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Diffstat (limited to 'moduli.c')
| -rw-r--r-- | moduli.c | 617 |
1 files changed, 617 insertions, 0 deletions
diff --git a/moduli.c b/moduli.c new file mode 100644 index 00000000..eb2c0fd1 --- /dev/null +++ b/moduli.c @@ -0,0 +1,617 @@ +/* $OpenBSD: moduli.c,v 1.1 2003/07/28 09:49:56 djm 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 "moduli.h" +#include "xmalloc.h" +#include "log.h" + +#include <openssl/bn.h> + + +/* + * Debugging defines + */ + +/* define DEBUG_LARGE 1 */ +/* define DEBUG_SMALL 1 */ +/* define DEBUG_TEST 1 */ + +/* + * 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_SCHNOOR (3) +#define QTYPE_SOPHIE_GERMAINE (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) + +/* + * 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 + */ + +/* + * 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; + + +/* + * 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; + + debug2("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-Germaine 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, int memory, int 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; + int i, ret = 0; + + largememory = memory; + + /* + * 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 = calloc(tinywords, sizeof(u_int32_t)); + if (TinySieve == NULL) { + error("Insufficient memory for tiny sieve: need %u bytes", + tinywords << SHIFT_BYTE); + exit(1); + } + tinybits = tinywords << SHIFT_WORD; + + SmallSieve = calloc(smallwords, sizeof(u_int32_t)); + if (SmallSieve == NULL) { + error("Insufficient memory for small sieve: need %u bytes", + smallwords << SHIFT_BYTE); + xfree(TinySieve); + exit(1); + } + 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_GERMAINE, 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; + + 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_GERMAINE: + debug2("%10u: (%u) Sophie-Germaine", 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; + default: + debug2("%10u: (%u)", count_in, in_type); + a = p; + BN_hex2bn(&a, cp); + /* q = (p-1) / 2 */ + BN_rshift(q, p, 1); + break; + } + + /* + * due to earlier inconsistencies in interpretation, check + * the proposed bit size. + */ + if (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; + } + + 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) { + debug2("%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)) { + debug2("%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); +} |