| /* $OpenBSD: moduli.c,v 1.16 2006/07/26 13:57:17 stevesk Exp $ */ |
| /* |
| * Copyright 1994 Phil Karn <karn@qualcomm.com> |
| * Copyright 1996-1998, 2003 William Allen Simpson <wsimpson@greendragon.com> |
| * Copyright 2000 Niels Provos <provos@citi.umich.edu> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR |
| * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
| * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. |
| * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, |
| * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF |
| * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| */ |
| |
| /* |
| * Two-step process to generate safe primes for DHGEX |
| * |
| * Sieve candidates for "safe" primes, |
| * suitable for use as Diffie-Hellman moduli; |
| * that is, where q = (p-1)/2 is also prime. |
| * |
| * First step: generate candidate primes (memory intensive) |
| * Second step: test primes' safety (processor intensive) |
| */ |
| |
| #include "includes.h" |
| |
| #include <sys/types.h> |
| |
| #include <openssl/bn.h> |
| |
| #include <stdlib.h> |
| #include <string.h> |
| #include <time.h> |
| |
| #include "xmalloc.h" |
| #include "log.h" |
| |
| /* |
| * File output defines |
| */ |
| |
| /* need line long enough for largest moduli plus headers */ |
| #define QLINESIZE (100+8192) |
| |
| /* Type: decimal. |
| * Specifies the internal structure of the prime modulus. |
| */ |
| #define QTYPE_UNKNOWN (0) |
| #define QTYPE_UNSTRUCTURED (1) |
| #define QTYPE_SAFE (2) |
| #define QTYPE_SCHNORR (3) |
| #define QTYPE_SOPHIE_GERMAIN (4) |
| #define QTYPE_STRONG (5) |
| |
| /* Tests: decimal (bit field). |
| * Specifies the methods used in checking for primality. |
| * Usually, more than one test is used. |
| */ |
| #define QTEST_UNTESTED (0x00) |
| #define QTEST_COMPOSITE (0x01) |
| #define QTEST_SIEVE (0x02) |
| #define QTEST_MILLER_RABIN (0x04) |
| #define QTEST_JACOBI (0x08) |
| #define QTEST_ELLIPTIC (0x10) |
| |
| /* |
| * Size: decimal. |
| * Specifies the number of the most significant bit (0 to M). |
| * WARNING: internally, usually 1 to N. |
| */ |
| #define QSIZE_MINIMUM (511) |
| |
| /* |
| * Prime sieving defines |
| */ |
| |
| /* Constant: assuming 8 bit bytes and 32 bit words */ |
| #define SHIFT_BIT (3) |
| #define SHIFT_BYTE (2) |
| #define SHIFT_WORD (SHIFT_BIT+SHIFT_BYTE) |
| #define SHIFT_MEGABYTE (20) |
| #define SHIFT_MEGAWORD (SHIFT_MEGABYTE-SHIFT_BYTE) |
| |
| /* |
| * Using virtual memory can cause thrashing. This should be the largest |
| * number that is supported without a large amount of disk activity -- |
| * that would increase the run time from hours to days or weeks! |
| */ |
| #define LARGE_MINIMUM (8UL) /* megabytes */ |
| |
| /* |
| * Do not increase this number beyond the unsigned integer bit size. |
| * Due to a multiple of 4, it must be LESS than 128 (yielding 2**30 bits). |
| */ |
| #define LARGE_MAXIMUM (127UL) /* megabytes */ |
| |
| /* |
| * Constant: when used with 32-bit integers, the largest sieve prime |
| * has to be less than 2**32. |
| */ |
| #define SMALL_MAXIMUM (0xffffffffUL) |
| |
| /* Constant: can sieve all primes less than 2**32, as 65537**2 > 2**32-1. */ |
| #define TINY_NUMBER (1UL<<16) |
| |
| /* Ensure enough bit space for testing 2*q. */ |
| #define TEST_MAXIMUM (1UL<<16) |
| #define TEST_MINIMUM (QSIZE_MINIMUM + 1) |
| /* real TEST_MINIMUM (1UL << (SHIFT_WORD - TEST_POWER)) */ |
| #define TEST_POWER (3) /* 2**n, n < SHIFT_WORD */ |
| |
| /* bit operations on 32-bit words */ |
| #define BIT_CLEAR(a,n) ((a)[(n)>>SHIFT_WORD] &= ~(1L << ((n) & 31))) |
| #define BIT_SET(a,n) ((a)[(n)>>SHIFT_WORD] |= (1L << ((n) & 31))) |
| #define BIT_TEST(a,n) ((a)[(n)>>SHIFT_WORD] & (1L << ((n) & 31))) |
| |
| /* |
| * Prime testing defines |
| */ |
| |
| /* Minimum number of primality tests to perform */ |
| #define TRIAL_MINIMUM (4) |
| |
| /* |
| * Sieving data (XXX - move to struct) |
| */ |
| |
| /* sieve 2**16 */ |
| static u_int32_t *TinySieve, tinybits; |
| |
| /* sieve 2**30 in 2**16 parts */ |
| static u_int32_t *SmallSieve, smallbits, smallbase; |
| |
| /* sieve relative to the initial value */ |
| static u_int32_t *LargeSieve, largewords, largetries, largenumbers; |
| static u_int32_t largebits, largememory; /* megabytes */ |
| static BIGNUM *largebase; |
| |
| int gen_candidates(FILE *, u_int32_t, u_int32_t, BIGNUM *); |
| int prime_test(FILE *, FILE *, u_int32_t, u_int32_t); |
| |
| /* |
| * print moduli out in consistent form, |
| */ |
| static int |
| qfileout(FILE * ofile, u_int32_t otype, u_int32_t otests, u_int32_t otries, |
| u_int32_t osize, u_int32_t ogenerator, BIGNUM * omodulus) |
| { |
| struct tm *gtm; |
| time_t time_now; |
| int res; |
| |
| time(&time_now); |
| gtm = gmtime(&time_now); |
| |
| res = fprintf(ofile, "%04d%02d%02d%02d%02d%02d %u %u %u %u %x ", |
| gtm->tm_year + 1900, gtm->tm_mon + 1, gtm->tm_mday, |
| gtm->tm_hour, gtm->tm_min, gtm->tm_sec, |
| otype, otests, otries, osize, ogenerator); |
| |
| if (res < 0) |
| return (-1); |
| |
| if (BN_print_fp(ofile, omodulus) < 1) |
| return (-1); |
| |
| res = fprintf(ofile, "\n"); |
| fflush(ofile); |
| |
| return (res > 0 ? 0 : -1); |
| } |
| |
| |
| /* |
| ** Sieve p's and q's with small factors |
| */ |
| static void |
| sieve_large(u_int32_t s) |
| { |
| u_int32_t r, u; |
| |
| debug3("sieve_large %u", s); |
| largetries++; |
| /* r = largebase mod s */ |
| r = BN_mod_word(largebase, s); |
| if (r == 0) |
| u = 0; /* s divides into largebase exactly */ |
| else |
| u = s - r; /* largebase+u is first entry divisible by s */ |
| |
| if (u < largebits * 2) { |
| /* |
| * The sieve omits p's and q's divisible by 2, so ensure that |
| * largebase+u is odd. Then, step through the sieve in |
| * increments of 2*s |
| */ |
| if (u & 0x1) |
| u += s; /* Make largebase+u odd, and u even */ |
| |
| /* Mark all multiples of 2*s */ |
| for (u /= 2; u < largebits; u += s) |
| BIT_SET(LargeSieve, u); |
| } |
| |
| /* r = p mod s */ |
| r = (2 * r + 1) % s; |
| if (r == 0) |
| u = 0; /* s divides p exactly */ |
| else |
| u = s - r; /* p+u is first entry divisible by s */ |
| |
| if (u < largebits * 4) { |
| /* |
| * The sieve omits p's divisible by 4, so ensure that |
| * largebase+u is not. Then, step through the sieve in |
| * increments of 4*s |
| */ |
| while (u & 0x3) { |
| if (SMALL_MAXIMUM - u < s) |
| return; |
| u += s; |
| } |
| |
| /* Mark all multiples of 4*s */ |
| for (u /= 4; u < largebits; u += s) |
| BIT_SET(LargeSieve, u); |
| } |
| } |
| |
| /* |
| * list candidates for Sophie-Germain primes (where q = (p-1)/2) |
| * to standard output. |
| * The list is checked against small known primes (less than 2**30). |
| */ |
| int |
| gen_candidates(FILE *out, u_int32_t memory, u_int32_t power, BIGNUM *start) |
| { |
| BIGNUM *q; |
| u_int32_t j, r, s, t; |
| u_int32_t smallwords = TINY_NUMBER >> 6; |
| u_int32_t tinywords = TINY_NUMBER >> 6; |
| time_t time_start, time_stop; |
| u_int32_t i; |
| int ret = 0; |
| |
| largememory = memory; |
| |
| if (memory != 0 && |
| (memory < LARGE_MINIMUM || memory > LARGE_MAXIMUM)) { |
| error("Invalid memory amount (min %ld, max %ld)", |
| LARGE_MINIMUM, LARGE_MAXIMUM); |
| return (-1); |
| } |
| |
| /* |
| * Set power to the length in bits of the prime to be generated. |
| * This is changed to 1 less than the desired safe prime moduli p. |
| */ |
| if (power > TEST_MAXIMUM) { |
| error("Too many bits: %u > %lu", power, TEST_MAXIMUM); |
| return (-1); |
| } else if (power < TEST_MINIMUM) { |
| error("Too few bits: %u < %u", power, TEST_MINIMUM); |
| return (-1); |
| } |
| power--; /* decrement before squaring */ |
| |
| /* |
| * The density of ordinary primes is on the order of 1/bits, so the |
| * density of safe primes should be about (1/bits)**2. Set test range |
| * to something well above bits**2 to be reasonably sure (but not |
| * guaranteed) of catching at least one safe prime. |
| */ |
| largewords = ((power * power) >> (SHIFT_WORD - TEST_POWER)); |
| |
| /* |
| * Need idea of how much memory is available. We don't have to use all |
| * of it. |
| */ |
| if (largememory > LARGE_MAXIMUM) { |
| logit("Limited memory: %u MB; limit %lu MB", |
| largememory, LARGE_MAXIMUM); |
| largememory = LARGE_MAXIMUM; |
| } |
| |
| if (largewords <= (largememory << SHIFT_MEGAWORD)) { |
| logit("Increased memory: %u MB; need %u bytes", |
| largememory, (largewords << SHIFT_BYTE)); |
| largewords = (largememory << SHIFT_MEGAWORD); |
| } else if (largememory > 0) { |
| logit("Decreased memory: %u MB; want %u bytes", |
| largememory, (largewords << SHIFT_BYTE)); |
| largewords = (largememory << SHIFT_MEGAWORD); |
| } |
| |
| TinySieve = xcalloc(tinywords, sizeof(u_int32_t)); |
| tinybits = tinywords << SHIFT_WORD; |
| |
| SmallSieve = xcalloc(smallwords, sizeof(u_int32_t)); |
| smallbits = smallwords << SHIFT_WORD; |
| |
| /* |
| * dynamically determine available memory |
| */ |
| while ((LargeSieve = calloc(largewords, sizeof(u_int32_t))) == NULL) |
| largewords -= (1L << (SHIFT_MEGAWORD - 2)); /* 1/4 MB chunks */ |
| |
| largebits = largewords << SHIFT_WORD; |
| largenumbers = largebits * 2; /* even numbers excluded */ |
| |
| /* validation check: count the number of primes tried */ |
| largetries = 0; |
| q = BN_new(); |
| |
| /* |
| * Generate random starting point for subprime search, or use |
| * specified parameter. |
| */ |
| largebase = BN_new(); |
| if (start == NULL) |
| BN_rand(largebase, power, 1, 1); |
| else |
| BN_copy(largebase, start); |
| |
| /* ensure odd */ |
| BN_set_bit(largebase, 0); |
| |
| time(&time_start); |
| |
| logit("%.24s Sieve next %u plus %u-bit", ctime(&time_start), |
| largenumbers, power); |
| debug2("start point: 0x%s", BN_bn2hex(largebase)); |
| |
| /* |
| * TinySieve |
| */ |
| for (i = 0; i < tinybits; i++) { |
| if (BIT_TEST(TinySieve, i)) |
| continue; /* 2*i+3 is composite */ |
| |
| /* The next tiny prime */ |
| t = 2 * i + 3; |
| |
| /* Mark all multiples of t */ |
| for (j = i + t; j < tinybits; j += t) |
| BIT_SET(TinySieve, j); |
| |
| sieve_large(t); |
| } |
| |
| /* |
| * Start the small block search at the next possible prime. To avoid |
| * fencepost errors, the last pass is skipped. |
| */ |
| for (smallbase = TINY_NUMBER + 3; |
| smallbase < (SMALL_MAXIMUM - TINY_NUMBER); |
| smallbase += TINY_NUMBER) { |
| for (i = 0; i < tinybits; i++) { |
| if (BIT_TEST(TinySieve, i)) |
| continue; /* 2*i+3 is composite */ |
| |
| /* The next tiny prime */ |
| t = 2 * i + 3; |
| r = smallbase % t; |
| |
| if (r == 0) { |
| s = 0; /* t divides into smallbase exactly */ |
| } else { |
| /* smallbase+s is first entry divisible by t */ |
| s = t - r; |
| } |
| |
| /* |
| * The sieve omits even numbers, so ensure that |
| * smallbase+s is odd. Then, step through the sieve |
| * in increments of 2*t |
| */ |
| if (s & 1) |
| s += t; /* Make smallbase+s odd, and s even */ |
| |
| /* Mark all multiples of 2*t */ |
| for (s /= 2; s < smallbits; s += t) |
| BIT_SET(SmallSieve, s); |
| } |
| |
| /* |
| * SmallSieve |
| */ |
| for (i = 0; i < smallbits; i++) { |
| if (BIT_TEST(SmallSieve, i)) |
| continue; /* 2*i+smallbase is composite */ |
| |
| /* The next small prime */ |
| sieve_large((2 * i) + smallbase); |
| } |
| |
| memset(SmallSieve, 0, smallwords << SHIFT_BYTE); |
| } |
| |
| time(&time_stop); |
| |
| logit("%.24s Sieved with %u small primes in %ld seconds", |
| ctime(&time_stop), largetries, (long) (time_stop - time_start)); |
| |
| for (j = r = 0; j < largebits; j++) { |
| if (BIT_TEST(LargeSieve, j)) |
| continue; /* Definitely composite, skip */ |
| |
| debug2("test q = largebase+%u", 2 * j); |
| BN_set_word(q, 2 * j); |
| BN_add(q, q, largebase); |
| if (qfileout(out, QTYPE_SOPHIE_GERMAIN, QTEST_SIEVE, |
| largetries, (power - 1) /* MSB */, (0), q) == -1) { |
| ret = -1; |
| break; |
| } |
| |
| r++; /* count q */ |
| } |
| |
| time(&time_stop); |
| |
| xfree(LargeSieve); |
| xfree(SmallSieve); |
| xfree(TinySieve); |
| |
| logit("%.24s Found %u candidates", ctime(&time_stop), r); |
| |
| return (ret); |
| } |
| |
| /* |
| * perform a Miller-Rabin primality test |
| * on the list of candidates |
| * (checking both q and p) |
| * The result is a list of so-call "safe" primes |
| */ |
| int |
| prime_test(FILE *in, FILE *out, u_int32_t trials, u_int32_t generator_wanted) |
| { |
| BIGNUM *q, *p, *a; |
| BN_CTX *ctx; |
| char *cp, *lp; |
| u_int32_t count_in = 0, count_out = 0, count_possible = 0; |
| u_int32_t generator_known, in_tests, in_tries, in_type, in_size; |
| time_t time_start, time_stop; |
| int res; |
| |
| if (trials < TRIAL_MINIMUM) { |
| error("Minimum primality trials is %d", TRIAL_MINIMUM); |
| return (-1); |
| } |
| |
| time(&time_start); |
| |
| p = BN_new(); |
| q = BN_new(); |
| ctx = BN_CTX_new(); |
| |
| debug2("%.24s Final %u Miller-Rabin trials (%x generator)", |
| ctime(&time_start), trials, generator_wanted); |
| |
| res = 0; |
| lp = xmalloc(QLINESIZE + 1); |
| while (fgets(lp, QLINESIZE, in) != NULL) { |
| int ll = strlen(lp); |
| |
| count_in++; |
| if (ll < 14 || *lp == '!' || *lp == '#') { |
| debug2("%10u: comment or short line", count_in); |
| continue; |
| } |
| |
| /* XXX - fragile parser */ |
| /* time */ |
| cp = &lp[14]; /* (skip) */ |
| |
| /* type */ |
| in_type = strtoul(cp, &cp, 10); |
| |
| /* tests */ |
| in_tests = strtoul(cp, &cp, 10); |
| |
| if (in_tests & QTEST_COMPOSITE) { |
| debug2("%10u: known composite", count_in); |
| continue; |
| } |
| |
| /* tries */ |
| in_tries = strtoul(cp, &cp, 10); |
| |
| /* size (most significant bit) */ |
| in_size = strtoul(cp, &cp, 10); |
| |
| /* generator (hex) */ |
| generator_known = strtoul(cp, &cp, 16); |
| |
| /* Skip white space */ |
| cp += strspn(cp, " "); |
| |
| /* modulus (hex) */ |
| switch (in_type) { |
| case QTYPE_SOPHIE_GERMAIN: |
| debug2("%10u: (%u) Sophie-Germain", count_in, in_type); |
| a = q; |
| BN_hex2bn(&a, cp); |
| /* p = 2*q + 1 */ |
| BN_lshift(p, q, 1); |
| BN_add_word(p, 1); |
| in_size += 1; |
| generator_known = 0; |
| break; |
| case QTYPE_UNSTRUCTURED: |
| case QTYPE_SAFE: |
| case QTYPE_SCHNORR: |
| case QTYPE_STRONG: |
| case QTYPE_UNKNOWN: |
| debug2("%10u: (%u)", count_in, in_type); |
| a = p; |
| BN_hex2bn(&a, cp); |
| /* q = (p-1) / 2 */ |
| BN_rshift(q, p, 1); |
| break; |
| default: |
| debug2("Unknown prime type"); |
| break; |
| } |
| |
| /* |
| * due to earlier inconsistencies in interpretation, check |
| * the proposed bit size. |
| */ |
| if ((u_int32_t)BN_num_bits(p) != (in_size + 1)) { |
| debug2("%10u: bit size %u mismatch", count_in, in_size); |
| continue; |
| } |
| if (in_size < QSIZE_MINIMUM) { |
| debug2("%10u: bit size %u too short", count_in, in_size); |
| continue; |
| } |
| |
| if (in_tests & QTEST_MILLER_RABIN) |
| in_tries += trials; |
| else |
| in_tries = trials; |
| |
| /* |
| * guess unknown generator |
| */ |
| if (generator_known == 0) { |
| if (BN_mod_word(p, 24) == 11) |
| generator_known = 2; |
| else if (BN_mod_word(p, 12) == 5) |
| generator_known = 3; |
| else { |
| u_int32_t r = BN_mod_word(p, 10); |
| |
| if (r == 3 || r == 7) |
| generator_known = 5; |
| } |
| } |
| /* |
| * skip tests when desired generator doesn't match |
| */ |
| if (generator_wanted > 0 && |
| generator_wanted != generator_known) { |
| debug2("%10u: generator %d != %d", |
| count_in, generator_known, generator_wanted); |
| continue; |
| } |
| |
| /* |
| * Primes with no known generator are useless for DH, so |
| * skip those. |
| */ |
| if (generator_known == 0) { |
| debug2("%10u: no known generator", count_in); |
| continue; |
| } |
| |
| count_possible++; |
| |
| /* |
| * The (1/4)^N performance bound on Miller-Rabin is |
| * extremely pessimistic, so don't spend a lot of time |
| * really verifying that q is prime until after we know |
| * that p is also prime. A single pass will weed out the |
| * vast majority of composite q's. |
| */ |
| if (BN_is_prime(q, 1, NULL, ctx, NULL) <= 0) { |
| debug("%10u: q failed first possible prime test", |
| count_in); |
| continue; |
| } |
| |
| /* |
| * q is possibly prime, so go ahead and really make sure |
| * that p is prime. If it is, then we can go back and do |
| * the same for q. If p is composite, chances are that |
| * will show up on the first Rabin-Miller iteration so it |
| * doesn't hurt to specify a high iteration count. |
| */ |
| if (!BN_is_prime(p, trials, NULL, ctx, NULL)) { |
| debug("%10u: p is not prime", count_in); |
| continue; |
| } |
| debug("%10u: p is almost certainly prime", count_in); |
| |
| /* recheck q more rigorously */ |
| if (!BN_is_prime(q, trials - 1, NULL, ctx, NULL)) { |
| debug("%10u: q is not prime", count_in); |
| continue; |
| } |
| debug("%10u: q is almost certainly prime", count_in); |
| |
| if (qfileout(out, QTYPE_SAFE, (in_tests | QTEST_MILLER_RABIN), |
| in_tries, in_size, generator_known, p)) { |
| res = -1; |
| break; |
| } |
| |
| count_out++; |
| } |
| |
| time(&time_stop); |
| xfree(lp); |
| BN_free(p); |
| BN_free(q); |
| BN_CTX_free(ctx); |
| |
| logit("%.24s Found %u safe primes of %u candidates in %ld seconds", |
| ctime(&time_stop), count_out, count_possible, |
| (long) (time_stop - time_start)); |
| |
| return (res); |
| } |