/* gf128mul.h - GF(2^128) multiplication functions
*
* Copyright (c) 2003, Dr Brian Gladman, Worcester, UK.
* Copyright (c) 2006 Rik Snel <[email protected]>
*
* 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.
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ALTERNATIVELY, provided that this notice is retained in full, this product
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---------------------------------------------------------------------------
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)
{
kfree_sensitive(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 */
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