[CRYPTO] lib: table driven multiplications in GF(2^128)
A lot of cypher modes need multiplications in GF(2^128). LRW, ABL, GCM... I use functions from this library in my LRW implementation and I will also use them in my ABL (Arbitrary Block Length, an unencumbered (correct me if I am wrong, wide block cipher mode). Elements of GF(2^128) must be presented as u128 *, it encourages automatic and proper alignment. The library contains support for two different representations of GF(2^128), see the comment in gf128mul.h. There different levels of optimization (memory/speed tradeoff). The code is based on work by Dr Brian Gladman. Notable changes: - deletion of two optimization modes - change from u32 to u64 for faster handling on 64bit machines - support for 'bbe' representation in addition to the, already implemented, 'lle' representation. - move 'inline void' functions from header to 'static void' in the source file - update to use the linux coding style conventions The original can be found at: http://fp.gladman.plus.com/AES/modes.vc8.19-06-06.zip The copyright (and GPL statement) of the original author is preserved. Signed-off-by: Rik Snel <rsnel@cube.dyndns.org> Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>hifive-unleashed-5.1
Rik Snel
David S. Miller
parent
aec3694b98
commit
c494e0705d
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@ -139,6 +139,16 @@ config CRYPTO_TGR192
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See also:
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<http://www.cs.technion.ac.il/~biham/Reports/Tiger/>.
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config CRYPTO_GF128MUL
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tristate "GF(2^128) multiplication functions (EXPERIMENTAL)"
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depends on EXPERIMENTAL
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help
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Efficient table driven implementation of multiplications in the
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field GF(2^128). This is needed by some cypher modes. This
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option will be selected automatically if you select such a
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cipher mode. Only select this option by hand if you expect to load
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an external module that requires these functions.
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config CRYPTO_ECB
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tristate "ECB support"
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select CRYPTO_BLKCIPHER
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@ -24,6 +24,7 @@ obj-$(CONFIG_CRYPTO_SHA256) += sha256.o
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obj-$(CONFIG_CRYPTO_SHA512) += sha512.o
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obj-$(CONFIG_CRYPTO_WP512) += wp512.o
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obj-$(CONFIG_CRYPTO_TGR192) += tgr192.o
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obj-$(CONFIG_CRYPTO_GF128MUL) += gf128mul.o
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obj-$(CONFIG_CRYPTO_ECB) += ecb.o
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obj-$(CONFIG_CRYPTO_CBC) += cbc.o
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obj-$(CONFIG_CRYPTO_DES) += des.o
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@ -0,0 +1,466 @@
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/* gf128mul.c - 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 31/01/2006
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This file provides fast multiplication in GF(128) as required by several
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cryptographic authentication modes
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*/
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#include <crypto/gf128mul.h>
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#include <linux/kernel.h>
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#include <linux/module.h>
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#include <linux/slab.h>
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#define gf128mul_dat(q) { \
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q(0x00), q(0x01), q(0x02), q(0x03), q(0x04), q(0x05), q(0x06), q(0x07),\
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q(0x08), q(0x09), q(0x0a), q(0x0b), q(0x0c), q(0x0d), q(0x0e), q(0x0f),\
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q(0x10), q(0x11), q(0x12), q(0x13), q(0x14), q(0x15), q(0x16), q(0x17),\
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q(0x18), q(0x19), q(0x1a), q(0x1b), q(0x1c), q(0x1d), q(0x1e), q(0x1f),\
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q(0x20), q(0x21), q(0x22), q(0x23), q(0x24), q(0x25), q(0x26), q(0x27),\
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q(0x28), q(0x29), q(0x2a), q(0x2b), q(0x2c), q(0x2d), q(0x2e), q(0x2f),\
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q(0x30), q(0x31), q(0x32), q(0x33), q(0x34), q(0x35), q(0x36), q(0x37),\
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q(0x38), q(0x39), q(0x3a), q(0x3b), q(0x3c), q(0x3d), q(0x3e), q(0x3f),\
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q(0x40), q(0x41), q(0x42), q(0x43), q(0x44), q(0x45), q(0x46), q(0x47),\
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q(0x48), q(0x49), q(0x4a), q(0x4b), q(0x4c), q(0x4d), q(0x4e), q(0x4f),\
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q(0x50), q(0x51), q(0x52), q(0x53), q(0x54), q(0x55), q(0x56), q(0x57),\
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q(0x58), q(0x59), q(0x5a), q(0x5b), q(0x5c), q(0x5d), q(0x5e), q(0x5f),\
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q(0x60), q(0x61), q(0x62), q(0x63), q(0x64), q(0x65), q(0x66), q(0x67),\
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q(0x68), q(0x69), q(0x6a), q(0x6b), q(0x6c), q(0x6d), q(0x6e), q(0x6f),\
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q(0x70), q(0x71), q(0x72), q(0x73), q(0x74), q(0x75), q(0x76), q(0x77),\
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q(0x78), q(0x79), q(0x7a), q(0x7b), q(0x7c), q(0x7d), q(0x7e), q(0x7f),\
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q(0x80), q(0x81), q(0x82), q(0x83), q(0x84), q(0x85), q(0x86), q(0x87),\
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q(0x88), q(0x89), q(0x8a), q(0x8b), q(0x8c), q(0x8d), q(0x8e), q(0x8f),\
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q(0x90), q(0x91), q(0x92), q(0x93), q(0x94), q(0x95), q(0x96), q(0x97),\
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q(0x98), q(0x99), q(0x9a), q(0x9b), q(0x9c), q(0x9d), q(0x9e), q(0x9f),\
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q(0xa0), q(0xa1), q(0xa2), q(0xa3), q(0xa4), q(0xa5), q(0xa6), q(0xa7),\
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q(0xa8), q(0xa9), q(0xaa), q(0xab), q(0xac), q(0xad), q(0xae), q(0xaf),\
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q(0xb0), q(0xb1), q(0xb2), q(0xb3), q(0xb4), q(0xb5), q(0xb6), q(0xb7),\
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q(0xb8), q(0xb9), q(0xba), q(0xbb), q(0xbc), q(0xbd), q(0xbe), q(0xbf),\
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q(0xc0), q(0xc1), q(0xc2), q(0xc3), q(0xc4), q(0xc5), q(0xc6), q(0xc7),\
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q(0xc8), q(0xc9), q(0xca), q(0xcb), q(0xcc), q(0xcd), q(0xce), q(0xcf),\
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q(0xd0), q(0xd1), q(0xd2), q(0xd3), q(0xd4), q(0xd5), q(0xd6), q(0xd7),\
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q(0xd8), q(0xd9), q(0xda), q(0xdb), q(0xdc), q(0xdd), q(0xde), q(0xdf),\
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q(0xe0), q(0xe1), q(0xe2), q(0xe3), q(0xe4), q(0xe5), q(0xe6), q(0xe7),\
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q(0xe8), q(0xe9), q(0xea), q(0xeb), q(0xec), q(0xed), q(0xee), q(0xef),\
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q(0xf0), q(0xf1), q(0xf2), q(0xf3), q(0xf4), q(0xf5), q(0xf6), q(0xf7),\
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q(0xf8), q(0xf9), q(0xfa), q(0xfb), q(0xfc), q(0xfd), q(0xfe), q(0xff) \
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}
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/* Given the value i in 0..255 as the byte overflow when a field element
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in GHASH is multipled by x^8, this function will return the values that
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are generated in the lo 16-bit word of the field value by applying the
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modular polynomial. The values lo_byte and hi_byte are returned via the
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macro xp_fun(lo_byte, hi_byte) so that the values can be assembled into
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memory as required by a suitable definition of this macro operating on
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the table above
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*/
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#define xx(p, q) 0x##p##q
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#define xda_bbe(i) ( \
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(i & 0x80 ? xx(43, 80) : 0) ^ (i & 0x40 ? xx(21, c0) : 0) ^ \
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(i & 0x20 ? xx(10, e0) : 0) ^ (i & 0x10 ? xx(08, 70) : 0) ^ \
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(i & 0x08 ? xx(04, 38) : 0) ^ (i & 0x04 ? xx(02, 1c) : 0) ^ \
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(i & 0x02 ? xx(01, 0e) : 0) ^ (i & 0x01 ? xx(00, 87) : 0) \
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)
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#define xda_lle(i) ( \
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(i & 0x80 ? xx(e1, 00) : 0) ^ (i & 0x40 ? xx(70, 80) : 0) ^ \
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(i & 0x20 ? xx(38, 40) : 0) ^ (i & 0x10 ? xx(1c, 20) : 0) ^ \
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(i & 0x08 ? xx(0e, 10) : 0) ^ (i & 0x04 ? xx(07, 08) : 0) ^ \
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(i & 0x02 ? xx(03, 84) : 0) ^ (i & 0x01 ? xx(01, c2) : 0) \
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)
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static const u16 gf128mul_table_lle[256] = gf128mul_dat(xda_lle);
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static const u16 gf128mul_table_bbe[256] = gf128mul_dat(xda_bbe);
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/* These functions multiply a field element by x, by x^4 and by x^8
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* in the polynomial field representation. It uses 32-bit word operations
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* to gain speed but compensates for machine endianess and hence works
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* correctly on both styles of machine.
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*/
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static void gf128mul_x_lle(be128 *r, const be128 *x)
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{
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u64 a = be64_to_cpu(x->a);
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u64 b = be64_to_cpu(x->b);
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u64 _tt = gf128mul_table_lle[(b << 7) & 0xff];
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r->b = cpu_to_be64((b >> 1) | (a << 63));
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r->a = cpu_to_be64((a >> 1) ^ (_tt << 48));
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}
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static void gf128mul_x_bbe(be128 *r, const be128 *x)
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{
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u64 a = be64_to_cpu(x->a);
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u64 b = be64_to_cpu(x->b);
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u64 _tt = gf128mul_table_bbe[a >> 63];
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r->a = cpu_to_be64((a << 1) | (b >> 63));
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r->b = cpu_to_be64((b << 1) ^ _tt);
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}
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static void gf128mul_x8_lle(be128 *x)
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{
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u64 a = be64_to_cpu(x->a);
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u64 b = be64_to_cpu(x->b);
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u64 _tt = gf128mul_table_lle[b & 0xff];
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x->b = cpu_to_be64((b >> 8) | (a << 56));
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x->a = cpu_to_be64((a >> 8) ^ (_tt << 48));
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}
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static void gf128mul_x8_bbe(be128 *x)
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{
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u64 a = be64_to_cpu(x->a);
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u64 b = be64_to_cpu(x->b);
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u64 _tt = gf128mul_table_bbe[a >> 56];
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x->a = cpu_to_be64((a << 8) | (b >> 56));
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x->b = cpu_to_be64((b << 8) ^ _tt);
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}
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void gf128mul_lle(be128 *r, const be128 *b)
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{
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be128 p[8];
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int i;
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p[0] = *r;
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for (i = 0; i < 7; ++i)
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gf128mul_x_lle(&p[i + 1], &p[i]);
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memset(r, 0, sizeof(r));
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for (i = 0;;) {
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u8 ch = ((u8 *)b)[15 - i];
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if (ch & 0x80)
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be128_xor(r, r, &p[0]);
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if (ch & 0x40)
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be128_xor(r, r, &p[1]);
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if (ch & 0x20)
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be128_xor(r, r, &p[2]);
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if (ch & 0x10)
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be128_xor(r, r, &p[3]);
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if (ch & 0x08)
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be128_xor(r, r, &p[4]);
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if (ch & 0x04)
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be128_xor(r, r, &p[5]);
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if (ch & 0x02)
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be128_xor(r, r, &p[6]);
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if (ch & 0x01)
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be128_xor(r, r, &p[7]);
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if (++i >= 16)
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break;
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gf128mul_x8_lle(r);
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}
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}
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EXPORT_SYMBOL(gf128mul_lle);
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void gf128mul_bbe(be128 *r, const be128 *b)
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{
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be128 p[8];
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int i;
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p[0] = *r;
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for (i = 0; i < 7; ++i)
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gf128mul_x_bbe(&p[i + 1], &p[i]);
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memset(r, 0, sizeof(r));
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for (i = 0;;) {
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u8 ch = ((u8 *)b)[i];
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if (ch & 0x80)
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be128_xor(r, r, &p[7]);
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if (ch & 0x40)
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be128_xor(r, r, &p[6]);
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if (ch & 0x20)
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be128_xor(r, r, &p[5]);
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if (ch & 0x10)
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be128_xor(r, r, &p[4]);
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if (ch & 0x08)
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be128_xor(r, r, &p[3]);
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if (ch & 0x04)
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be128_xor(r, r, &p[2]);
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if (ch & 0x02)
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be128_xor(r, r, &p[1]);
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if (ch & 0x01)
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be128_xor(r, r, &p[0]);
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if (++i >= 16)
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break;
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gf128mul_x8_bbe(r);
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}
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}
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EXPORT_SYMBOL(gf128mul_bbe);
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/* This version uses 64k bytes of table space.
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A 16 byte buffer has to be multiplied by a 16 byte key
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value in GF(128). If we consider a GF(128) value in
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the buffer's lowest byte, we can construct a table of
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the 256 16 byte values that result from the 256 values
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of this byte. This requires 4096 bytes. But we also
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need tables for each of the 16 higher bytes in the
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buffer as well, which makes 64 kbytes in total.
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*/
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/* additional explanation
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* t[0][BYTE] contains g*BYTE
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* t[1][BYTE] contains g*x^8*BYTE
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* ..
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* t[15][BYTE] contains g*x^120*BYTE */
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struct gf128mul_64k *gf128mul_init_64k_lle(const be128 *g)
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{
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struct gf128mul_64k *t;
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int i, j, k;
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t = kzalloc(sizeof(*t), GFP_KERNEL);
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if (!t)
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goto out;
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for (i = 0; i < 16; i++) {
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t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
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if (!t->t[i]) {
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gf128mul_free_64k(t);
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t = NULL;
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goto out;
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}
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}
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t->t[0]->t[128] = *g;
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for (j = 64; j > 0; j >>= 1)
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gf128mul_x_lle(&t->t[0]->t[j], &t->t[0]->t[j + j]);
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for (i = 0;;) {
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for (j = 2; j < 256; j += j)
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for (k = 1; k < j; ++k)
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be128_xor(&t->t[i]->t[j + k],
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&t->t[i]->t[j], &t->t[i]->t[k]);
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if (++i >= 16)
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break;
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for (j = 128; j > 0; j >>= 1) {
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t->t[i]->t[j] = t->t[i - 1]->t[j];
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gf128mul_x8_lle(&t->t[i]->t[j]);
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}
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}
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out:
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return t;
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}
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EXPORT_SYMBOL(gf128mul_init_64k_lle);
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struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g)
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{
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struct gf128mul_64k *t;
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int i, j, k;
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t = kzalloc(sizeof(*t), GFP_KERNEL);
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if (!t)
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goto out;
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for (i = 0; i < 16; i++) {
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t->t[i] = kzalloc(sizeof(*t->t[i]), GFP_KERNEL);
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if (!t->t[i]) {
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gf128mul_free_64k(t);
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t = NULL;
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goto out;
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}
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}
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t->t[0]->t[1] = *g;
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for (j = 1; j <= 64; j <<= 1)
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gf128mul_x_bbe(&t->t[0]->t[j + j], &t->t[0]->t[j]);
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for (i = 0;;) {
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for (j = 2; j < 256; j += j)
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for (k = 1; k < j; ++k)
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be128_xor(&t->t[i]->t[j + k],
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&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)");
|
||||
|
|
@ -0,0 +1,198 @@
|
|||
/* 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 */
|
||||
Loading…
Reference in New Issue