- stevesk@cvs.openbsd.org 2006/07/22 19:08:54

[openssh-git.git] / moduli.c

/* $OpenBSD: moduli.c,v 1.14 2006/07/22 19:08:54 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 <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);
}