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416 lines
12 KiB
416 lines
12 KiB
/* 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 <[email protected]> |
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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^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_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_x8_ble(le128 *r, const le128 *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[a >> 56]; |
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r->a = cpu_to_le64((a << 8) | (b >> 56)); |
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r->b = cpu_to_le64((b << 8) ^ _tt); |
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} |
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EXPORT_SYMBOL(gf128mul_x8_ble); |
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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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kfree_sensitive(t->t[i]); |
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kfree_sensitive(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; |
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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[1] = *g; |
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for (j = 1; j <= 64; j <<= 1) |
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gf128mul_x_bbe(&t->t[j + j], &t->t[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_bbe); |
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void gf128mul_4k_lle(be128 *a, const struct gf128mul_4k *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 = 15; |
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*r = t->t[ap[15]]; |
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while (i--) { |
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gf128mul_x8_lle(r); |
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be128_xor(r, r, &t->t[ap[i]]); |
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} |
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*a = *r; |
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} |
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EXPORT_SYMBOL(gf128mul_4k_lle); |
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void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *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 = 0; |
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*r = t->t[ap[0]]; |
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while (++i < 16) { |
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gf128mul_x8_bbe(r); |
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be128_xor(r, r, &t->t[ap[i]]); |
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} |
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*a = *r; |
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} |
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EXPORT_SYMBOL(gf128mul_4k_bbe); |
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MODULE_LICENSE("GPL"); |
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MODULE_DESCRIPTION("Functions for multiplying elements of GF(2^128)");
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