Pollard's rho algorithm for computing discrete logs.

[u/mdw/catacomb] / twofish-mktab.c

/* -*-c-*-
 *
 * $Id: twofish-mktab.c,v 1.3 2000/06/26 17:14:42 mdw Exp $
 *
 * Build constant tables for Twofish
 *
 * (c) 2000 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: twofish-mktab.c,v $
 * Revision 1.3  2000/06/26 17:14:42  mdw
 * (rslog): Ensure that log(1) = 0 (not 255, as previously).  While the two
 * are strictly equivalent, it means that the exp table is larger than it
 * otherwise needs to be.
 *
 * Revision 1.2  2000/06/18 23:12:15  mdw
 * Change typesetting of Galois Field names.
 *
 * Revision 1.1  2000/06/17 12:10:17  mdw
 * New cipher.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include <stdio.h>
#include <stdlib.h>

#include <mLib/bits.h>

/*----- Data structures ---------------------------------------------------*/

typedef struct { octet t[4][16]; } t_tab;
typedef struct { octet q[256]; } q_tab;

/*----- Various Twofish tables --------------------------------------------*/

/* --- The t-tables --- */

static const t_tab qt0 = {{
  { 0x8, 0x1, 0x7, 0xd, 0x6, 0xf, 0x3, 0x2,
    0x0, 0xb, 0x5, 0x9, 0xe, 0xc, 0xa, 0x4 },
  { 0xe, 0xc, 0xb, 0x8, 0x1, 0x2, 0x3, 0x5,
    0xf, 0x4, 0xa, 0x6, 0x7, 0x0, 0x9, 0xd },
  { 0xb, 0xa, 0x5, 0xe, 0x6, 0xd, 0x9, 0x0,
    0xc, 0x8, 0xf, 0x3, 0x2, 0x4, 0x7, 0x1 },
  { 0xd, 0x7, 0xf, 0x4, 0x1, 0x2, 0x6, 0xe,
    0x9, 0xb, 0x3, 0x0, 0x8, 0x5, 0xc, 0xa }
}};

static const t_tab qt1 = {{
  { 0x2, 0x8, 0xb, 0xd, 0xf, 0x7, 0x6, 0xe,
    0x3, 0x1, 0x9, 0x4, 0x0, 0xa, 0xc, 0x5 },
  { 0x1, 0xe, 0x2, 0xb, 0x4, 0xc, 0x3, 0x7,
    0x6, 0xd, 0xa, 0x5, 0xf, 0x9, 0x0, 0x8 },
  { 0x4, 0xc, 0x7, 0x5, 0x1, 0x6, 0x9, 0xa,
    0x0, 0xe, 0xd, 0x8, 0x2, 0xb, 0x3, 0xf },
  { 0xb, 0x9, 0x5, 0x1, 0xc, 0x3, 0xd, 0xe,
    0x6, 0x4, 0x7, 0xf, 0x2, 0x0, 0x8, 0xa }
}};

static q_tab q0, q1;

/* --- The MDS and Reed-Solomon matrices --- */

static const octet mds[16] = {
  0x01, 0xef, 0x5b, 0x5b,
  0x5b, 0xef, 0xef, 0x01,
  0xef, 0x5b, 0x01, 0xef,
  0xef, 0x01, 0xef, 0x5b
};

static const octet rs[32] = {
  0x01, 0xa4, 0x55, 0x87, 0x5a, 0x58, 0xdb, 0x9e,
  0xa4, 0x56, 0x82, 0xf3, 0x1e, 0xc6, 0x68, 0xe5,
  0x02, 0xa1, 0xfc, 0xc1, 0x47, 0xae, 0x3d, 0x19,
  0xa4, 0x55, 0x87, 0x5a, 0x58, 0xdb, 0x9e, 0x03
};

/*----- Magic macros ------------------------------------------------------*/

#define ROR4(x) ((((x) >> 1) | ((x) << 3)) & 15)

/*----- Building and printing @q@ tables ----------------------------------*/

/* --- @mkq@ --- *
 *
 * Arguments:	@q_tab *q@ = pointer to output @q@ table
 *		@const t_tab *t@ = pointer to input @t@ table
 *		@const char *name@ = name of @q@ table
 *
 * Returns:	---
 *
 * Use:		Constructs a 256-entry @q@-table.
 */

static void mkq(q_tab *q, const t_tab *t, const char *name)
{
  int i;
  int ok = 1;

  /* --- Ensure the t-table is well-formed --- */

  for (i = 0; i < 4; i++) {
    octet f[16] = { 0 };
    int j;

    for (j = 0; j < 16; j++) {
      if (f[t->t[i][j]]) {
	fprintf(stderr, "duplicate %i in %s[%i] (col %i and %i)\n",
		t->t[i][j], name, i, j, f[t->t[i][j]]);
	ok = 0;
      }
      f[t->t[i][j]] = j;
    }
  }

  if (!ok)
    exit(EXIT_FAILURE);

  /* --- Construct the @q@ table --- */

  for (i = 0; i < 256; i++) {
    int a = i >> 4, b = i & 15;
    int aa = t->t[0][a ^ b], bb = t->t[1][a ^ ((a << 3) & 15) ^ ROR4(b)];
    a = t->t[2][aa ^ bb], b = t->t[3][aa ^ ((aa << 3) & 15) ^ ROR4(bb)];
    q->q[i] = a | (b << 4);
  }

  /* Consider testing @q@ for linear and differential properties here */
}

/* --- @printq@ --- *
 *
 * Arguments:	@const q_tab *t@ = pointer to table
 *		@const char *name@ = pointer to table name
 *
 * Returns:	---
 *
 * Use:		Prints a q table.
 */

static void printq(const q_tab *q, const char *name)
{
  int i;
  int j;

  printf("\
#define TWOFISH_%s {							\\\n\
  ", name);
  j = 0;
  for (i = 0; i < 256; i++) {
    printf("0x%02x", q->q[i]);
    j = (j + 1) & 7;
    if (i == 255)
      fputs("			\\\n}\n\n", stdout);
    else if (j == 0)
      fputs(",			\\\n  ", stdout);
    else
      fputs(", ", stdout);
  }
}

/*----- %$\gf{2^8}$% arithmetic -------------------------------------------*/

#define MDS_MOD 0x169
#define RS_MOD 0x14d

/* --- @mul@ --- *
 *
 * Arguments:	@unsigned x, y@ = polynomials over %$\gf{2^8}$%
 *		@unsigned m@ = modulus
 *
 * Returns:	The product of two polynomials.
 *
 * Use:		Computes a product of polynomials, quite slowly.
 */

static unsigned mul(unsigned x, unsigned y, unsigned m)
{
  unsigned a = 0;
  unsigned i;

  for (i = 0; i < 8; i++) {
    if (y & 1)
      a ^= x;
    y >>= 1;
    x <<= 1;
    if (x & 0x100)
      x ^= m;
  }

  return (a);
}

/* --- @mmul@ --- *
 *
 * Arguments:	@octet *d@ = destination vector
 *		@const octet *p@ = matrix of bytes
 *		@const octet *q@ = vector from somewhere else
 *		@size_t r@ = size of destination or number of rows in matrix
 *		@size_t n@ = length of row and vector
 *		@unsigned m@ = modulus polynomial
 *
 * Returns:	---
 *
 * Use:		Computes an inner product of matrices over the finite field
 *		%$\gf{2^8}[x]/(m(x))$%.  This isn't particularly rapid.
 */

static void mmul(octet *d, const octet *p, const octet *q,
		 size_t r, size_t n, unsigned m)
{
  while (r) {
    const octet *qq = q;
    unsigned a = 0;
    unsigned i;

    for (i = 0; i < n; i++)
      a ^= mul(*p++, *qq++, m);
    *d++ = a;
    r--;
  }
}

/* --- @qrds@ --- *
 *
 * Arguments:	---
 *
 * Returns:	---
 *
 * Use:		Prints the MDS/q table.
 */

static void qmds(void)
{
  uint32 t[4][256];
  int i, j;
  static const q_tab *q[4] = { &q1, &q0, &q1, &q0 };

  for (i = 0; i < 4; i++) {
    octet in[4] = { 0, 0, 0, 0 };
    octet out[4];

    for (j = 0; j < 256; j++) {
      in[i] = q[i]->q[j];
      mmul(out, mds, in, 4, 4, MDS_MOD);
      t[i][j] = LOAD32_L(out);
    }
  }

  puts("\
/* --- Expanded MDS tables --- *\n\
 *\n\
 * The table contains output vectors for computing the result of pushing\n\
 * bytes through appropriate @q@ tables and the MDS matrix.\n\
 */\n\
\n\
#define TWOFISH_QMDS {							\\");
  for (i = 0; i < 4; i++) {
    fputs("  { ", stdout);
    for (j = 0; j < 256; j++) {
      printf("0x%08lx", (unsigned long)t[i][j]);
      if (j == 255) {
	if (i == 3)
	  puts(" }			\\\n}");
	else
	  puts(" },			\\\n\
									\\");
      } else if (j % 4 == 3)
	fputs(",			\\\n    ", stdout);
      else
	fputs(", ", stdout);
    }
  }

  putchar('\n');
}

/* --- @rslog@ --- *
 *
 * Arguments:	---
 *
 * Returns:	---
 *
 * Use:		Produces the log and antilog tables for doing the RS
 *		arithmetic efficiently.
 */

static void rslog(void)
{
  octet rslog[256];
  octet rsexp[256];

  unsigned x = 1;
  unsigned i;

  rslog[0] = 0;
  for (i = 0; i < 255; i++) {
    rslog[x] = i;
    rsexp[i] = x;
    x <<= 1;
    if (x & 0x100)
      x ^= RS_MOD;
  }

  x = 0;
  for (i = 0; i < 32; i++) {
    if (rslog[rs[i]] > x)
      x = rslog[rs[i]];
  }

  fputs("\
/* --- Reed-Solomon log tables --- *\n\
 *\n\
 * The Reed-Solomon multiplies are accelerated by using log tables.\n\
 */\n\
\n\
#define TWOFISH_RSLOG {							\\\n\
  ", stdout);

  for (i = 0; i < 256; i++) {
    printf("0x%02x", rslog[i]);
    if (i == 255)
      puts("			\\\n}\n");
    else if (i % 8 == 7)
      fputs(",			\\\n  ", stdout);
    else
      fputs(", ", stdout);
  }

  fputs("\
#define TWOFISH_RSEXP {							\\\n\
  ", stdout);

  for (i = 0; i < 255 + x + 1; i++) {
    printf("0x%02x", rsexp[i % 255]);
    if (i == 255 + x)
      puts("						\\\n}\n");
    else if (i % 8 == 7)
      fputs(",			\\\n  ", stdout);
    else
      fputs(", ", stdout);
  }

  fputs("\
/* --- Reed-Solomon matrix with log entries --- */\n\
\n\
#define TWOFISH_RS {							\\\n\
  ", stdout);

  for (i = 0; i < 32; i++) {
    printf("0x%02x", rslog[rs[i]]);
    if (i == 31)
      puts("			\\\n}\n");
    else if (i % 8 == 7)
      fputs(",			\\\n  ", stdout);
    else
      fputs(", ", stdout);
  }
}

/*----- Main program ------------------------------------------------------*/

/* --- @main@ --- */

int main(void)
{
  fputs("\
/* -*-c-*-
 *
 * Twofish q tables [generated]\n\
 */

#ifndef CATACOMB_TWOFISH_TAB_H
#define CATACOMB_TWOFISH_TAB_H

", stdout);

  /* --- The q tables --- */

  puts("\
/* --- Precomputed @q@ tables --- */\n\
");
  mkq(&q0, &qt0, "qt0");
  mkq(&q1, &qt1, "qt1");
  printq(&q0, "Q0");
  printq(&q1, "Q1");

  /* --- The MDS/q tables --- */

  qmds();
  rslog();

  /* --- Done --- */

  puts("#endif");

  if (fclose(stdout)) {
    fprintf(stderr, "error writing data\n");
    exit(EXIT_FAILURE);
  }

  return (0);
}

/*----- That's all, folks -------------------------------------------------*/