/* $NetBSD: qsieve.c,v 1.4 2025/02/17 22:58:34 andvar 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.
 */

/*
 * Sieve candidates for "safe" primes,
 *  suitable for use as Diffie-Hellman moduli;
 *  that is, where q = (p-1)/2 is also prime.
 *
 * This is the first of two steps.
 * This step is memory intensive.
 *
 * 1996 May     William Allen Simpson
 *              extracted from earlier code by Phil Karn, April 1994.
 *              save large primes list for later processing.
 * 1998 May     William Allen Simpson
 *              parameterized.
 * 2000 Dec     Niels Provos
 *              convert from GMP to openssl BN.
 * 2003 Jun     William Allen Simpson
 *              change outfile definition slightly to match openssh mistake.
 *              move common file i/o to own file for better documentation.
 *              redo memory again.
 */

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <openssl/bn.h>
#include <string.h>
#include <err.h>
#include "qfile.h"

/* define DEBUG_LARGE 1 */
/* define DEBUG_SMALL 1 */

/*
 * 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: 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] &= ~(1U << ((n) & 31)))
#define BIT_SET(a,n)    ((a)[(n)>>SHIFT_WORD] |= (1U << ((n) & 31)))
#define BIT_TEST(a,n)   ((a)[(n)>>SHIFT_WORD] & (1U << ((n) & 31)))

/*
 * sieve relative to the initial value
 */
static uint32_t       *LargeSieve;
static uint32_t        largewords;
static uint32_t        largetries;
static uint32_t        largenumbers;
static uint32_t        largememory;     /* megabytes */
static uint32_t        largebits;
static BIGNUM         *largebase;

/*
 * sieve 2**30 in 2**16 parts
 */
static uint32_t       *SmallSieve;
static uint32_t        smallbits;
static uint32_t        smallbase;

/*
 * sieve 2**16
 */
static uint32_t       *TinySieve;
static uint32_t        tinybits;

__dead static void     usage(void);
static void            sieve_large(uint32_t);

/*
 * Sieve p's and q's with small factors
 */
static void
sieve_large(uint32_t s)
{
        BN_ULONG        r;
        BN_ULONG        u;

#ifdef  DEBUG_SMALL
        (void)fprintf(stderr, "%lu\n", s);
#endif
        largetries++;
        /* r = largebase mod s */
        r = BN_mod_word(largebase, (BN_ULONG) s);
        if (r == 0) {
                /* s divides into largebase exactly */
                u = 0;
        } else {
                /* largebase+u is first entry divisible by s */
                u = s - r;
        }

        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) {
                        /* Make largebase+u odd, and u even */
                        u += s;
                }

                /* Mark all multiples of 2*s */
                for (u /= 2; u < largebits; u += s) {
                        BIT_SET(LargeSieve, (uint32_t)u);
                }
        }

        /* r = p mod s */
        r = (2 * r + 1) % s;

        if (r == 0) {
                /* s divides p exactly */
                u = 0;
        } else {
                /* p+u is first entry divisible by s */
                u = s - r;
        }

        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, (uint32_t)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
main(int argc, char *argv[])
{
        BIGNUM         *q;
        uint32_t        j;
        int             power;
        uint32_t        r;
        uint32_t        s;
        uint32_t        smallwords = TINY_NUMBER >> 6;
        uint32_t        t;
        time_t          time_start;
        time_t          time_stop;
        uint32_t        tinywords = TINY_NUMBER >> 6;
        unsigned int    i;

        setprogname(argv[0]);

        if (argc < 3) {
                usage();
        }

        /*
         * 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.
         */
        power = (int) strtoul(argv[2], NULL, 10);
        if ((unsigned)power > TEST_MAXIMUM) {
                errx(1, "Too many bits: %d > %lu.", power,
                     (unsigned long)TEST_MAXIMUM);
        } else if (power < TEST_MINIMUM) {
                errx(1, "Too few bits: %d < %lu.", power,
                     (unsigned long)TEST_MINIMUM);
        }

        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 = (uint32_t)((unsigned long)
                        (power * power) >> (SHIFT_WORD - TEST_POWER));

        /*
         * Need idea of how much memory is available. We don't have to use all
         * of it.
         */
        largememory = (uint32_t)strtoul(argv[1], NULL, 10);
        if (largememory > LARGE_MAXIMUM) {
                warnx("Limited memory: %u MB; limit %lu MB.", largememory,
                      LARGE_MAXIMUM);
                largememory = LARGE_MAXIMUM;
        }

        if (largewords <= (largememory << SHIFT_MEGAWORD)) {
                warnx("Increased memory: %u MB; need %u bytes.",
                      largememory, (largewords << SHIFT_BYTE));
                largewords = (largememory << SHIFT_MEGAWORD);
        } else if (largememory > 0) {
                warnx("Decreased memory: %u MB; want %u bytes.",
                      largememory, (largewords << SHIFT_BYTE));
                largewords = (largememory << SHIFT_MEGAWORD);
        }

        if ((TinySieve = (uint32_t *) calloc((size_t) tinywords, sizeof(uint32_t))) == NULL) {
                errx(1, "Insufficient memory for tiny sieve: need %u bytes.",
                     tinywords << SHIFT_BYTE);
        }
        tinybits = tinywords << SHIFT_WORD;

        if ((SmallSieve = (uint32_t *) calloc((size_t) smallwords, sizeof(uint32_t))) == NULL) {
                errx(1, "Insufficient memory for small sieve: need %u bytes.",
                     smallwords << SHIFT_BYTE);
        }
        smallbits = smallwords << SHIFT_WORD;

        /*
         * dynamically determine available memory
         */
        while ((LargeSieve = (uint32_t *)calloc((size_t)largewords,
                                                sizeof(uint32_t))) == NULL) {
                /* 1/4 MB chunks */
                largewords -= (1L << (SHIFT_MEGAWORD - 2));
        }
        largebits = largewords << SHIFT_WORD;
        largenumbers = largebits * 2;   /* even numbers excluded */

        /* validation check: count the number of primes tried */
        largetries = 0;

        q = BN_new();
        largebase = BN_new();

        /*
         * Generate random starting point for subprime search, or use
         * specified parameter.
         */
        if (argc < 4) {
                BN_rand(largebase, power, 1, 1);
        } else {
                BIGNUM         *a;

                a = largebase;
                BN_hex2bn(&a, argv[2]);
        }

        /* ensure odd */
        if (!BN_is_odd(largebase)) {
                BN_set_bit(largebase, 0);
        }

        time(&time_start);
        (void)fprintf(stderr,
                "%.24s Sieve next %u plus %d-bit start point:\n# ",
                ctime(&time_start), largenumbers, power);
        BN_print_fp(stderr, largebase);
        (void)fprintf(stderr, "\n");

        /*
         * TinySieve
         */
        for (i = 0; i < tinybits; i++) {
                if (BIT_TEST(TinySieve, i)) {
                        /* 2*i+3 is composite */
                        continue;
                }

                /* 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)) {
                                /* 2*i+3 is composite */
                                continue;
                        }

                        /* The next tiny prime */
                        t = 2 * i + 3;
                        r = smallbase % t;

                        if (r == 0) {
                                /* t divides into smallbase exactly */
                                s = 0;
                        } 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) {
                                /* Make smallbase+s odd, and s even */
                                s += t;
                        }

                        /* 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)) {
                                /* 2*i+smallbase is composite */
                                continue;
                        }

                        /* The next small prime */
                        sieve_large((2 * i) + smallbase);
                }

                memset(SmallSieve, 0, (size_t)(smallwords << SHIFT_BYTE));
        }

        time(&time_stop);
        (void)fprintf(stderr,
                "%.24s Sieved with %u small primes in %lu seconds\n",
                ctime(&time_stop), largetries,
                (long) (time_stop - time_start));

        for (j = r = 0; j < largebits; j++) {
                if (BIT_TEST(LargeSieve, j)) {
                        /* Definitely composite, skip */
                        continue;
                }

#ifdef  DEBUG_LARGE
                (void)fprintf(stderr, "test q = largebase+%lu\n", 2 * j);
#endif

                BN_set_word(q, (unsigned long)(2 * j));
                BN_add(q, q, largebase);

                if (0 > qfileout(stdout,
                                 (uint32_t) QTYPE_SOPHIE_GERMAINE,
                                 (uint32_t) QTEST_SIEVE,
                                 largetries,
                                 (uint32_t) (power - 1), /* MSB */
                                 (uint32_t) (0), /* generator unknown */
                                 q)) {
                        break;
                }

                r++;            /* count q */
        }

        time(&time_stop);

        free(LargeSieve);
        free(SmallSieve);
        free(TinySieve);

        fflush(stdout);
        /* fclose(stdout); */

        (void) fprintf(stderr, "%.24s Found %u candidates\n",
            ctime(&time_stop), r);

        return (0);
}

static void
usage(void)
{
        (void)fprintf(stderr, "Usage: %s <megabytes> <bits> [initial]\n"
                "Possible values for <megabytes>: 0, %lu to %lu\n"
                "Possible values for <bits>: %lu to %lu\n",
                getprogname(),
                LARGE_MINIMUM,
                LARGE_MAXIMUM,
                (unsigned long) TEST_MINIMUM,
                (unsigned long) TEST_MAXIMUM);

        exit(1);
}