)); 473 } 474 475 static unsigned long 476 read_checkpoint(char *cpfile) 477 { 478 FILE *fp; 479 unsigned long lineno = 0; 480 481 if ((fp = fopen(cpfile, "r")) == NULL) 482 return 0; 483 if (fscanf(fp, "%lu\n", &lineno) < 1) 484 logit("Failed to load checkpoint from '%s'", cpfile); 485 else 486 logit("Loaded checkpoint from '%s' line %lu", cpfile, lineno); 487 fclose(fp); 488 return lineno; 489 } 490 491 static unsigned long 492 count_lines(FILE *f) 493 { 494 unsigned long count = 0; 495 char lp[QLINESIZE + 1]; 496 497 if (fseek(f, 0, SEEK_SET) != 0) { 498 debug("input file is not seekable"); 499 return ULONG_MAX; 500 } 501 while (fgets(lp, QLINESIZE + 1, f) != NULL) 502 count++; 503 rewind(f); 504 debug("input file has %lu lines", count); 505 return count; 506 } 507 508 static char * 509 fmt_time(time_t seconds) 510 { 511 int day, hr, min; 512 static char buf[128]; 513 514 min = (seconds / 60) % 60; 515 hr = (seconds / 60 / 60) % 24; 516 day = seconds / 60 / 60 / 24; 517 if (day > 0) 518 snprintf(buf, sizeof buf, "%dd %d:%02d", day, hr, min); 519 else 520 snprintf(buf, sizeof buf, "%d:%02d", hr, min); 521 return buf; 522 } 523 524 static void 525 print_progress(unsigned long start_lineno, unsigned long current_lineno, 526 unsigned long end_lineno) 527 { 528 static time_t time_start, time_prev; 529 time_t time_now, elapsed; 530 unsigned long num_to_process, processed, remaining, percent, eta; 531 double time_per_line; 532 char *eta_str; 533 534 time_now = monotime(); 535 if (time_start == 0) { 536 time_start = time_prev = time_now; 537 return; 538 } 539 /* print progress after 1m then once per 5m */ 540 if (time_now - time_prev < 5 * 60) 541 return; 542 time_prev = time_now; 543 elapsed = time_now - time_start; 544 processed = current_lineno - start_lineno; 545 remaining = end_lineno - current_lineno; 546 num_to_process = end_lineno - start_lineno; 547 time_per_line = (double)elapsed / processed; 548 /* if we don't know how many we're processing just report count+time */ 549 time(&time_now); 550 if (end_lineno == ULONG_MAX) { 551 logit("%.24s processed %lu in %s", ctime(&time_now), 552 processed, fmt_time(elapsed)); 553 return; 554 } 555 percent = 100 * processed / num_to_process; 556 eta = time_per_line * remaining; 557 eta_str = xstrdup(fmt_time(eta)); 558 logit("%.24s processed %lu of %lu (%lu%%) in %s, ETA %s", 559 ctime(&time_now), processed, num_to_process, percent, 560 fmt_time(elapsed), eta_str); 561 free(eta_str); 562 } 563 564 /* 565 * perform a Miller-Rabin primality test 566 * on the list of candidates 567 * (checking both q and p) 568 * The result is a list of so-call "safe" primes 569 */ 570 int 571 prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted, 572 char *checkpoint_file, unsigned long start_lineno, unsigned long num_lines) 573 { 574 BIGNUM *q, *p, *a; 575 char *cp, *lp; 576 u_int32_t count_in = 0, count_out = 0, count_possible = 0; 577 u_int32_t generator_known, in_tests, in_tries, in_type, in_size; 578 unsigned long last_processed = 0, end_lineno; 579 time_t time_start, time_stop; 580 int res, is_prime; 581 582 if (trials < TRIAL_MINIMUM) { 583 error("Minimum primality trials is %d", TRIAL_MINIMUM); 584 return (-1); 585 } 586 587 if (num_lines == 0) 588 end_lineno = count_lines(in); 589 else 590 end_lineno = start_lineno + num_lines; 591 592 time(&time_start); 593 594 if ((p = BN_new()) == NULL) 595 fatal("BN_new failed"); 596 if ((q = BN_new()) == NULL) 597 fatal("BN_new failed"); 598 599 debug2("%.24s Final %u Miller-Rabin trials (%x generator)", 600 ctime(&time_start), trials, generator_wanted); 601 602 if (checkpoint_file != NULL) 603 last_processed = read_checkpoint(checkpoint_file); 604 last_processed = start_lineno = MAXIMUM(last_processed, start_lineno); 605 if (end_lineno == ULONG_MAX) 606 debug("process from line %lu from pipe", last_processed); 607 else 608 debug("process from line %lu to line %lu", last_processed, 609 end_lineno); 610 611 res = 0; 612 lp = xmalloc(QLINESIZE + 1); 613 while (fgets(lp, QLINESIZE + 1, in) != NULL && count_in < end_lineno) { 614 count_in++; 615 if (count_in <= last_processed) { 616 debug3("skipping line %u, before checkpoint or " 617 "specified start line", count_in); 618 continue; 619 } 620 if (checkpoint_file != NULL) 621 write_checkpoint(checkpoint_file, count_in); 622 print_progress(start_lineno, count_in, end_lineno); 623 if (strlen(lp) < 14 || *lp == '!' || *lp == '#') { 624 debug2("%10u: comment or short line", count_in); 625 continue; 626 } 627 628 /* XXX - fragile parser */ 629 /* time */ 630 cp = &lp[14]; /* (skip) */ 631 632 /* type */ 633 in_type = strtoul(cp, &cp, 10); 634 635 /* tests */ 636 in_tests = strtoul(cp, &cp, 10); 637 638 if (in_tests & MODULI_TESTS_COMPOSITE) { 639 debug2("%10u: known composite", count_in); 640 continue; 641 } 642 643 /* tries */ 644 in_tries = strtoul(cp, &cp, 10); 645 646 /* size (most significant bit) */ 647 in_size = strtoul(cp, &cp, 10); 648 649 /* generator (hex) */ 650 generator_known = strtoul(cp, &cp, 16); 651 652 /* Skip white space */ 653 cp += strspn(cp, " "); 654 655 /* modulus (hex) */ 656 switch (in_type) { 657 case MODULI_TYPE_SOPHIE_GERMAIN: 658 debug2("%10u: (%u) Sophie-Germain", count_in, in_type); 659 a = q; 660 if (BN_hex2bn(&a, cp) == 0) 661 fatal("BN_hex2bn failed"); 662 /* p = 2*q + 1 */ 663 if (BN_lshift(p, q, 1) == 0) 664 fatal("BN_lshift failed"); 665 if (BN_add_word(p, 1) == 0) 666 fatal("BN_add_word failed"); 667 in_size += 1; 668 generator_known = 0; 669 break; 670 case MODULI_TYPE_UNSTRUCTURED: 671 case MODULI_TYPE_SAFE: 672 case MODULI_TYPE_SCHNORR: 673 case MODULI_TYPE_STRONG: 674 case MODULI_TYPE_UNKNOWN: 675 debug2("%10u: (%u)", count_in, in_type); 676 a = p; 677 if (BN_hex2bn(&a, cp) == 0) 678 fatal("BN_hex2bn failed"); 679 /* q = (p-1) / 2 */ 680 if (BN_rshift(q, p, 1) == 0) 681 fatal("BN_rshift failed"); 682 break; 683 default: 684 debug2("Unknown prime type"); 685 break; 686 } 687 688 /* 689 * due to earlier inconsistencies in interpretation, check 690 * the proposed bit size. 691 */ 692 if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { 693 debug2("%10u: bit size %u mismatch", count_in, in_size); 694 continue; 695 } 696 if (in_size < QSIZE_MINIMUM) { 697 debug2("%10u: bit size %u too short", count_in, in_size); 698 continue; 699 } 700 701 if (in_tests & MODULI_TESTS_MILLER_RABIN) 702 in_tries += trials; 703 else 704 in_tries = trials; 705 706 /* 707 * guess unknown generator 708 */ 709 if (generator_known == 0) { 710 if (BN_mod_word(p, 24) == 11) 711 generator_known = 2; 712 else { 713 u_int32_t r = BN_mod_word(p, 10); 714 715 if (r == 3 || r == 7) 716 generator_known = 5; 717 } 718 } 719 /* 720 * skip tests when desired generator doesn't match 721 */ 722 if (generator_wanted > 0 && 723 generator_wanted != generator_known) { 724 debug2("%10u: generator %d != %d", 725 count_in, generator_known, generator_wanted); 726 continue; 727 } 728 729 /* 730 * Primes with no known generator are useless for DH, so 731 * skip those. 732 */ 733 if (generator_known == 0) { 734 debug2("%10u: no known generator", count_in); 735 continue; 736 } 737 738 count_possible++; 739 740 /* 741 * The (1/4)^N performance bound on Miller-Rabin is 742 * extremely pessimistic, so don't spend a lot of time 743 * really verifying that q is prime until after we know 744 * that p is also prime. A single pass will weed out the 745 * vast majority of composite q's. 746 */ 747 is_prime = BN_is_prime_ex(q, 1, NULL, NULL); 748 if (is_prime < 0) 749 fatal("BN_is_prime_ex failed"); 750 if (is_prime == 0) { 751 debug("%10u: q failed first possible prime test", 752 count_in); 753 continue; 754 } 755 756 /* 757 * q is possibly prime, so go ahead and really make sure 758 * that p is prime. If it is, then we can go back and do 759 * the same for q. If p is composite, chances are that 760 * will show up on the first Rabin-Miller iteration so it 761 * doesn't hurt to specify a high iteration count. 762 */ 763 is_prime = BN_is_prime_ex(p, trials, NULL, NULL); 764 if (is_prime < 0) 765 fatal("BN_is_prime_ex failed"); 766 if (is_prime == 0) { 767 debug("%10u: p is not prime", count_in); 768 continue; 769 } 770 debug("%10u: p is almost certainly prime", count_in); 771 772 /* recheck q more rigorously */ 773 is_prime = BN_is_prime_ex(q, trials - 1, NULL, NULL); 774 if (is_prime < 0) 775 fatal("BN_is_prime_ex failed"); 776 if (is_prime == 0) { 777 debug("%10u: q is not prime", count_in); 778 continue; 779 } 780 debug("%10u: q is almost certainly prime", count_in); 781 782 if (qfileout(out, MODULI_TYPE_SAFE, 783 in_tests | MODULI_TESTS_MILLER_RABIN, 784 in_tries, in_size, generator_known, p)) { 785 res = -1; 786 break; 787 } 788 789 count_out++; 790 } 791 792 time(&time_stop); 793 free(lp); 794 BN_free(p); 795 BN_free(q); 796 797 if (checkpoint_file != NULL) 798 unlink(checkpoint_file); 799 800 logit("%.24s Found %u safe primes of %u candidates in %ld seconds", 801 ctime(&time_stop), count_out, count_possible, 802 (long) (time_stop - time_start)); 803 804 return (res); 805 } 806