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diff --git a/include/crypto/gf128mul.h b/include/crypto/gf128mul.h new file mode 100644 index 000000000..fa0a63d29 --- /dev/null +++ b/include/crypto/gf128mul.h @@ -0,0 +1,252 @@ +/* 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(2^128) +*/ + +#ifndef _CRYPTO_GF128MUL_H +#define _CRYPTO_GF128MUL_H + +#include <asm/byteorder.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/groups/ST/toolkit/BCM/documents/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. + * + * 10000000 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. + * + * XTS and EME (the latter of which is patent encumbered) use 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 implementation uses 64-bit words 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 GF(2^128) 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); + +/* + * The following functions multiply a field element by x in + * the polynomial field representation. They use 64-bit word operations + * to gain speed but compensate for machine endianness and hence work + * correctly on both styles of machine. + * + * They are defined here for performance. + */ + +static inline u64 gf128mul_mask_from_bit(u64 x, int which) +{ + /* a constant-time version of 'x & ((u64)1 << which) ? (u64)-1 : 0' */ + return ((s64)(x << (63 - which)) >> 63); +} + +static inline void gf128mul_x_lle(be128 *r, const be128 *x) +{ + u64 a = be64_to_cpu(x->a); + u64 b = be64_to_cpu(x->b); + + /* equivalent to gf128mul_table_le[(b << 7) & 0xff] << 48 + * (see crypto/gf128mul.c): */ + u64 _tt = gf128mul_mask_from_bit(b, 0) & ((u64)0xe1 << 56); + + r->b = cpu_to_be64((b >> 1) | (a << 63)); + r->a = cpu_to_be64((a >> 1) ^ _tt); +} + +static inline void gf128mul_x_bbe(be128 *r, const be128 *x) +{ + u64 a = be64_to_cpu(x->a); + u64 b = be64_to_cpu(x->b); + + /* equivalent to gf128mul_table_be[a >> 63] (see crypto/gf128mul.c): */ + u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87; + + r->a = cpu_to_be64((a << 1) | (b >> 63)); + r->b = cpu_to_be64((b << 1) ^ _tt); +} + +/* needed by XTS */ +static inline void gf128mul_x_ble(le128 *r, const le128 *x) +{ + u64 a = le64_to_cpu(x->a); + u64 b = le64_to_cpu(x->b); + + /* equivalent to gf128mul_table_be[b >> 63] (see crypto/gf128mul.c): */ + u64 _tt = gf128mul_mask_from_bit(a, 63) & 0x87; + + r->a = cpu_to_le64((a << 1) | (b >> 63)); + r->b = cpu_to_le64((b << 1) ^ _tt); +} + +/* 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, const struct gf128mul_4k *t); +void gf128mul_4k_bbe(be128 *a, const struct gf128mul_4k *t); +void gf128mul_x8_ble(le128 *r, const le128 *x); +static inline void gf128mul_free_4k(struct gf128mul_4k *t) +{ + kzfree(t); +} + + +/* 64k table optimization, implemented for bbe */ + +struct gf128mul_64k { + struct gf128mul_4k *t[16]; +}; + +/* First initialize with the constant factor with which you + * want to multiply and then call gf128mul_64k_bbe with the other + * factor in the first argument, and the table in the second. + * Afterwards, the result is stored in *a. + */ +struct gf128mul_64k *gf128mul_init_64k_bbe(const be128 *g); +void gf128mul_free_64k(struct gf128mul_64k *t); +void gf128mul_64k_bbe(be128 *a, const struct gf128mul_64k *t); + +#endif /* _CRYPTO_GF128MUL_H */ |