gf128mul.h

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/* gf128mul.h - GF(2^128) multiplication functions
 *
 * Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
 * Copyright (c) 2006 Rik Snel <[email protected]>
 *
 * 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.
 */
/*
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 Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.   All rights reserved.

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 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/groups/ST/toolkit/BCM/documents/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);

/* multiply by x in ble format, needed by XTS */
void gf128mul_x_ble(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 */