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1/* gf128mul.h - GF(2^128) multiplication functions2 *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 at7 * http://fp.gladman.plus.com/cryptography_technology/index.htm8 * See the original copyright notice below.9 *10 * This program is free software; you can redistribute it and/or modify it11 * under the terms of the GNU General Public License as published by the Free12 * 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 TERMS20 21 The free distribution and use of this software in both source and binary22 form is allowed (with or without changes) provided that:23 24 1. distributions of this source code include the above copyright25 notice, this list of conditions and the following disclaimer;26 27 2. distributions in binary form include the above copyright28 notice, this list of conditions and the following disclaimer29 in the documentation and/or other associated materials;30 31 3. the copyright holder's name is not used to endorse products32 built using this software without specific written permission.33 34 ALTERNATIVELY, provided that this notice is retained in full, this product35 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 DISCLAIMER39 40 This software is provided 'as is' with no explicit or implied warranties41 in respect of its properties, including, but not limited to, correctness42 and/or fitness for purpose.43 ---------------------------------------------------------------------------44 Issue Date: 31/01/200645 46 An implementation of field multiplication in Galois Field GF(2^128)47*/48 49#ifndef _CRYPTO_GF128MUL_H50#define _CRYPTO_GF128MUL_H51 52#include <asm/byteorder.h>53#include <crypto/b128ops.h>54#include <linux/slab.h>55 56/* Comment by Rik:57 *58 * For some background on GF(2^128) see for example: 59 * http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf 60 *61 * The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can62 * be mapped to computer memory in a variety of ways. Let's examine63 * three common cases.64 *65 * Take a look at the 16 binary octets below in memory order. The msb's66 * are left and the lsb's are right. char b[16] is an array and b[0] is67 * the first octet.68 *69 * 10000000 00000000 00000000 00000000 .... 00000000 00000000 0000000070 * b[0] b[1] b[2] b[3] b[13] b[14] b[15]71 *72 * Every bit is a coefficient of some power of X. We can store the bits73 * in every byte in little-endian order and the bytes themselves also in74 * little endian order. I will call this lle (little-little-endian).75 * The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks76 * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.77 * This format was originally implemented in gf128mul and is used78 * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).79 *80 * Another convention says: store the bits in bigendian order and the81 * bytes also. This is bbe (big-big-endian). Now the buffer above82 * represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111,83 * b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe84 * is partly implemented.85 *86 * Both of the above formats are easy to implement on big-endian87 * machines.88 *89 * XTS and EME (the latter of which is patent encumbered) use the ble90 * format (bits are stored in big endian order and the bytes in little91 * endian). The above buffer represents X^7 in this case and the92 * primitive polynomial is b[0] = 0x87.93 *94 * The common machine word-size is smaller than 128 bits, so to make95 * an efficient implementation we must split into machine word sizes.96 * This implementation uses 64-bit words for the moment. Machine97 * endianness comes into play. The lle format in relation to machine98 * endianness is discussed below by the original author of gf128mul Dr99 * Brian Gladman.100 *101 * Let's look at the bbe and ble format on a little endian machine.102 *103 * bbe on a little endian machine u32 x[4]:104 *105 * MS x[0] LS MS x[1] LS106 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls107 * 103..96 111.104 119.112 127.120 71...64 79...72 87...80 95...88108 *109 * MS x[2] LS MS x[3] LS110 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls111 * 39...32 47...40 55...48 63...56 07...00 15...08 23...16 31...24112 *113 * ble on a little endian machine114 *115 * MS x[0] LS MS x[1] LS116 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls117 * 31...24 23...16 15...08 07...00 63...56 55...48 47...40 39...32118 *119 * MS x[2] LS MS x[3] LS120 * ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls121 * 95...88 87...80 79...72 71...64 127.120 199.112 111.104 103..96122 *123 * Multiplications in GF(2^128) are mostly bit-shifts, so you see why124 * ble (and lbe also) are easier to implement on a little-endian125 * machine than on a big-endian machine. The converse holds for bbe126 * and lle.127 *128 * Note: to have good alignment, it seems to me that it is sufficient129 * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize130 * machines this will automatically aligned to wordsize and on a 64-bit131 * machine also.132 */133/* Multiply a GF(2^128) field element by x. Field elements are134 held in arrays of bytes in which field bits 8n..8n + 7 are held in135 byte[n], with lower indexed bits placed in the more numerically136 significant bit positions within bytes.137 138 On little endian machines the bit indexes translate into the bit139 positions within four 32-bit words in the following way140 141 MS x[0] LS MS x[1] LS142 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls143 24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39144 145 MS x[2] LS MS x[3] LS146 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls147 88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103148 149 On big endian machines the bit indexes translate into the bit150 positions within four 32-bit words in the following way151 152 MS x[0] LS MS x[1] LS153 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls154 00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63155 156 MS x[2] LS MS x[3] LS157 ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls158 64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127159*/160 161/* A slow generic version of gf_mul, implemented for lle and bbe162 * It multiplies a and b and puts the result in a */163void gf128mul_lle(be128 *a, const be128 *b);164 165void gf128mul_bbe(be128 *a, const be128 *b);166 167/*168 * The following functions multiply a field element by x in169 * the polynomial field representation. They use 64-bit word operations170 * to gain speed but compensate for machine endianness and hence work171 * correctly on both styles of machine.172 *173 * They are defined here for performance.174 */175 176static inline u64 gf128mul_mask_from_bit(u64 x, int which)177{178 /* a constant-time version of 'x & ((u64)1 << which) ? (u64)-1 : 0' */179 return ((s64)(x << (63 - which)) >> 63);180}181 182static inline void gf128mul_x_lle(be128 *r, const be128 *x)183{184 u64 a = be64_to_cpu(x->a);185 u64 b = be64_to_cpu(x->b);186 187 /* equivalent to gf128mul_table_le[(b << 7) & 0xff] << 48188 * (see crypto/gf128mul.c): */189 u64 _tt = gf128mul_mask_from_bit(b, 0) & ((u64)0xe1 << 56);190 191 r->b = cpu_to_be64((b >> 1) | (a << 63));192 r->a = cpu_to_be64((a >> 1) ^ _tt);193}194 195static inline void gf128mul_x_bbe(be128 *r, const be128 *x)196{197 u64 a = be64_to_cpu(x->a);198 u64 b = be64_to_cpu(x->b);199 200 /* equivalent to gf128mul_table_be[a >> 63] (see crypto/gf128mul.c): */201 u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87;202 203 r->a = cpu_to_be64((a << 1) | (b >> 63));204 r->b = cpu_to_be64((b << 1) ^ _tt);205}206 207/* needed by XTS */208static inline void gf128mul_x_ble(le128 *r, const le128 *x)209{210 u64 a = le64_to_cpu(x->a);211 u64 b = le64_to_cpu(x->b);212 213 /* equivalent to gf128mul_table_be[b >> 63] (see crypto/gf128mul.c): */214 u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87;215 216 r->a = cpu_to_le64((a << 1) | (b >> 63));217 r->b = cpu_to_le64((b << 1) ^ _tt);218}219 220/* 4k table optimization */221 222struct gf128mul_4k {223 be128 t[256];224};225 226struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);227struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);228void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t);229void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t);230void gf128mul_x8_ble(le128 *r, const le128 *x);231static inline void gf128mul_free_4k(struct gf128mul_4k *t)232{233 kfree_sensitive(t);234}235 236 237/* 64k table optimization, implemented for bbe */238 239struct gf128mul_64k {240 struct gf128mul_4k *t[16];241};242 243/* First initialize with the constant factor with which you244 * want to multiply and then call gf128mul_64k_bbe with the other245 * factor in the first argument, and the table in the second.246 * Afterwards, the result is stored in *a.247 */248struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);249void gf128mul_free_64k(struct gf128mul_64k *t);250void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t);251 252#endif /* _CRYPTO_GF128MUL_H */253