twofish.c 18.6 KB
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/* twofish.c
 *
 * $Id$
 */
  
/* twofish - An implementation of the twofish cipher.
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 * Copyright (C) 1999 Ruud de Rooij <ruud@debian.org>
 *
 * Modifications for lsh, integrated testing
 * Copyright (C) 1999 J.H.M. Dassen (Ray) <jdassen@wi.LeidenUniv.nl>
 *
 * This library 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.
 *
 * This library 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 this library; if not, write to the Free
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

/* ------------------------------------------------------------------------- */

#include "twofish.h"

#include <stdlib.h>
#include <string.h>
#include <assert.h>

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static char cvs_id[] UNUSED =
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"$Id$";

/* ------------------------------------------------------------------------- */

/* Type definitions for byte and word.  word refers to a 32-bit unsigned
 * value.
 */

typedef UINT8 byte;
typedef UINT32 word;

/* Bitwise rotations on 32-bit words.  These are defined as macros that
 * evaluate their argument twice, so do not apply to any expressions with
 * side effects.
 */

#define rol1(x) (((x) << 1) | (((x) & 0x80000000) >> 31))
#define rol8(x) (((x) << 8) | (((x) & 0xFF000000) >> 24))
#define rol9(x) (((x) << 9) | (((x) & 0xFF800000) >> 23))
#define ror1(x) (((x) >> 1) | (((x) & 0x00000001) << 31))

/* void bytes_to_words(word * dest, const byte * src, int n);
 * void words_to_bytes(byte * dest, const byte * src, int n);
 *
 * Copy n*4 bytes to n words and vice versa.
 */

#if defined(__i386__)

/* In the i386 case, these are simply memcpy's since the memory layout
 * of an array of bytes and an array of words is identical.
 */

#define bytes_to_words(dest,src,n) memcpy(dest,src,(n)*4)
#define words_to_bytes(dest,src,n) memcpy(dest,src,(n)*4)

#else

/* These versions are independent of endianness and word size. */

static void
bytes_to_words(word *dest, const byte *src, int n)
{
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  while (n-- > 0)
    {
      *dest++ = src[0] | src[1] << 8 | src[2] << 16 | src[3] << 24;
      src += 4;
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    }
}

static void
words_to_bytes(byte *dest, const word *src, int n)
{
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  while (n-- > 0)
    {
      *dest++ = *src;
      *dest++ = *src >> 8;
      *dest++ = *src >> 16;
      *dest++ = *src >> 24;
      src++;
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    }
}

#endif

/* ------------------------------------------------------------------------- */

/* The permutations q0 and q1.  These are fixed permutations on 8-bit values.
 * The permutations have been computed using the program generate_q
 * which is distributed along with this file.
 */

static byte q0[] = { 0xA9, 0x67, 0xB3, 0xE8, 0x04, 0xFD, 0xA3, 0x76,
                     0x9A, 0x92, 0x80, 0x78, 0xE4, 0xDD, 0xD1, 0x38,
                     0x0D, 0xC6, 0x35, 0x98, 0x18, 0xF7, 0xEC, 0x6C,
                     0x43, 0x75, 0x37, 0x26, 0xFA, 0x13, 0x94, 0x48,
                     0xF2, 0xD0, 0x8B, 0x30, 0x84, 0x54, 0xDF, 0x23,
                     0x19, 0x5B, 0x3D, 0x59, 0xF3, 0xAE, 0xA2, 0x82,
                     0x63, 0x01, 0x83, 0x2E, 0xD9, 0x51, 0x9B, 0x7C,
                     0xA6, 0xEB, 0xA5, 0xBE, 0x16, 0x0C, 0xE3, 0x61,
                     0xC0, 0x8C, 0x3A, 0xF5, 0x73, 0x2C, 0x25, 0x0B,
                     0xBB, 0x4E, 0x89, 0x6B, 0x53, 0x6A, 0xB4, 0xF1,
                     0xE1, 0xE6, 0xBD, 0x45, 0xE2, 0xF4, 0xB6, 0x66,
                     0xCC, 0x95, 0x03, 0x56, 0xD4, 0x1C, 0x1E, 0xD7,
                     0xFB, 0xC3, 0x8E, 0xB5, 0xE9, 0xCF, 0xBF, 0xBA,
                     0xEA, 0x77, 0x39, 0xAF, 0x33, 0xC9, 0x62, 0x71,
                     0x81, 0x79, 0x09, 0xAD, 0x24, 0xCD, 0xF9, 0xD8,
                     0xE5, 0xC5, 0xB9, 0x4D, 0x44, 0x08, 0x86, 0xE7,
                     0xA1, 0x1D, 0xAA, 0xED, 0x06, 0x70, 0xB2, 0xD2,
                     0x41, 0x7B, 0xA0, 0x11, 0x31, 0xC2, 0x27, 0x90,
                     0x20, 0xF6, 0x60, 0xFF, 0x96, 0x5C, 0xB1, 0xAB,
                     0x9E, 0x9C, 0x52, 0x1B, 0x5F, 0x93, 0x0A, 0xEF,
                     0x91, 0x85, 0x49, 0xEE, 0x2D, 0x4F, 0x8F, 0x3B,
                     0x47, 0x87, 0x6D, 0x46, 0xD6, 0x3E, 0x69, 0x64,
                     0x2A, 0xCE, 0xCB, 0x2F, 0xFC, 0x97, 0x05, 0x7A,
                     0xAC, 0x7F, 0xD5, 0x1A, 0x4B, 0x0E, 0xA7, 0x5A,
                     0x28, 0x14, 0x3F, 0x29, 0x88, 0x3C, 0x4C, 0x02,
                     0xB8, 0xDA, 0xB0, 0x17, 0x55, 0x1F, 0x8A, 0x7D,
                     0x57, 0xC7, 0x8D, 0x74, 0xB7, 0xC4, 0x9F, 0x72,
                     0x7E, 0x15, 0x22, 0x12, 0x58, 0x07, 0x99, 0x34,
                     0x6E, 0x50, 0xDE, 0x68, 0x65, 0xBC, 0xDB, 0xF8,
                     0xC8, 0xA8, 0x2B, 0x40, 0xDC, 0xFE, 0x32, 0xA4,
                     0xCA, 0x10, 0x21, 0xF0, 0xD3, 0x5D, 0x0F, 0x00,
                     0x6F, 0x9D, 0x36, 0x42, 0x4A, 0x5E, 0xC1, 0xE0, };

static byte q1[] = { 0x75, 0xF3, 0xC6, 0xF4, 0xDB, 0x7B, 0xFB, 0xC8,
                     0x4A, 0xD3, 0xE6, 0x6B, 0x45, 0x7D, 0xE8, 0x4B,
                     0xD6, 0x32, 0xD8, 0xFD, 0x37, 0x71, 0xF1, 0xE1,
                     0x30, 0x0F, 0xF8, 0x1B, 0x87, 0xFA, 0x06, 0x3F,
                     0x5E, 0xBA, 0xAE, 0x5B, 0x8A, 0x00, 0xBC, 0x9D,
                     0x6D, 0xC1, 0xB1, 0x0E, 0x80, 0x5D, 0xD2, 0xD5,
                     0xA0, 0x84, 0x07, 0x14, 0xB5, 0x90, 0x2C, 0xA3,
                     0xB2, 0x73, 0x4C, 0x54, 0x92, 0x74, 0x36, 0x51,
                     0x38, 0xB0, 0xBD, 0x5A, 0xFC, 0x60, 0x62, 0x96,
                     0x6C, 0x42, 0xF7, 0x10, 0x7C, 0x28, 0x27, 0x8C,
                     0x13, 0x95, 0x9C, 0xC7, 0x24, 0x46, 0x3B, 0x70,
                     0xCA, 0xE3, 0x85, 0xCB, 0x11, 0xD0, 0x93, 0xB8,
                     0xA6, 0x83, 0x20, 0xFF, 0x9F, 0x77, 0xC3, 0xCC,
                     0x03, 0x6F, 0x08, 0xBF, 0x40, 0xE7, 0x2B, 0xE2,
                     0x79, 0x0C, 0xAA, 0x82, 0x41, 0x3A, 0xEA, 0xB9,
                     0xE4, 0x9A, 0xA4, 0x97, 0x7E, 0xDA, 0x7A, 0x17,
                     0x66, 0x94, 0xA1, 0x1D, 0x3D, 0xF0, 0xDE, 0xB3,
                     0x0B, 0x72, 0xA7, 0x1C, 0xEF, 0xD1, 0x53, 0x3E,
                     0x8F, 0x33, 0x26, 0x5F, 0xEC, 0x76, 0x2A, 0x49,
                     0x81, 0x88, 0xEE, 0x21, 0xC4, 0x1A, 0xEB, 0xD9,
                     0xC5, 0x39, 0x99, 0xCD, 0xAD, 0x31, 0x8B, 0x01,
                     0x18, 0x23, 0xDD, 0x1F, 0x4E, 0x2D, 0xF9, 0x48,
                     0x4F, 0xF2, 0x65, 0x8E, 0x78, 0x5C, 0x58, 0x19,
                     0x8D, 0xE5, 0x98, 0x57, 0x67, 0x7F, 0x05, 0x64,
                     0xAF, 0x63, 0xB6, 0xFE, 0xF5, 0xB7, 0x3C, 0xA5,
                     0xCE, 0xE9, 0x68, 0x44, 0xE0, 0x4D, 0x43, 0x69,
                     0x29, 0x2E, 0xAC, 0x15, 0x59, 0xA8, 0x0A, 0x9E,
                     0x6E, 0x47, 0xDF, 0x34, 0x35, 0x6A, 0xCF, 0xDC,
                     0x22, 0xC9, 0xC0, 0x9B, 0x89, 0xD4, 0xED, 0xAB,
                     0x12, 0xA2, 0x0D, 0x52, 0xBB, 0x02, 0x2F, 0xA9,
                     0xD7, 0x61, 0x1E, 0xB4, 0x50, 0x04, 0xF6, 0xC2,
                     0x16, 0x25, 0x86, 0x56, 0x55, 0x09, 0xBE, 0x91, };

/* ------------------------------------------------------------------------- */

/* byte gf_multiply(byte p, byte a, byte b)
 *
 * Multiplication in GF(2^8).
 *
 * This function multiplies a times b in the Galois Field GF(2^8) with
 * primitive polynomial p.
 * The representation of the polynomials a, b, and p uses bits with
 * values 2^i to represent the terms x^i.  The polynomial p contains an
 * implicit term x^8.
 *
 * Note that addition and subtraction in GF(2^8) is simply the XOR
 * operation.
 */

static byte
gf_multiply(byte p, byte a, byte b)
{
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  word shift  = b;
  byte result = 0;
  while (a)
    {
      if (a & 1) result ^= shift;
      a = a >> 1;
      shift = shift << 1;
      if (shift & 0x100) shift ^= p;
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    }
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  return result;
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}

/* ------------------------------------------------------------------------- */

/* The matrix RS as specified in section 4.3 the twofish paper. */

static byte rs_matrix[4][8] = {
    { 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 } };

/* word compute_s(word m1, word m2);
 *
 * Computes the value RS * M, where M is a byte vector composed of the
 * bytes of m1 and m2.  Arithmetic is done in GF(2^8) with primitive
 * polynomial x^8 + x^6 + x^3 + x^2 + 1.
 *
 * This function is used to compute the sub-keys S which are in turn used
 * to generate the S-boxes.
 */

static word
compute_s(word m1, word m2)
{
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  word s = 0;
  int i;
  for (i = 0; i < 4; i++)
    s |=  ((  gf_multiply(0x4D, m1,       rs_matrix[i][0])
	    ^ gf_multiply(0x4D, m1 >> 8,  rs_matrix[i][1])
	    ^ gf_multiply(0x4D, m1 >> 16, rs_matrix[i][2])
	    ^ gf_multiply(0x4D, m1 >> 24, rs_matrix[i][3])
	    ^ gf_multiply(0x4D, m2,       rs_matrix[i][4])
	    ^ gf_multiply(0x4D, m2 >> 8,  rs_matrix[i][5])
	    ^ gf_multiply(0x4D, m2 >> 16, rs_matrix[i][6])
	    ^ gf_multiply(0x4D, m2 >> 24, rs_matrix[i][7])) << (i*8));
  return s;
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}

/* ------------------------------------------------------------------------- */

/* This table describes which q S-boxes are used for each byte in each stage
 * of the function h, cf. figure 2 of the twofish paper.
 */

static byte * q_table[4][5] = { { q1, q1, q0, q0, q1 },
                                { q0, q1, q1, q0, q0 },
                                { q0, q0, q0, q1, q1 },
                                { q1, q0, q1, q1, q0 } };

/* The matrix MDS as specified in section 4.3.2 of the twofish paper. */

static byte mds_matrix[4][4] = { { 0x01, 0xEF, 0x5B, 0x5B },
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				 { 0x5B, 0xEF, 0xEF, 0x01 },
				 { 0xEF, 0x5B, 0x01, 0xEF },
				 { 0xEF, 0x01, 0xEF, 0x5B } };
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/* word h_byte(int k, int i, byte x, byte l0, byte l1, byte l2, byte l3);
 *
 * Perform the h function (section 4.3.2) on one byte.  It consists of
 * repeated applications of the q permutation, followed by a XOR with
 * part of a sub-key.  Finally, the value is multiplied by one column of
 * the MDS matrix.  To obtain the result for a full word, the results of
 * h for the individual bytes are XORed.
 *
 * k is the key size (/ 64 bits), i is the byte number (0 = LSB), x is the
 * actual byte to apply the function to; l0, l1, l2, and l3 are the
 * appropriate bytes from the subkey.  Note that only l0..lk are used.
 */

static word
h_byte(int k, int i, byte x, byte l0, byte l1, byte l2, byte l3)
{
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  byte y = q_table[i][4][l0 ^
            q_table[i][3][l1 ^
              q_table[i][2][k == 2 ? x : l2 ^
                q_table[i][1][k == 3 ? x : l3 ^ q_table[i][0][x]]]]];

  return ( ((word)gf_multiply(0x69, mds_matrix[0][i], y))
	   | ((word)gf_multiply(0x69, mds_matrix[1][i], y) << 8)
	   | ((word)gf_multiply(0x69, mds_matrix[2][i], y) << 16)
	   | ((word)gf_multiply(0x69, mds_matrix[3][i], y) << 24) );
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}

/* word h(int k, byte x, word l0, word l1, word l2, word l3);
 *
 * Perform the function h on a word.  See the description of h_byte() above.
 */

static word
h(int k, byte x, word l0, word l1, word l2, word l3)
{
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  return (  h_byte(k, 0, x, l0,       l1,       l2,       l3)
	  ^ h_byte(k, 1, x, l0 >> 8,  l1 >> 8,  l2 >> 8,  l3 >> 8)
	  ^ h_byte(k, 2, x, l0 >> 16, l1 >> 16, l2 >> 16, l3 >> 16)
	  ^ h_byte(k, 3, x, l0 >> 24, l1 >> 24, l2 >> 24, l3 >> 24) );
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}


/*
 * Sanity check using the test vectors from appendix 2 of the Twofish paper.
 */
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int
twofish_selftest(void)
{
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  byte testkey128[16] =
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  { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
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  byte ciphertext128[16] =
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  {
    0x5D, 0x9D, 0x4E, 0xEF, 0xFA, 0x91, 0x51, 0x57,
    0x55, 0x24, 0xF1, 0x15, 0x81, 0x5A, 0x12, 0xE0 };
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  byte testkey192[24] =
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  { 0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF,
    0xFE, 0xDC, 0xBA, 0x98, 0x76, 0x54, 0x32, 0x10,
    0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77 };
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  byte ciphertext192[16] =
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  { 0xE7, 0x54, 0x49, 0x21, 0x2B, 0xEE, 0xF9, 0xF4,
    0xA3, 0x90, 0xBD, 0x86, 0x0A, 0x64, 0x09, 0x41 };
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  byte testkey256[32] =
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  { 0x01, 0x23, 0x45, 0x67, 0x89, 0xAB, 0xCD, 0xEF,
    0xFE, 0xDC, 0xBA, 0x98, 0x76, 0x54, 0x32, 0x10,
    0x00, 0x11, 0x22, 0x33, 0x44, 0x55, 0x66, 0x77,
    0x88, 0x99, 0xAA, 0xBB, 0xCC, 0xDD, 0xEE, 0xFF };
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  byte ciphertext256[16] =
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  { 0x37, 0xFE, 0x26, 0xFF, 0x1C, 0xF6, 0x61, 0x75,
    0xF5, 0xDD, 0xF4, 0xC3, 0x3B, 0x97, 0xA2, 0x05 };
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  TWOFISH_context context;
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  int i;
  byte plaintext[16], ciphertext[16];

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  twofish_setup(&context, 16, testkey128);
  memset(plaintext, 0, 16);
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  for (i = 0 ; i < 50; i++) {
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    twofish_encrypt(&context, plaintext, ciphertext);
    memcpy(plaintext, ciphertext, 16);
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  }
  if (!memcmp(ciphertext, ciphertext128, 16)) {
    return 0;
  }

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  twofish_setup(&context, 24, testkey192);
  memset(plaintext, 0, 16);
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  for (i = 0 ; i < 50; i++) {
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    twofish_encrypt(&context, plaintext, ciphertext);
    memcpy(plaintext, ciphertext, 16);
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  }
  if (!memcmp(ciphertext, ciphertext192, 16)) {
    return 0;
  }

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  twofish_setup(&context, 32, testkey256);
  memset(plaintext, 0, 16);
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  for (i = 0 ; i < 50; i++) {
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    twofish_encrypt(&context, plaintext, ciphertext);
    memcpy(plaintext, ciphertext, 16);
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  }
  if (!memcmp(ciphertext, ciphertext256, 16)) {
    return 0;
  }

  return 1;
}

/* ------------------------------------------------------------------------- */

/* API */

/* Structure which contains the tables containing the subkeys and the
 * key-dependent s-boxes.
 */


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/* void twofish_setup(TWOFISH_context *ctx, size_t keysize, const UINT8 * key);
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 *
 * Set up internal tables required for twofish encryption and decryption.
 *
 * The key size is specified in bytes.  Key sizes up to 32 bytes are
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 * supported.  Larger key sizes are silently truncated.  
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 */

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void
twofish_setup(TWOFISH_context * context, size_t keysize, const UINT8 *key)
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{
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  byte key_copy[32];
  word m[8], s[4], t;
  int i, j, k;
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#ifndef NDEBUG
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  static int initialized = 0;
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  if (!initialized)
    {
      initialized = 1;
      assert(twofish_selftest());
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    }
#endif

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  /* Extend or truncate key as necessary */

  memset(key_copy, 0, 32);
  if (keysize > 32)
    keysize = 32;
  memcpy(key_copy, key, keysize);

  /* FIXME: This truncates the key if it is not a multiple of 4 octets.
   * Is this really indended? */
  bytes_to_words(m, key_copy, keysize/4);

  if (keysize <= 16)
    k = 2;
  else if (keysize <= 24)
    k = 3;
  else
    k = 4;

  /* Compute sub-keys */

  for (i = 0; i < 20; i++)
    {
      t = h(k, 2*i+1, m[1], m[3], m[5], m[7]);
      t = rol8(t);
      t += (context->keys[2*i] =
	    t + h(k, 2*i, m[0], m[2], m[4], m[6]));
      t = rol9(t);
      context->keys[2*i+1] = t;
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    }

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  /* Compute key-dependent S-boxes */
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  for (i = 0; i < k; i++)
    s[k-1-i] = compute_s(m[2*i], m[2*i+1]);
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  for (i = 0; i < 4; i++)
    for (j = 0; j < 256; j++)
      context->s_box[i][j] = h_byte(k, i, j,
				    s[0] >> (i*8),
				    s[1] >> (i*8),
				    s[2] >> (i*8),
				    s[3] >> (i*8));
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}

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/* void twofish_encrypt(TWOFISH_context *context,
 *                      const UINT8 *plaintext,
 *                      UINT8 *ciphertext);
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 *
 * Encrypt 16 bytes of data with the twofish algorithm.
 *
 * Before this function can be used, twofish_setup() must be used in order to
 * set up various tables required for the encryption algorithm.
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 * 
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 * This function always encrypts 16 bytes of plaintext to 16 bytes of
 * ciphertext.  The memory areas of the plaintext and the ciphertext can
 * overlap.
 */

void
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twofish_encrypt(TWOFISH_context *context,
		const UINT8 *plaintext,
		UINT8 *ciphertext)
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{
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  word words[4];
  word r0, r1, r2, r3, t0, t1;
  int i;
  word * keys        = context->keys;
  word (*s_box)[256] = context->s_box;

  bytes_to_words(words, plaintext, 4);

  r0 = words[0] ^ keys[0];
  r1 = words[1] ^ keys[1];
  r2 = words[2] ^ keys[2];
  r3 = words[3] ^ keys[3];

  for (i = 0; i < 8; i++) {
    t1 = (  s_box[1][r1 & 0xFF]
	  ^ s_box[2][(r1 >> 8) & 0xFF]
	  ^ s_box[3][(r1 >> 16) & 0xFF]
	  ^ s_box[0][(r1 >> 24) & 0xFF]);
    t0 = (  s_box[0][r0 & 0xFF]
	  ^ s_box[1][(r0 >> 8) & 0xFF]
	  ^ s_box[2][(r0 >> 16) & 0xFF]
	  ^ s_box[3][(r0 >> 24) & 0xFF]) + t1;
    r3 = (t1 + t0 + keys[4*i+9]) ^ rol1(r3);
    r2 = (t0 + keys[4*i+8]) ^ r2;
    r2 = ror1(r2);

    t1 = (  s_box[1][r3 & 0xFF]
	  ^ s_box[2][(r3 >> 8) & 0xFF]
	  ^ s_box[3][(r3 >> 16) & 0xFF]
	  ^ s_box[0][(r3 >> 24) & 0xFF]);
    t0 = (  s_box[0][r2 & 0xFF]
	  ^ s_box[1][(r2 >> 8) & 0xFF]
	  ^ s_box[2][(r2 >> 16) & 0xFF]
	  ^ s_box[3][(r2 >> 24) & 0xFF]) + t1;
    r1 = (t1 + t0 + keys[4*i+11]) ^ rol1(r1);
    r0 = (t0 + keys[4*i+10]) ^ r0;
    r0 = ror1(r0);
  }
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  words[0] = r2 ^ keys[4];
  words[1] = r3 ^ keys[5];
  words[2] = r0 ^ keys[6];
  words[3] = r1 ^ keys[7];
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  words_to_bytes(ciphertext, words, 4);
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}

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/* void twofish_decrypt(TWOFISH_context *context,
 *                      const UINT8 *ciphertext,
 *                      UINT8 *plaintext);
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 *
 * Decrypt 16 bytes of data with the twofish algorithm.
 *
 * Before this function can be used, twofish_setup() must be used in order to
 * set up various tables required for the decryption algorithm.
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 * 
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 * This function always decrypts 16 bytes of ciphertext to 16 bytes of
 * plaintext.  The memory areas of the plaintext and the ciphertext can
 * overlap.
 */

void
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twofish_decrypt(TWOFISH_context *context,
		const UINT8 *ciphertext,
		UINT8 *plaintext)
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{
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  word words[4];
  word r0, r1, r2, r3, t0, t1;
  int i;
  word *keys  = context->keys;
  word (*s_box)[256] = context->s_box;

  bytes_to_words(words, ciphertext, 4);

  r0 = words[2] ^ keys[6];
  r1 = words[3] ^ keys[7];
  r2 = words[0] ^ keys[4];
  r3 = words[1] ^ keys[5];

  for (i = 0; i < 8; i++) {
    t1 = (  s_box[1][r3 & 0xFF]
	  ^ s_box[2][(r3 >> 8) & 0xFF]
	  ^ s_box[3][(r3 >> 16) & 0xFF]
	  ^ s_box[0][(r3 >> 24) & 0xFF]);
    t0 = (  s_box[0][r2 & 0xFF]
	  ^ s_box[1][(r2 >> 8) & 0xFF]
	  ^ s_box[2][(r2 >> 16) & 0xFF]
	  ^ s_box[3][(r2 >> 24) & 0xFF]) + t1;
    r1 = (t1 + t0 + keys[39-4*i]) ^ r1;
    r1 = ror1(r1);
    r0 = (t0 + keys[38-4*i]) ^ rol1(r0);

    t1 = (  s_box[1][r1 & 0xFF]
	  ^ s_box[2][(r1 >> 8) & 0xFF]
	  ^ s_box[3][(r1 >> 16) & 0xFF]
	  ^ s_box[0][(r1 >> 24) & 0xFF]);
    t0 = (  s_box[0][r0 & 0xFF]
	  ^ s_box[1][(r0 >> 8) & 0xFF]
	  ^ s_box[2][(r0 >> 16) & 0xFF]
	  ^ s_box[3][(r0 >> 24) & 0xFF]) + t1;
    r3 = (t1 + t0 + keys[37-4*i]) ^ r3;
    r3 = ror1(r3);
    r2 = (t0 + keys[36-4*i]) ^ rol1(r2);
  }
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  words[0] = r0 ^ keys[0];
  words[1] = r1 ^ keys[1];
  words[2] = r2 ^ keys[2];
  words[3] = r3 ^ keys[3];
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  words_to_bytes(plaintext, words, 4);
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}