| /* gf128mul.h - GF(2^128) multiplication functions |
| * |
| * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK. |
| * Copyright (c) 2006 Rik Snel <rsnel@cube.dyndns.org> |
| * |
| * Based on Dr Brian Gladman's (GPL'd) work published at |
| * http://fp.gladman.plus.com/cryptography_technology/index.htm |
| * See the original copyright notice below. |
| * |
| * This program is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License as published by the Free |
| * Software Foundation; either version 2 of the License, or (at your option) |
| * any later version. |
| */ |
| /* |
| --------------------------------------------------------------------------- |
| Copyright (c) 2003, Dr Brian Gladman, Worcester, UK. All rights reserved. |
| |
| LICENSE TERMS |
| |
| The free distribution and use of this software in both source and binary |
| form is allowed (with or without changes) provided that: |
| |
| 1. distributions of this source code include the above copyright |
| notice, this list of conditions and the following disclaimer; |
| |
| 2. distributions in binary form include the above copyright |
| notice, this list of conditions and the following disclaimer |
| in the documentation and/or other associated materials; |
| |
| 3. the copyright holder's name is not used to endorse products |
| built using this software without specific written permission. |
| |
| ALTERNATIVELY, provided that this notice is retained in full, this product |
| may be distributed under the terms of the GNU General Public License (GPL), |
| in which case the provisions of the GPL apply INSTEAD OF those given above. |
| |
| DISCLAIMER |
| |
| This software is provided 'as is' with no explicit or implied warranties |
| in respect of its properties, including, but not limited to, correctness |
| and/or fitness for purpose. |
| --------------------------------------------------------------------------- |
| Issue Date: 31/01/2006 |
| |
| An implementation of field multiplication in Galois Field GF(128) |
| */ |
| |
| #ifndef _CRYPTO_GF128MUL_H |
| #define _CRYPTO_GF128MUL_H |
| |
| #include <crypto/b128ops.h> |
| #include <linux/slab.h> |
| |
| /* Comment by Rik: |
| * |
| * For some background on GF(2^128) see for example: http://- |
| * csrc.nist.gov/CryptoToolkit/modes/proposedmodes/gcm/gcm-revised-spec.pdf |
| * |
| * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can |
| * be mapped to computer memory in a variety of ways. Let's examine |
| * three common cases. |
| * |
| * Take a look at the 16 binary octets below in memory order. The msb's |
| * are left and the lsb's are right. char b[16] is an array and b[0] is |
| * the first octet. |
| * |
| * 80000000 00000000 00000000 00000000 .... 00000000 00000000 00000000 |
| * b[0] b[1] b[2] b[3] b[13] b[14] b[15] |
| * |
| * Every bit is a coefficient of some power of X. We can store the bits |
| * in every byte in little-endian order and the bytes themselves also in |
| * little endian order. I will call this lle (little-little-endian). |
| * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks |
| * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }. |
| * This format was originally implemented in gf128mul and is used |
| * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length). |
| * |
| * Another convention says: store the bits in bigendian order and the |
| * bytes also. This is bbe (big-big-endian). Now the buffer above |
| * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111, |
| * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe |
| * is partly implemented. |
| * |
| * Both of the above formats are easy to implement on big-endian |
| * machines. |
| * |
| * EME (which is patent encumbered) uses the ble format (bits are stored |
| * in big endian order and the bytes in little endian). The above buffer |
| * represents X^7 in this case and the primitive polynomial is b[0] = 0x87. |
| * |
| * The common machine word-size is smaller than 128 bits, so to make |
| * an efficient implementation we must split into machine word sizes. |
| * This file uses one 32bit for the moment. Machine endianness comes into |
| * play. The lle format in relation to machine endianness is discussed |
| * below by the original author of gf128mul Dr Brian Gladman. |
| * |
| * Let's look at the bbe and ble format on a little endian machine. |
| * |
| * bbe on a little endian machine u32 x[4]: |
| * |
| * MS x[0] LS MS x[1] LS |
| * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| * 103..96 111.104 119.112 127.120 71...64 79...72 87...80 95...88 |
| * |
| * MS x[2] LS MS x[3] LS |
| * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| * 39...32 47...40 55...48 63...56 07...00 15...08 23...16 31...24 |
| * |
| * ble on a little endian machine |
| * |
| * MS x[0] LS MS x[1] LS |
| * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| * 31...24 23...16 15...08 07...00 63...56 55...48 47...40 39...32 |
| * |
| * MS x[2] LS MS x[3] LS |
| * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| * 95...88 87...80 79...72 71...64 127.120 199.112 111.104 103..96 |
| * |
| * Multiplications in GF(2^128) are mostly bit-shifts, so you see why |
| * ble (and lbe also) are easier to implement on a little-endian |
| * machine than on a big-endian machine. The converse holds for bbe |
| * and lle. |
| * |
| * Note: to have good alignment, it seems to me that it is sufficient |
| * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize |
| * machines this will automatically aligned to wordsize and on a 64-bit |
| * machine also. |
| */ |
| /* Multiply a GF128 field element by x. Field elements are held in arrays |
| of bytes in which field bits 8n..8n + 7 are held in byte[n], with lower |
| indexed bits placed in the more numerically significant bit positions |
| within bytes. |
| |
| On little endian machines the bit indexes translate into the bit |
| positions within four 32-bit words in the following way |
| |
| MS x[0] LS MS x[1] LS |
| ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| 24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39 |
| |
| MS x[2] LS MS x[3] LS |
| ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| 88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103 |
| |
| On big endian machines the bit indexes translate into the bit |
| positions within four 32-bit words in the following way |
| |
| MS x[0] LS MS x[1] LS |
| ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| 00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63 |
| |
| MS x[2] LS MS x[3] LS |
| ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls |
| 64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127 |
| */ |
| |
| /* A slow generic version of gf_mul, implemented for lle and bbe |
| * It multiplies a and b and puts the result in a */ |
| void gf128mul_lle(be128 *a, const be128 *b); |
| |
| void gf128mul_bbe(be128 *a, const be128 *b); |
| |
| |
| /* 4k table optimization */ |
| |
| struct gf128mul_4k { |
| be128 t[256]; |
| }; |
| |
| struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g); |
| struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g); |
| void gf128mul_4k_lle(be128 *a, struct gf128mul_4k *t); |
| void gf128mul_4k_bbe(be128 *a, struct gf128mul_4k *t); |
| |
| static inline void gf128mul_free_4k(struct gf128mul_4k *t) |
| { |
| kfree(t); |
| } |
| |
| |
| /* 64k table optimization, implemented for lle and bbe */ |
| |
| struct gf128mul_64k { |
| struct gf128mul_4k *t[16]; |
| }; |
| |
| /* first initialize with the constant factor with which you |
| * want to multiply and then call gf128_64k_lle with the other |
| * factor in the first argument, the table in the second and a |
| * scratch register in the third. Afterwards *a = *r. */ |
| struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g); |
| struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g); |
| void gf128mul_free_64k(struct gf128mul_64k *t); |
| void gf128mul_64k_lle(be128 *a, struct gf128mul_64k *t); |
| void gf128mul_64k_bbe(be128 *a, struct gf128mul_64k *t); |
| |
| #endif /* _CRYPTO_GF128MUL_H */ |