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