mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-12-05 05:58:23 +00:00
216 lines
6.7 KiB
C
216 lines
6.7 KiB
C
/*
|
|
---------------------------------------------------------------------------
|
|
Copyright (c) 1998-2010, Brian Gladman, Worcester, UK. All rights reserved.
|
|
|
|
The redistribution and use of this software (with or without changes)
|
|
is allowed without the payment of fees or royalties provided that:
|
|
|
|
source code distributions include the above copyright notice, this
|
|
list of conditions and the following disclaimer;
|
|
|
|
binary distributions include the above copyright notice, this list
|
|
of conditions and the following disclaimer in their documentation.
|
|
|
|
This software is provided 'as is' with no explicit or implied warranties
|
|
in respect of its operation, including, but not limited to, correctness
|
|
and fitness for purpose.
|
|
---------------------------------------------------------------------------
|
|
Issue Date: 11/01/2011
|
|
|
|
I am grateful for the work done by Mark Rodenkirch and Jason Papadopoulos
|
|
in helping to remove a bug in the operation of this code on big endian
|
|
systems when fast buffer operations are enabled.
|
|
---------------------------------------------------------------------------
|
|
|
|
An implementation of field multiplication in the Galois Field GF(2^128)
|
|
|
|
A polynomial representation is used for the field with the coefficients
|
|
held in bit sequences in which the bit numbers are the powers of x that
|
|
a bit represents. The field polynomial used is (x^128+x^7+x^2+x+1).
|
|
|
|
The obvious way of representing field elements in a computer system is
|
|
to map 'x' in the field to the binary integer '2'. But this was way too
|
|
obvious for cryptographers!
|
|
|
|
Here bytes are numbered in their memory order and bits within bytes are
|
|
numbered according to their integer numeric significance (that is as is
|
|
now normal with bit 0 representing unity). The term 'little endian'
|
|
will then used to describe mappings where numeric (power of 2) or field
|
|
(power of x) significance increases with increasing bit or byte numbers
|
|
with 'big endian' being used to describe the inverse situation.
|
|
|
|
The GF bit sequence can then be mapped onto 8-bit bytes in computer
|
|
memory in one of four simple ways:
|
|
|
|
A mapping in which x maps to the integer 2 in little endian
|
|
form for both bytes and bits within bytes:
|
|
|
|
LL: bit for x^n ==> bit for 2^(n % 8) in byte[n / 8]
|
|
|
|
A mapping in which x maps to the integer 2 in big endian form
|
|
for both bytes and bits within bytes:
|
|
|
|
BL: bit for x^n ==> bit for 2^(n % 8) in byte[15 - n / 8]
|
|
|
|
A little endian mapping for bytes but with the bits within
|
|
bytes in reverse order (big endian bytes):
|
|
|
|
LB: bit for x^n ==> bit for 2^(7 - n % 8) in byte[n / 8]
|
|
|
|
A big endian mapping for bytes but with the bits within
|
|
bytes in reverse order (big endian bytes):
|
|
|
|
BB: bit for x^n ==> bit for 2^(7 - n % 8) in byte[15 - n / 8]
|
|
|
|
128-bit field elements are represented by 16 byte buffers but for
|
|
processing efficiency reasons it is often desirable to process arrays
|
|
of bytes using longer types such as, for example, unsigned long values.
|
|
The type used for representing these buffers will be called a 'gf_unit'
|
|
and the buffer itself will be referred to as a 'gf_t' type.
|
|
|
|
THe field multiplier is based on the assumption that one of the two
|
|
field elements involved in multiplication will change only relatively
|
|
infrequently, making it worthwhile to precompute tables to speed up
|
|
multiplication by this value.
|
|
*/
|
|
|
|
#ifndef _GF128MUL_H
|
|
#define _GF128MUL_H
|
|
|
|
#include <stdlib.h>
|
|
#include <string.h>
|
|
|
|
#include "brg_endian.h"
|
|
|
|
/* USER DEFINABLE OPTIONS */
|
|
/* UNIT_BITS sets the size of variables used to process 16 byte buffers
|
|
when the buffer alignment allows this. When buffers are processed
|
|
in bytes, 16 individual operations are invoolved. But if, say, such
|
|
a buffer is divided into 4 32 bit variables, it can then be processed
|
|
in 4 operations, making the code typically much faster. In general
|
|
it will pay to use the longest natively supported size, which will
|
|
probably be 32 or 64 bits in 32 and 64 bit systems respectively.
|
|
*/
|
|
|
|
#if defined( UNIT_BITS )
|
|
# undef UNIT_BITS
|
|
#endif
|
|
|
|
#if !defined( UNIT_BITS )
|
|
# if PLATFORM_BYTE_ORDER == IS_BIG_ENDIAN
|
|
# if 0
|
|
# define UNIT_BITS 8
|
|
# elif 0
|
|
# define UNIT_BITS 32
|
|
# elif 1
|
|
# define UNIT_BITS 64
|
|
# endif
|
|
# elif defined( _WIN64 )
|
|
# define UNIT_BITS 64
|
|
# else
|
|
# define UNIT_BITS 32
|
|
# endif
|
|
#endif
|
|
|
|
#if UNIT_BITS == 64 && !defined( NEED_UINT_64T )
|
|
# define NEED_UINT_64T
|
|
#endif
|
|
|
|
#include "mode_hdr.h"
|
|
|
|
/* Choose the Galois Field representation to use (see above) */
|
|
#if 0
|
|
# define GF_MODE_LL
|
|
#elif 0
|
|
# define GF_MODE_BL
|
|
#elif 1
|
|
# define GF_MODE_LB /* the representation used by GCM */
|
|
#elif 0
|
|
# define GF_MODE_BB
|
|
#else
|
|
# error mode is not defined
|
|
#endif
|
|
|
|
/* Table sizes for GF(128) Multiply. Normally larger tables give
|
|
higher speed but cache loading might change this. Normally only
|
|
one table size (or none at all) will be specified here
|
|
*/
|
|
#if 0
|
|
# define TABLES_64K
|
|
#endif
|
|
#if 0
|
|
# define TABLES_8K
|
|
#endif
|
|
#if 0
|
|
# define TABLES_4K
|
|
#endif
|
|
#if 0
|
|
# define TABLES_256
|
|
#endif
|
|
|
|
/* END OF USER DEFINABLE OPTIONS */
|
|
|
|
#if !(defined( TABLES_64K ) || defined( TABLES_8K ) \
|
|
|| defined( TABLES_4K ) || defined( TABLES_256 ))
|
|
# define NO_TABLES
|
|
#endif
|
|
|
|
#if defined(__cplusplus)
|
|
extern "C"
|
|
{
|
|
#endif
|
|
|
|
#define GF_BYTE_LEN 16
|
|
#define GF_UNIT_LEN (GF_BYTE_LEN / (UNIT_BITS >> 3))
|
|
|
|
UNIT_TYPEDEF(gf_unit_t, UNIT_BITS);
|
|
BUFR_TYPEDEF(gf_t, UNIT_BITS, GF_BYTE_LEN);
|
|
|
|
/* Code for conversion between the four different galois field representations
|
|
is optionally available using gf_convert.c
|
|
*/
|
|
|
|
typedef enum { REVERSE_NONE = 0, REVERSE_BITS = 1, REVERSE_BYTES = 2 } transform;
|
|
|
|
void convert_representation(gf_t dest, const gf_t source, transform rev);
|
|
|
|
void gf_mul(gf_t a, const gf_t b); /* slow field multiply */
|
|
|
|
/* types and calls for 64k table driven field multiplier */
|
|
|
|
typedef gf_t gf_t64k_a[16][256];
|
|
typedef gf_t (*gf_t64k_t)[256];
|
|
|
|
void init_64k_table(const gf_t g, gf_t64k_t t);
|
|
void gf_mul_64k(gf_t a, const gf_t64k_t t, void *r);
|
|
|
|
/* types and calls for 8k table driven field multiplier */
|
|
|
|
typedef gf_t gf_t8k_a[32][16];
|
|
typedef gf_t (*gf_t8k_t)[16];
|
|
|
|
void init_8k_table(const gf_t g, gf_t8k_t t);
|
|
void gf_mul_8k(gf_t a, const gf_t8k_t t, gf_t r);
|
|
|
|
/* types and calls for 8k table driven field multiplier */
|
|
|
|
typedef gf_t gf_t4k_a[256];
|
|
typedef gf_t (*gf_t4k_t);
|
|
|
|
void init_4k_table(const gf_t g, gf_t4k_t t);
|
|
void gf_mul_4k(gf_t a, const gf_t4k_t t, gf_t r);
|
|
|
|
/* types and calls for 8k table driven field multiplier */
|
|
|
|
typedef gf_t gf_t256_a[16];
|
|
typedef gf_t (*gf_t256_t);
|
|
|
|
void init_256_table(const gf_t g, gf_t256_t t);
|
|
void gf_mul_256(gf_t a, const gf_t256_t t, gf_t r);
|
|
|
|
#if defined(__cplusplus)
|
|
}
|
|
#endif
|
|
|
|
#endif
|