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3ea996ddfb
Constify the multiplication tables passed to the 4k and 64k multiplication functions, as they are not modified by these functions. Cc: Alex Cope <alexcope@google.com> Signed-off-by: Eric Biggers <ebiggers@google.com> Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
437 lines
13 KiB
C
437 lines
13 KiB
C
/* 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://gladman.plushost.co.uk/oldsite/cryptography_technology/index.php
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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(2^128) 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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/*
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* Given a value i in 0..255 as the byte overflow when a field element
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* in GF(2^128) is multiplied by x^8, the following macro returns the
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* 16-bit value that must be XOR-ed into the low-degree end of the
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* product to reduce it modulo the polynomial x^128 + x^7 + x^2 + x + 1.
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*
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* There are two versions of the macro, and hence two tables: one for
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* the "be" convention where the highest-order bit is the coefficient of
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* the highest-degree polynomial term, and one for the "le" convention
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* where the highest-order bit is the coefficient of the lowest-degree
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* polynomial term. In both cases the values are stored in CPU byte
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* endianness such that the coefficients are ordered consistently across
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* bytes, i.e. in the "be" table bits 15..0 of the stored value
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* correspond to the coefficients of x^15..x^0, and in the "le" table
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* bits 15..0 correspond to the coefficients of x^0..x^15.
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*
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* Therefore, provided that the appropriate byte endianness conversions
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* are done by the multiplication functions (and these must be in place
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* anyway to support both little endian and big endian CPUs), the "be"
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* table can be used for multiplications of both "bbe" and "ble"
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* elements, and the "le" table can be used for multiplications of both
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* "lle" and "lbe" elements.
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*/
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#define xda_be(i) ( \
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(i & 0x80 ? 0x4380 : 0) ^ (i & 0x40 ? 0x21c0 : 0) ^ \
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(i & 0x20 ? 0x10e0 : 0) ^ (i & 0x10 ? 0x0870 : 0) ^ \
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(i & 0x08 ? 0x0438 : 0) ^ (i & 0x04 ? 0x021c : 0) ^ \
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(i & 0x02 ? 0x010e : 0) ^ (i & 0x01 ? 0x0087 : 0) \
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)
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#define xda_le(i) ( \
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(i & 0x80 ? 0xe100 : 0) ^ (i & 0x40 ? 0x7080 : 0) ^ \
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(i & 0x20 ? 0x3840 : 0) ^ (i & 0x10 ? 0x1c20 : 0) ^ \
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(i & 0x08 ? 0x0e10 : 0) ^ (i & 0x04 ? 0x0708 : 0) ^ \
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(i & 0x02 ? 0x0384 : 0) ^ (i & 0x01 ? 0x01c2 : 0) \
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)
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static const u16 gf128mul_table_le[256] = gf128mul_dat(xda_le);
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static const u16 gf128mul_table_be[256] = gf128mul_dat(xda_be);
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/*
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* The following functions multiply a field element by x or by x^8 in
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* the polynomial field representation. They use 64-bit word operations
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* to gain speed but compensate for machine endianness and hence work
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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_le[(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_be[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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void gf128mul_x_ble(be128 *r, const be128 *x)
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{
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u64 a = le64_to_cpu(x->a);
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u64 b = le64_to_cpu(x->b);
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u64 _tt = gf128mul_table_be[b >> 63];
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r->a = cpu_to_le64((a << 1) ^ _tt);
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r->b = cpu_to_le64((b << 1) | (a >> 63));
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}
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EXPORT_SYMBOL(gf128mul_x_ble);
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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_le[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_be[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(2^128). If we consider a GF(2^128) 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_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]);
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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_bbe(&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_bbe);
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void gf128mul_free_64k(struct gf128mul_64k *t)
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{
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int i;
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for (i = 0; i < 16; i++)
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kzfree(t->t[i]);
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kzfree(t);
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}
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EXPORT_SYMBOL(gf128mul_free_64k);
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void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t)
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{
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u8 *ap = (u8 *)a;
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be128 r[1];
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int i;
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*r = t->t[0]->t[ap[15]];
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for (i = 1; i < 16; ++i)
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be128_xor(r, r, &t->t[i]->t[ap[15 - i]]);
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*a = *r;
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}
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EXPORT_SYMBOL(gf128mul_64k_bbe);
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/* This version uses 4k 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(2^128). If we consider a GF(2^128) value in a
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single byte, we can construct a table of the 256 16 byte
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values that result from the 256 values of this byte.
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This requires 4096 bytes. If we take the highest byte in
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the buffer and use this table to get the result, we then
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have to multiply by x^120 to get the final value. For the
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next highest byte the result has to be multiplied by x^112
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and so on. But we can do this by accumulating the result
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in an accumulator starting with the result for the top
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byte. We repeatedly multiply the accumulator value by
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x^8 and then add in (i.e. xor) the 16 bytes of the next
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lower byte in the buffer, stopping when we reach the
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lowest byte. This requires a 4096 byte table.
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*/
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struct gf128mul_4k *gf128mul_init_4k_lle(const be128 *g)
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{
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struct gf128mul_4k *t;
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int 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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t->t[128] = *g;
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for (j = 64; j > 0; j >>= 1)
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gf128mul_x_lle(&t->t[j], &t->t[j+j]);
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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[j + k], &t->t[j], &t->t[k]);
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out:
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return t;
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}
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EXPORT_SYMBOL(gf128mul_init_4k_lle);
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struct gf128mul_4k *gf128mul_init_4k_bbe(const be128 *g)
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{
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struct gf128mul_4k *t;
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|
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, const 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, const 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)");
|