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