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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(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                 :          0 : 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                 :          0 :         return ((s64)(x << (63 - which)) >> 63);
     180                 :            : }
     181                 :            : 
     182                 :          0 : static inline void gf128mul_x_lle(be128 *r, const be128 *x)
     183                 :            : {
     184                 :          0 :         u64 a = be64_to_cpu(x->a);
     185                 :          0 :         u64 b = be64_to_cpu(x->b);
     186                 :            : 
     187                 :            :         /* equivalent to gf128mul_table_le[(b << 7) & 0xff] << 48
     188                 :            :          * (see crypto/gf128mul.c): */
     189                 :          0 :         u64 _tt = gf128mul_mask_from_bit(b, 0) & ((u64)0xe1 << 56);
     190                 :            : 
     191                 :          0 :         r->b = cpu_to_be64((b >> 1) | (a << 63));
     192                 :          0 :         r->a = cpu_to_be64((a >> 1) ^ _tt);
     193                 :            : }
     194                 :            : 
     195                 :          0 : static inline void gf128mul_x_bbe(be128 *r, const be128 *x)
     196                 :            : {
     197                 :          0 :         u64 a = be64_to_cpu(x->a);
     198                 :          0 :         u64 b = be64_to_cpu(x->b);
     199                 :            : 
     200                 :            :         /* equivalent to gf128mul_table_be[a >> 63] (see crypto/gf128mul.c): */
     201                 :          0 :         u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87;
     202                 :            : 
     203                 :          0 :         r->a = cpu_to_be64((a << 1) | (b >> 63));
     204                 :          0 :         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                 :            : void gf128mul_x8_ble(le128 *r, const le128 *x);
     231                 :          0 : static inline void gf128mul_free_4k(struct gf128mul_4k *t)
     232                 :            : {
     233                 :          0 :         kzfree(t);
     234                 :          0 : }
     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 */