linux/include/crypto/gf128mul.h
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   1/* gf128mul.h - GF(2^128) multiplication functions
   2 *
   3 * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
   4 * Copyright (c) 2006 Rik Snel <rsnel@cube.dyndns.org>
   5 *
   6 * Based on Dr Brian Gladman's (GPL'd) work published at
   7 * http://fp.gladman.plus.com/cryptography_technology/index.htm
   8 * See the original copyright notice below.
   9 *
  10 * This program is free software; you can redistribute it and/or modify it
  11 * under the terms of the GNU General Public License as published by the Free
  12 * Software Foundation; either version 2 of the License, or (at your option)
  13 * any later version.
  14 */
  15/*
  16 ---------------------------------------------------------------------------
  17 Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.
  18
  19 LICENSE TERMS
  20
  21 The free distribution and use of this software in both source and binary
  22 form is allowed (with or without changes) provided that:
  23
  24   1. distributions of this source code include the above copyright
  25      notice, this list of conditions and the following disclaimer;
  26
  27   2. distributions in binary form include the above copyright
  28      notice, this list of conditions and the following disclaimer
  29      in the documentation and/or other associated materials;
  30
  31   3. the copyright holder's name is not used to endorse products
  32      built using this software without specific written permission.
  33
  34 ALTERNATIVELY, provided that this notice is retained in full, this product
  35 may be distributed under the terms of the GNU General Public License (GPL),
  36 in which case the provisions of the GPL apply INSTEAD OF those given above.
  37
  38 DISCLAIMER
  39
  40 This software is provided 'as is' with no explicit or implied warranties
  41 in respect of its properties, including, but not limited to, correctness
  42 and/or fitness for purpose.
  43 ---------------------------------------------------------------------------
  44 Issue Date: 31/01/2006
  45
  46 An implementation of field multiplication in Galois Field GF(128)
  47*/
  48
  49#ifndef _CRYPTO_GF128MUL_H
  50#define _CRYPTO_GF128MUL_H
  51
  52#include <crypto/b128ops.h>
  53#include <linux/slab.h>
  54
  55/* Comment by Rik:
  56 *
  57 * For some background on GF(2^128) see for example: 
  58 * http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf 
  59 *
  60 * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can
  61 * be mapped to computer memory in a variety of ways. Let's examine
  62 * three common cases.
  63 *
  64 * Take a look at the 16 binary octets below in memory order. The msb's
  65 * are left and the lsb's are right. char b[16] is an array and b[0] is
  66 * the first octet.
  67 *
  68 * 80000000 00000000 00000000 00000000 .... 00000000 00000000 00000000
  69 *   b[0]     b[1]     b[2]     b[3]          b[13]    b[14]    b[15]
  70 *
  71 * Every bit is a coefficient of some power of X. We can store the bits
  72 * in every byte in little-endian order and the bytes themselves also in
  73 * little endian order. I will call this lle (little-little-endian).
  74 * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks
  75 * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.
  76 * This format was originally implemented in gf128mul and is used
  77 * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).
  78 *
  79 * Another convention says: store the bits in bigendian order and the
  80 * bytes also. This is bbe (big-big-endian). Now the buffer above
  81 * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111,
  82 * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe
  83 * is partly implemented.
  84 *
  85 * Both of the above formats are easy to implement on big-endian
  86 * machines.
  87 *
  88 * EME (which is patent encumbered) uses the ble format (bits are stored
  89 * in big endian order and the bytes in little endian). The above buffer
  90 * represents X^7 in this case and the primitive polynomial is b[0] = 0x87.
  91 *
  92 * The common machine word-size is smaller than 128 bits, so to make
  93 * an efficient implementation we must split into machine word sizes.
  94 * This file uses one 32bit for the moment. Machine endianness comes into
  95 * play. The lle format in relation to machine endianness is discussed
  96 * below by the original author of gf128mul Dr Brian Gladman.
  97 *
  98 * Let's look at the bbe and ble format on a little endian machine.
  99 *
 100 * bbe on a little endian machine u32 x[4]:
 101 *
 102 *  MS            x[0]           LS  MS            x[1]           LS
 103 *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 104 *  103..96 111.104 119.112 127.120  71...64 79...72 87...80 95...88
 105 *
 106 *  MS            x[2]           LS  MS            x[3]           LS
 107 *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 108 *  39...32 47...40 55...48 63...56  07...00 15...08 23...16 31...24
 109 *
 110 * ble on a little endian machine
 111 *
 112 *  MS            x[0]           LS  MS            x[1]           LS
 113 *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 114 *  31...24 23...16 15...08 07...00  63...56 55...48 47...40 39...32
 115 *
 116 *  MS            x[2]           LS  MS            x[3]           LS
 117 *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 118 *  95...88 87...80 79...72 71...64  127.120 199.112 111.104 103..96
 119 *
 120 * Multiplications in GF(2^128) are mostly bit-shifts, so you see why
 121 * ble (and lbe also) are easier to implement on a little-endian
 122 * machine than on a big-endian machine. The converse holds for bbe
 123 * and lle.
 124 *
 125 * Note: to have good alignment, it seems to me that it is sufficient
 126 * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize
 127 * machines this will automatically aligned to wordsize and on a 64-bit
 128 * machine also.
 129 */
 130/*      Multiply a GF128 field element by x. Field elements are held in arrays
 131    of bytes in which field bits 8n..8n + 7 are held in byte[n], with lower
 132    indexed bits placed in the more numerically significant bit positions
 133    within bytes.
 134
 135    On little endian machines the bit indexes translate into the bit
 136    positions within four 32-bit words in the following way
 137
 138    MS            x[0]           LS  MS            x[1]           LS
 139    ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 140    24...31 16...23 08...15 00...07  56...63 48...55 40...47 32...39
 141
 142    MS            x[2]           LS  MS            x[3]           LS
 143    ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 144    88...95 80...87 72...79 64...71  120.127 112.119 104.111 96..103
 145
 146    On big endian machines the bit indexes translate into the bit
 147    positions within four 32-bit words in the following way
 148
 149    MS            x[0]           LS  MS            x[1]           LS
 150    ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 151    00...07 08...15 16...23 24...31  32...39 40...47 48...55 56...63
 152
 153    MS            x[2]           LS  MS            x[3]           LS
 154    ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 155    64...71 72...79 80...87 88...95  96..103 104.111 112.119 120.127
 156*/
 157
 158/*      A slow generic version of gf_mul, implemented for lle and bbe
 159 *      It multiplies a and b and puts the result in a */
 160void gf128mul_lle(be128 *a, const be128 *b);
 161
 162void gf128mul_bbe(be128 *a, const be128 *b);
 163
 164/* multiply by x in ble format, needed by XTS */
 165void gf128mul_x_ble(be128 *a, const be128 *b);
 166
 167/* 4k table optimization */
 168
 169struct gf128mul_4k {
 170        be128 t[256];
 171};
 172
 173struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
 174struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);
 175void gf128mul_4k_lle(be128 *a, struct gf128mul_4k *t);
 176void gf128mul_4k_bbe(be128 *a, struct gf128mul_4k *t);
 177
 178static inline void gf128mul_free_4k(struct gf128mul_4k *t)
 179{
 180        kfree(t);
 181}
 182
 183
 184/* 64k table optimization, implemented for lle and bbe */
 185
 186struct gf128mul_64k {
 187        struct gf128mul_4k *t[16];
 188};
 189
 190/* first initialize with the constant factor with which you
 191 * want to multiply and then call gf128_64k_lle with the other
 192 * factor in the first argument, the table in the second and a
 193 * scratch register in the third. Afterwards *a = *r. */
 194struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g);
 195struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
 196void gf128mul_free_64k(struct gf128mul_64k *t);
 197void gf128mul_64k_lle(be128 *a, struct gf128mul_64k *t);
 198void gf128mul_64k_bbe(be128 *a, struct gf128mul_64k *t);
 199
 200#endif /* _CRYPTO_GF128MUL_H */
 201
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