moduli.c

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/* $OpenBSD: moduli.c,v 1.10 2005/01/17 03:25:46 dtucker Exp $ */
/*
 * Copyright 1994 Phil Karn <[e-mail]>
 * Copyright 1996-1998, 2003 William Allen Simpson <[e-mail]>
 * Copyright 2000 Niels Provos <[e-mail]>
 * 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 "xmalloc.h"
#include "log.h"

#include <openssl/bn.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 *, int, int, 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, 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;

	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 = 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 */