include/crypto/gf128mul.h

   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(2^128)
  47 */
  48
  49 #ifndef _CRYPTO_GF128MUL_H
  50 #define _CRYPTO_GF128MUL_H
  51
  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) can
  62  * be mapped to computer memory in a variety of ways. Let's examine
  63  * three common cases.
  64  *
  65  * Take a look at the 16 binary octets below in memory order. The msb's
  66  * are left and the lsb's are right. char b[16] is an array and b[0] is
  67  * the first octet.
  68  *
  69  * 10000000 00000000 00000000 00000000 .... 00000000 00000000 00000000
  70  *   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 bits
  73  * in every byte in little-endian order and the bytes themselves also in
  74  * 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 looks
  76  * like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.
  77  * This format was originally implemented in gf128mul and is used
  78  * in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).
  79  *
  80  * Another convention says: store the bits in bigendian order and the
  81  * bytes also. This is bbe (big-big-endian). Now the buffer above
  82  * 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 bbe
  84  * is partly implemented.
  85  *
  86  * Both of the above formats are easy to implement on big-endian
  87  * machines.
  88  *
  89  * XTS and EME (the latter of which is patent encumbered) use the ble
  90  * format (bits are stored in big endian order and the bytes in little
  91  * endian). The above buffer represents X^7 in this case and the
  92  * primitive polynomial is b[0] = 0x87.
  93  *
  94  * The common machine word-size is smaller than 128 bits, so to make
  95  * an efficient implementation we must split into machine word sizes.
  96  * This implementation uses 64-bit words for the moment. Machine
  97  * endianness comes into play. The lle format in relation to machine
  98  * endianness is discussed below by the original author of gf128mul Dr
  99  * 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]           LS
 106  *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 107  *  103..96 111.104 119.112 127.120  71...64 79...72 87...80 95...88
 108  *
 109  *  MS            x[2]           LS  MS            x[3]           LS
 110  *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 111  *  39...32 47...40 55...48 63...56  07...00 15...08 23...16 31...24
 112  *
 113  * ble on a little endian machine
 114  *
 115  *  MS            x[0]           LS  MS            x[1]           LS
 116  *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 117  *  31...24 23...16 15...08 07...00  63...56 55...48 47...40 39...32
 118  *
 119  *  MS            x[2]           LS  MS            x[3]           LS
 120  *  ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 121  *  95...88 87...80 79...72 71...64  127.120 199.112 111.104 103..96
 122  *
 123  * Multiplications in GF(2^128) are mostly bit-shifts, so you see why
 124  * ble (and lbe also) are easier to implement on a little-endian
 125  * machine than on a big-endian machine. The converse holds for bbe
 126  * and lle.
 127  *
 128  * Note: to have good alignment, it seems to me that it is sufficient
 129  * to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize
 130  * machines this will automatically aligned to wordsize and on a 64-bit
 131  * machine also.
 132  */
 133 /*      Multiply a GF(2^128) field element by x. Field elements are
 134     held in arrays of bytes in which field bits 8n..8n + 7 are held in
 135     byte[n], with lower indexed bits placed in the more numerically
 136     significant bit positions within bytes.
 137
 138     On little endian machines the bit indexes translate into the bit
 139     positions within four 32-bit words in the following way
 140
 141     MS            x[0]           LS  MS            x[1]           LS
 142     ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 143     24...31 16...23 08...15 00...07  56...63 48...55 40...47 32...39
 144
 145     MS            x[2]           LS  MS            x[3]           LS
 146     ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 147     88...95 80...87 72...79 64...71  120.127 112.119 104.111 96..103
 148
 149     On big endian machines the bit indexes translate into the bit
 150     positions within four 32-bit words in the following way
 151
 152     MS            x[0]           LS  MS            x[1]           LS
 153     ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 154     00...07 08...15 16...23 24...31  32...39 40...47 48...55 56...63
 155
 156     MS            x[2]           LS  MS            x[3]           LS
 157     ms   ls ms   ls ms   ls ms   ls  ms   ls ms   ls ms   ls ms   ls
 158     64...71 72...79 80...87 88...95  96..103 104.111 112.119 120.127
 159 */
 160
 161 /*      A slow generic version of gf_mul, implemented for lle and bbe
 162  *      It multiplies a and b and puts the result in a */
 163 void gf128mul_lle(be128 *a, const be128 *b);
 164
 165 void gf128mul_bbe(be128 *a, const be128 *b);
 166
 167 /*
 168  * The following functions multiply a field element by x in
 169  * the polynomial field representation.  They use 64-bit word operations
 170  * to gain speed but compensate for machine endianness and hence work
 171  * correctly on both styles of machine.
 172  *
 173  * They are defined here for performance.
 174  */
 175
 176 static 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
 182 static 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] << 48
 188          * (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
 195 static 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 */
 208 static 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
 222 struct gf128mul_4k {
 223         be128 t[256];
 224 };
 225
 226 struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
 227 struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);
 228 void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *t);
 229 void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t);
 230
 231 static inline void gf128mul_free_4k(struct gf128mul_4k *t)
 232 {
 233         kzfree(t);
 234 }
 235
 236
 237 /* 64k table optimization, implemented for bbe */
 238
 239 struct gf128mul_64k {
 240         struct gf128mul_4k *t[16];
 241 };
 242
 243 /* First initialize with the constant factor with which you
 244  * want to multiply and then call gf128mul_64k_bbe with the other
 245  * factor in the first argument, and the table in the second.
 246  * Afterwards, the result is stored in *a.
 247  */
 248 struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
 249 void gf128mul_free_64k(struct gf128mul_64k *t);
 250 void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t);
 251
 252 #endif /* _CRYPTO_GF128MUL_H */