[CRYPTO] lib: table driven multiplications in GF(2^128) (c494e070) · Commits · 戴 / test

crypto/Kconfig

+10 −0

Original line number	Diff line number	Diff line
		@@ -139,6 +139,16 @@ config CRYPTO_TGR192
		See also:
		<http://www.cs.technion.ac.il/~biham/Reports/Tiger/>.

		config CRYPTO_GF128MUL
		tristate "GF(2^128) multiplication functions (EXPERIMENTAL)"
		depends on EXPERIMENTAL
		help
		Efficient table driven implementation of multiplications in the
		field GF(2^128). This is needed by some cypher modes. This
		option will be selected automatically if you select such a
		cipher mode. Only select this option by hand if you expect to load
		an external module that requires these functions.

		config CRYPTO_ECB
		tristate "ECB support"
		select CRYPTO_BLKCIPHER

crypto/Makefile

+1 −0

Original line number	Diff line number	Diff line
		@@ -24,6 +24,7 @@ obj-$(CONFIG_CRYPTO_SHA256) += sha256.o
		obj-$(CONFIG_CRYPTO_SHA512) += sha512.o
		obj-$(CONFIG_CRYPTO_WP512) += wp512.o
		obj-$(CONFIG_CRYPTO_TGR192) += tgr192.o
		obj-$(CONFIG_CRYPTO_GF128MUL) += gf128mul.o
		obj-$(CONFIG_CRYPTO_ECB) += ecb.o
		obj-$(CONFIG_CRYPTO_CBC) += cbc.o
		obj-$(CONFIG_CRYPTO_DES) += des.o

crypto/gf128mul.c

0 → 100644

+466 −0

Original line number	Diff line number	Diff line
		/* gf128mul.c - 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 31/01/2006

		This file provides fast multiplication in GF(128) as required by several
		cryptographic authentication modes
		*/

		#include <crypto/gf128mul.h>
		#include <linux/kernel.h>
		#include <linux/module.h>
		#include <linux/slab.h>

		#define gf128mul_dat(q) { \
		q(0x00), q(0x01), q(0x02), q(0x03), q(0x04), q(0x05), q(0x06), q(0x07),\
		q(0x08), q(0x09), q(0x0a), q(0x0b), q(0x0c), q(0x0d), q(0x0e), q(0x0f),\
		q(0x10), q(0x11), q(0x12), q(0x13), q(0x14), q(0x15), q(0x16), q(0x17),\
		q(0x18), q(0x19), q(0x1a), q(0x1b), q(0x1c), q(0x1d), q(0x1e), q(0x1f),\
		q(0x20), q(0x21), q(0x22), q(0x23), q(0x24), q(0x25), q(0x26), q(0x27),\
		q(0x28), q(0x29), q(0x2a), q(0x2b), q(0x2c), q(0x2d), q(0x2e), q(0x2f),\
		q(0x30), q(0x31), q(0x32), q(0x33), q(0x34), q(0x35), q(0x36), q(0x37),\
		q(0x38), q(0x39), q(0x3a), q(0x3b), q(0x3c), q(0x3d), q(0x3e), q(0x3f),\
		q(0x40), q(0x41), q(0x42), q(0x43), q(0x44), q(0x45), q(0x46), q(0x47),\
		q(0x48), q(0x49), q(0x4a), q(0x4b), q(0x4c), q(0x4d), q(0x4e), q(0x4f),\
		q(0x50), q(0x51), q(0x52), q(0x53), q(0x54), q(0x55), q(0x56), q(0x57),\
		q(0x58), q(0x59), q(0x5a), q(0x5b), q(0x5c), q(0x5d), q(0x5e), q(0x5f),\
		q(0x60), q(0x61), q(0x62), q(0x63), q(0x64), q(0x65), q(0x66), q(0x67),\
		q(0x68), q(0x69), q(0x6a), q(0x6b), q(0x6c), q(0x6d), q(0x6e), q(0x6f),\
		q(0x70), q(0x71), q(0x72), q(0x73), q(0x74), q(0x75), q(0x76), q(0x77),\
		q(0x78), q(0x79), q(0x7a), q(0x7b), q(0x7c), q(0x7d), q(0x7e), q(0x7f),\
		q(0x80), q(0x81), q(0x82), q(0x83), q(0x84), q(0x85), q(0x86), q(0x87),\
		q(0x88), q(0x89), q(0x8a), q(0x8b), q(0x8c), q(0x8d), q(0x8e), q(0x8f),\
		q(0x90), q(0x91), q(0x92), q(0x93), q(0x94), q(0x95), q(0x96), q(0x97),\
		q(0x98), q(0x99), q(0x9a), q(0x9b), q(0x9c), q(0x9d), q(0x9e), q(0x9f),\
		q(0xa0), q(0xa1), q(0xa2), q(0xa3), q(0xa4), q(0xa5), q(0xa6), q(0xa7),\
		q(0xa8), q(0xa9), q(0xaa), q(0xab), q(0xac), q(0xad), q(0xae), q(0xaf),\
		q(0xb0), q(0xb1), q(0xb2), q(0xb3), q(0xb4), q(0xb5), q(0xb6), q(0xb7),\
		q(0xb8), q(0xb9), q(0xba), q(0xbb), q(0xbc), q(0xbd), q(0xbe), q(0xbf),\
		q(0xc0), q(0xc1), q(0xc2), q(0xc3), q(0xc4), q(0xc5), q(0xc6), q(0xc7),\
		q(0xc8), q(0xc9), q(0xca), q(0xcb), q(0xcc), q(0xcd), q(0xce), q(0xcf),\
		q(0xd0), q(0xd1), q(0xd2), q(0xd3), q(0xd4), q(0xd5), q(0xd6), q(0xd7),\
		q(0xd8), q(0xd9), q(0xda), q(0xdb), q(0xdc), q(0xdd), q(0xde), q(0xdf),\
		q(0xe0), q(0xe1), q(0xe2), q(0xe3), q(0xe4), q(0xe5), q(0xe6), q(0xe7),\
		q(0xe8), q(0xe9), q(0xea), q(0xeb), q(0xec), q(0xed), q(0xee), q(0xef),\
		q(0xf0), q(0xf1), q(0xf2), q(0xf3), q(0xf4), q(0xf5), q(0xf6), q(0xf7),\
		q(0xf8), q(0xf9), q(0xfa), q(0xfb), q(0xfc), q(0xfd), q(0xfe), q(0xff) \
		}

		/* Given the value i in 0..255 as the byte overflow when a field element
		in GHASH is multipled by x^8, this function will return the values that
		are generated in the lo 16-bit word of the field value by applying the
		modular polynomial. The values lo_byte and hi_byte are returned via the
		macro xp_fun(lo_byte, hi_byte) so that the values can be assembled into
		memory as required by a suitable definition of this macro operating on
		the table above
		*/

		#define xx(p, q) 0x##p##q

		#define xda_bbe(i) ( \
		(i & 0x80 ? xx(43, 80) : 0) ^ (i & 0x40 ? xx(21, c0) : 0) ^ \
		(i & 0x20 ? xx(10, e0) : 0) ^ (i & 0x10 ? xx(08, 70) : 0) ^ \
		(i & 0x08 ? xx(04, 38) : 0) ^ (i & 0x04 ? xx(02, 1c) : 0) ^ \
		(i & 0x02 ? xx(01, 0e) : 0) ^ (i & 0x01 ? xx(00, 87) : 0) \
		)

		#define xda_lle(i) ( \
		(i & 0x80 ? xx(e1, 00) : 0) ^ (i & 0x40 ? xx(70, 80) : 0) ^ \
		(i & 0x20 ? xx(38, 40) : 0) ^ (i & 0x10 ? xx(1c, 20) : 0) ^ \
		(i & 0x08 ? xx(0e, 10) : 0) ^ (i & 0x04 ? xx(07, 08) : 0) ^ \
		(i & 0x02 ? xx(03, 84) : 0) ^ (i & 0x01 ? xx(01, c2) : 0) \
		)

		static const u16 gf128mul_table_lle[256] = gf128mul_dat(xda_lle);
		static const u16 gf128mul_table_bbe[256] = gf128mul_dat(xda_bbe);

		/* These functions multiply a field element by x, by x^4 and by x^8
		* in the polynomial field representation. It uses 32-bit word operations
		* to gain speed but compensates for machine endianess and hence works
		* correctly on both styles of machine.
		*/

		static void gf128mul_x_lle(be128 r, const be128 x)
		{
		u64 a = be64_to_cpu(x->a);
		u64 b = be64_to_cpu(x->b);
		u64 _tt = gf128mul_table_lle[(b << 7) & 0xff];

		r->b = cpu_to_be64((b >> 1) \| (a << 63));
		r->a = cpu_to_be64((a >> 1) ^ (_tt << 48));
		}

		static void gf128mul_x_bbe(be128 r, const be128 x)
		{
		u64 a = be64_to_cpu(x->a);
		u64 b = be64_to_cpu(x->b);
		u64 _tt = gf128mul_table_bbe[a >> 63];

		r->a = cpu_to_be64((a << 1) \| (b >> 63));
		r->b = cpu_to_be64((b << 1) ^ _tt);
		}

		static void gf128mul_x8_lle(be128 *x)
		{
		u64 a = be64_to_cpu(x->a);
		u64 b = be64_to_cpu(x->b);
		u64 _tt = gf128mul_table_lle[b & 0xff];

		x->b = cpu_to_be64((b >> 8) \| (a << 56));
		x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
		}

		static void gf128mul_x8_bbe(be128 *x)
		{
		u64 a = be64_to_cpu(x->a);
		u64 b = be64_to_cpu(x->b);
		u64 _tt = gf128mul_table_bbe[a >> 56];

		x->a = cpu_to_be64((a << 8) \| (b >> 56));
		x->b = cpu_to_be64((b << 8) ^ _tt);
		}

		void gf128mul_lle(be128 r, const be128 b)
		{
		be128 p[8];
		int i;

		p[0] = *r;
		for (i = 0; i < 7; ++i)
		gf128mul_x_lle(&p[i + 1], &p[i]);

		memset(r, 0, sizeof(r));
		for (i = 0;;) {
		u8 ch = ((u8 *)b)[15 - i];

		if (ch & 0x80)
		be128_xor(r, r, &p[0]);
		if (ch & 0x40)
		be128_xor(r, r, &p[1]);
		if (ch & 0x20)
		be128_xor(r, r, &p[2]);
		if (ch & 0x10)
		be128_xor(r, r, &p[3]);
		if (ch & 0x08)
		be128_xor(r, r, &p[4]);
		if (ch & 0x04)
		be128_xor(r, r, &p[5]);
		if (ch & 0x02)
		be128_xor(r, r, &p[6]);
		if (ch & 0x01)
		be128_xor(r, r, &p[7]);

		if (++i >= 16)
		break;

		gf128mul_x8_lle(r);
		}
		}
		EXPORT_SYMBOL(gf128mul_lle);

		void gf128mul_bbe(be128 r, const be128 b)
		{
		be128 p[8];
		int i;

		p[0] = *r;
		for (i = 0; i < 7; ++i)
		gf128mul_x_bbe(&p[i + 1], &p[i]);

		memset(r, 0, sizeof(r));
		for (i = 0;;) {
		u8 ch = ((u8 *)b)[i];

		if (ch & 0x80)
		be128_xor(r, r, &p[7]);
		if (ch & 0x40)
		be128_xor(r, r, &p[6]);
		if (ch & 0x20)
		be128_xor(r, r, &p[5]);
		if (ch & 0x10)
		be128_xor(r, r, &p[4]);
		if (ch & 0x08)
		be128_xor(r, r, &p[3]);
		if (ch & 0x04)
		be128_xor(r, r, &p[2]);
		if (ch & 0x02)
		be128_xor(r, r, &p[1]);
		if (ch & 0x01)
		be128_xor(r, r, &p[0]);

		if (++i >= 16)
		break;

		gf128mul_x8_bbe(r);
		}
		}
		EXPORT_SYMBOL(gf128mul_bbe);

		/* This version uses 64k bytes of table space.
		A 16 byte buffer has to be multiplied by a 16 byte key
		value in GF(128). If we consider a GF(128) value in
		the buffer's lowest byte, we can construct a table of
		the 256 16 byte values that result from the 256 values
		of this byte. This requires 4096 bytes. But we also
		need tables for each of the 16 higher bytes in the
		buffer as well, which makes 64 kbytes in total.
		*/
		/* additional explanation
		* t[0][BYTE] contains g*BYTE
		* t[1][BYTE] contains gx^8BYTE
		* ..
		* t[15][BYTE] contains gx^120BYTE */
		struct gf128mul_64k gf128mul_init_64k_lle(const be128 g)
		{
		struct gf128mul_64k *t;
		int i, j, k;

		t = kzalloc(sizeof(*t), GFP_KERNEL);
		if (!t)
		goto out;

		for (i = 0; i < 16; i++) {
		t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
		if (!t->t[i]) {
		gf128mul_free_64k(t);
		t = NULL;
		goto out;
		}
		}

		t->t[0]->t[128] = *g;
		for (j = 64; j > 0; j >>= 1)
		gf128mul_x_lle(&t->t[0]->t[j], &t->t[0]->t[j + j]);

		for (i = 0;;) {
		for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
		be128_xor(&t->t[i]->t[j + k],
		&t->t[i]->t[j], &t->t[i]->t[k]);

		if (++i >= 16)
		break;

		for (j = 128; j > 0; j >>= 1) {
		t->t[i]->t[j] = t->t[i - 1]->t[j];
		gf128mul_x8_lle(&t->t[i]->t[j]);
		}
		}

		out:
		return t;
		}
		EXPORT_SYMBOL(gf128mul_init_64k_lle);

		struct gf128mul_64k gf128mul_init_64k_bbe(const be128 g)
		{
		struct gf128mul_64k *t;
		int i, j, k;

		t = kzalloc(sizeof(*t), GFP_KERNEL);
		if (!t)
		goto out;

		for (i = 0; i < 16; i++) {
		t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
		if (!t->t[i]) {
		gf128mul_free_64k(t);
		t = NULL;
		goto out;
		}
		}

		t->t[0]->t[1] = *g;
		for (j = 1; j <= 64; j <<= 1)
		gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);

		for (i = 0;;) {
		for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
		be128_xor(&t->t[i]->t[j + k],
		&t->t[i]->t[j], &t->t[i]->t[k]);

		if (++i >= 16)
		break;

		for (j = 128; j > 0; j >>= 1) {
		t->t[i]->t[j] = t->t[i - 1]->t[j];
		gf128mul_x8_bbe(&t->t[i]->t[j]);
		}
		}

		out:
		return t;
		}
		EXPORT_SYMBOL(gf128mul_init_64k_bbe);

		void gf128mul_free_64k(struct gf128mul_64k *t)
		{
		int i;

		for (i = 0; i < 16; i++)
		kfree(t->t[i]);
		kfree(t);
		}
		EXPORT_SYMBOL(gf128mul_free_64k);

		void gf128mul_64k_lle(be128 a, struct gf128mul_64k t)
		{
		u8 ap = (u8 )a;
		be128 r[1];
		int i;

		*r = t->t[0]->t[ap[0]];
		for (i = 1; i < 16; ++i)
		be128_xor(r, r, &t->t[i]->t[ap[i]]);
		a = r;
		}
		EXPORT_SYMBOL(gf128mul_64k_lle);

		void gf128mul_64k_bbe(be128 a, struct gf128mul_64k t)
		{
		u8 ap = (u8 )a;
		be128 r[1];
		int i;

		*r = t->t[0]->t[ap[15]];
		for (i = 1; i < 16; ++i)
		be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
		a = r;
		}
		EXPORT_SYMBOL(gf128mul_64k_bbe);

		/* This version uses 4k bytes of table space.
		A 16 byte buffer has to be multiplied by a 16 byte key
		value in GF(128). If we consider a GF(128) value in a
		single byte, we can construct a table of the 256 16 byte
		values that result from the 256 values of this byte.
		This requires 4096 bytes. If we take the highest byte in
		the buffer and use this table to get the result, we then
		have to multiply by x^120 to get the final value. For the
		next highest byte the result has to be multiplied by x^112
		and so on. But we can do this by accumulating the result
		in an accumulator starting with the result for the top
		byte. We repeatedly multiply the accumulator value by
		x^8 and then add in (i.e. xor) the 16 bytes of the next
		lower byte in the buffer, stopping when we reach the
		lowest byte. This requires a 4096 byte table.
		*/
		struct gf128mul_4k gf128mul_init_4k_lle(const be128 g)
		{
		struct gf128mul_4k *t;
		int j, k;

		t = kzalloc(sizeof(*t), GFP_KERNEL);
		if (!t)
		goto out;

		t->t[128] = *g;
		for (j = 64; j > 0; j >>= 1)
		gf128mul_x_lle(&t->t[j], &t->t[j+j]);

		for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
		be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);

		out:
		return t;
		}
		EXPORT_SYMBOL(gf128mul_init_4k_lle);

		struct gf128mul_4k gf128mul_init_4k_bbe(const be128 g)
		{
		struct gf128mul_4k *t;
		int j, k;

		t = kzalloc(sizeof(*t), GFP_KERNEL);
		if (!t)
		goto out;

		t->t[1] = *g;
		for (j = 1; j <= 64; j <<= 1)
		gf128mul_x_bbe(&t->t[j + j], &t->t[j]);

		for (j = 2; j < 256; j += j)
		for (k = 1; k < j; ++k)
		be128_xor(&t->t[j + k], &t->t[j], &t->t[k]);

		out:
		return t;
		}
		EXPORT_SYMBOL(gf128mul_init_4k_bbe);

		void gf128mul_4k_lle(be128 a, struct gf128mul_4k t)
		{
		u8 ap = (u8 )a;
		be128 r[1];
		int i = 15;

		*r = t->t[ap[15]];
		while (i--) {
		gf128mul_x8_lle(r);
		be128_xor(r, r, &t->t[ap[i]]);
		}
		a = r;
		}
		EXPORT_SYMBOL(gf128mul_4k_lle);

		void gf128mul_4k_bbe(be128 a, struct gf128mul_4k t)
		{
		u8 ap = (u8 )a;
		be128 r[1];
		int i = 0;

		*r = t->t[ap[0]];
		while (++i < 16) {
		gf128mul_x8_bbe(r);
		be128_xor(r, r, &t->t[ap[i]]);
		}
		a = r;
		}
		EXPORT_SYMBOL(gf128mul_4k_bbe);

		MODULE_LICENSE("GPL");
		MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");

include/crypto/gf128mul.h

0 → 100644

+198 −0

Original line number	Diff line number	Diff line
		/* 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 */

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