--- /dev/null
+/* $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);
+}
andersk / openssh.git / commitdiff
