include/crypto/gf128mul.h - kernel/msm - Gitiles

 /* 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);

 /* 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 */
	/* 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);

	/* 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 */