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marcus.erl |
/* gf128mul.h - GF(2^128) multiplication functions
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*
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* Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
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* Copyright (c) 2006 Rik Snel <rsnel@cube.dyndns.org>
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*
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* Based on Dr Brian Gladman's (GPL'd) work published at
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* http://fp.gladman.plus.com/cryptography_technology/index.htm
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* See the original copyright notice below.
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*
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* This program is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by the Free
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* Software Foundation; either version 2 of the License, or (at your option)
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* any later version.
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*/
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/*
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---------------------------------------------------------------------------
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Copyright (c) 2003, Dr Brian Gladman, Worcester, UK. All rights reserved.
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LICENSE TERMS
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The free distribution and use of this software in both source and binary
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form is allowed (with or without changes) provided that:
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1. distributions of this source code include the above copyright
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notice, this list of conditions and the following disclaimer;
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2. distributions in binary form include the above copyright
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notice, this list of conditions and the following disclaimer
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in the documentation and/or other associated materials;
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3. the copyright holder's name is not used to endorse products
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built using this software without specific written permission.
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ALTERNATIVELY, provided that this notice is retained in full, this product
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may be distributed under the terms of the GNU General Public License (GPL),
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in which case the provisions of the GPL apply INSTEAD OF those given above.
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DISCLAIMER
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This software is provided 'as is' with no explicit or implied warranties
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in respect of its properties, including, but not limited to, correctness
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and/or fitness for purpose.
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---------------------------------------------------------------------------
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Issue Date: 31/01/2006
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An implementation of field multiplication in Galois Field GF(128)
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*/
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#ifndef _CRYPTO_GF128MUL_H
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#define _CRYPTO_GF128MUL_H
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#include <crypto/b128ops.h>
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#include <linux/slab.h>
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/* Comment by Rik:
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*
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* For some background on GF(2^128) see for example: http://-
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* csrc.nist.gov/CryptoToolkit/modes/proposedmodes/gcm/gcm-revised-spec.pdf
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*
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* The elements of GF(2^128) := GF(2)[X]/(X^128-X^7-X^2-X^1-1) can
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* be mapped to computer memory in a variety of ways. Let's examine
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* three common cases.
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*
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* Take a look at the 16 binary octets below in memory order. The msb's
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* are left and the lsb's are right. char b[16] is an array and b[0] is
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* the first octet.
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*
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* 80000000 00000000 00000000 00000000 .... 00000000 00000000 00000000
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* b[0] b[1] b[2] b[3] b[13] b[14] b[15]
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*
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* Every bit is a coefficient of some power of X. We can store the bits
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* in every byte in little-endian order and the bytes themselves also in
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* little endian order. I will call this lle (little-little-endian).
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* The above buffer represents the polynomial 1, and X^7+X^2+X^1+1 looks
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* like 11100001 00000000 .... 00000000 = { 0xE1, 0x00, }.
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* This format was originally implemented in gf128mul and is used
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* in GCM (Galois/Counter mode) and in ABL (Arbitrary Block Length).
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*
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* Another convention says: store the bits in bigendian order and the
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* bytes also. This is bbe (big-big-endian). Now the buffer above
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* represents X^127. X^7+X^2+X^1+1 looks like 00000000 .... 10000111,
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* b[15] = 0x87 and the rest is 0. LRW uses this convention and bbe
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* is partly implemented.
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*
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* Both of the above formats are easy to implement on big-endian
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* machines.
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*
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* EME (which is patent encumbered) uses the ble format (bits are stored
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* in big endian order and the bytes in little endian). The above buffer
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* represents X^7 in this case and the primitive polynomial is b[0] = 0x87.
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*
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* The common machine word-size is smaller than 128 bits, so to make
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* an efficient implementation we must split into machine word sizes.
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* This file uses one 32bit for the moment. Machine endianness comes into
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* play. The lle format in relation to machine endianness is discussed
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* below by the original author of gf128mul Dr Brian Gladman.
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*
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* Let's look at the bbe and ble format on a little endian machine.
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*
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* bbe on a little endian machine u32 x[4]:
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*
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* MS x[0] LS MS x[1] LS
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* ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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* 103..96 111.104 119.112 127.120 71...64 79...72 87...80 95...88
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*
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* MS x[2] LS MS x[3] LS
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* ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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* 39...32 47...40 55...48 63...56 07...00 15...08 23...16 31...24
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*
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* ble on a little endian machine
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*
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* MS x[0] LS MS x[1] LS
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* ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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* 31...24 23...16 15...08 07...00 63...56 55...48 47...40 39...32
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*
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* MS x[2] LS MS x[3] LS
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* ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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* 95...88 87...80 79...72 71...64 127.120 199.112 111.104 103..96
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*
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* Multiplications in GF(2^128) are mostly bit-shifts, so you see why
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* ble (and lbe also) are easier to implement on a little-endian
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* machine than on a big-endian machine. The converse holds for bbe
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* and lle.
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*
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* Note: to have good alignment, it seems to me that it is sufficient
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* to keep elements of GF(2^128) in type u64[2]. On 32-bit wordsize
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* machines this will automatically aligned to wordsize and on a 64-bit
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* machine also.
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*/
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/* Multiply a GF128 field element by x. Field elements are held in arrays
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of bytes in which field bits 8n..8n + 7 are held in byte[n], with lower
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indexed bits placed in the more numerically significant bit positions
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within bytes.
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On little endian machines the bit indexes translate into the bit
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positions within four 32-bit words in the following way
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MS x[0] LS MS x[1] LS
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ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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24...31 16...23 08...15 00...07 56...63 48...55 40...47 32...39
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MS x[2] LS MS x[3] LS
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ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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88...95 80...87 72...79 64...71 120.127 112.119 104.111 96..103
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On big endian machines the bit indexes translate into the bit
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positions within four 32-bit words in the following way
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MS x[0] LS MS x[1] LS
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ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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00...07 08...15 16...23 24...31 32...39 40...47 48...55 56...63
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MS x[2] LS MS x[3] LS
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ms ls ms ls ms ls ms ls ms ls ms ls ms ls ms ls
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64...71 72...79 80...87 88...95 96..103 104.111 112.119 120.127
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*/
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/* A slow generic version of gf_mul, implemented for lle and bbe
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* It multiplies a and b and puts the result in a */
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void gf128mul_lle(be128 *a, const be128 *b);
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void gf128mul_bbe(be128 *a, const be128 *b);
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/* multiply by x in ble format, needed by XTS */
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void gf128mul_x_ble(be128 *a, const be128 *b);
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/* 4k table optimization */
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struct gf128mul_4k {
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be128 t[256];
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};
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struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g);
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struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g);
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void gf128mul_4k_lle(be128 *a, struct gf128mul_4k *t);
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void gf128mul_4k_bbe(be128 *a, struct gf128mul_4k *t);
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static inline void gf128mul_free_4k(struct gf128mul_4k *t)
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{
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kfree(t);
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}
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/* 64k table optimization, implemented for lle and bbe */
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struct gf128mul_64k {
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struct gf128mul_4k *t[16];
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};
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/* first initialize with the constant factor with which you
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* want to multiply and then call gf128_64k_lle with the other
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* factor in the first argument, the table in the second and a
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* scratch register in the third. Afterwards *a = *r. */
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struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g);
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struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g);
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void gf128mul_free_64k(struct gf128mul_64k *t);
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void gf128mul_64k_lle(be128 *a, struct gf128mul_64k *t);
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void gf128mul_64k_bbe(be128 *a, struct gf128mul_64k *t);
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#endif /* _CRYPTO_GF128MUL_H */
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