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Put headers on the C files.

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Jim Plank 2013-10-09 11:00:24 -04:00
parent 110523d6f3
commit b0e2ae07ab
26 changed files with 143 additions and 43 deletions
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License.txt
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Copyright (c) 2013, James S. Plank, Ethan L. Miller, William B. Houston Copyright (c) 2013, James S. Plank, Ethan L. Miller, Kevin M. Greenan,
Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride
All rights reserved. All rights reserved.
Redistribution and use in source and binary forms, with or without Redistribution and use in source and binary forms, with or without

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gf.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf.c * gf.c
* *
* Generic routines for Galois fields * Generic routines for Galois fields

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gf_add.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_add.c * gf_add.c
* *
* Adds two numbers in gf_2^w * Adds two numbers in gf_2^w

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gf_example_1.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_1.c * gf_example_1.c
* *
* Demonstrates using the procedures for examples in GF(2^w) for w <= 32. * Demonstrates using the procedures for examples in GF(2^w) for w <= 32.

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gf_example_2.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_2.c * gf_example_2.c
* *
* Demonstrates using the procedures for examples in GF(2^w) for w <= 32. * Demonstrates using the procedures for examples in GF(2^w) for w <= 32.

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gf_example_3.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_3.c * gf_example_3.c
* *
* Identical to example_2 except it works in GF(2^64) * Identical to example_2 except it works in GF(2^64)

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gf_example_4.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_4.c * gf_example_4.c
* *
* Identical to example_3 except it works in GF(2^128) * Identical to example_3 except it works in GF(2^128)

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gf_example_5.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_5.c * gf_example_5.c
* *
* Demonstrating altmap and extract_word * Demonstrating altmap and extract_word

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gf_example_6.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_6.c * gf_example_6.c
* *
* Demonstrating altmap and extract_word * Demonstrating altmap and extract_word

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gf_example_7.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_example_7.c * gf_example_7.c
* *
* Demonstrating extract_word and Cauchy * Demonstrating extract_word and Cauchy

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gf_general.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_general.c * gf_general.c
* *
* This file has helper routines for doing basic GF operations with any * This file has helper routines for doing basic GF operations with any

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gf_inline_time.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_inline_time.c * gf_inline_time.c
* *
* Times inline single multiplication when w = 4, 8 or 16 * Times inline single multiplication when w = 4, 8 or 16

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gf_method.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_method.c * gf_method.c
* *
* Parses argv to figure out the mult_type and arguments. Returns the gf. * Parses argv to figure out the mult_type and arguments. Returns the gf.

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gf_methods.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_methods.c * gf_methods.c
* *
* Lists supported methods (incomplete w.r.t. GROUP and COMPOSITE * Lists supported methods (incomplete w.r.t. GROUP and COMPOSITE)
*/ */
#include <stdio.h> #include <stdio.h>

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gf_mult.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_mult.c * gf_mult.c
* *
* Multiplies two numbers in gf_2^w * Multiplies two numbers in gf_2^w

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gf_poly.c
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/* /*
gf_poly.c - program to help find irreducible polynomials in composite fields, * GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
using the Ben-Or algorithm. * James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
James S. Plank *
* gf_poly.c - program to help find irreducible polynomials in composite fields,
Please see the following paper for a * using the Ben-Or algorithm.
description of the Ben-Or algorithm: *
* (This one was written by Jim)
author S. Gao and D. Panario *
title Tests and Constructions of Irreducible Polynomials over Finite Fields * Please see the following paper for a description of the Ben-Or algorithm:
booktitle Foundations of Computational Mathematics *
year 1997 * author S. Gao and D. Panario
publisher Springer Verlag * title Tests and Constructions of Irreducible Polynomials over Finite Fields
pages 346-361 * booktitle Foundations of Computational Mathematics
* year 1997
The basic technique is this. You have a polynomial f(x) whose coefficients are * publisher Springer Verlag
in a base field GF(2^w). The polynomial is of degree n. You need to do the * pages 346-361
following for all i from 1 to n/2: *
* The basic technique is this. You have a polynomial f(x) whose coefficients are
Construct x^(2^w)^i modulo f. That will be a polynomial of maximum degree n-1 * in a base field GF(2^w). The polynomial is of degree n. You need to do the
with coefficients in GF(2^w). You construct that polynomial by starting with x * following for all i from 1 to n/2:
and doubling it w times, each time taking the result modulo f. Then you *
multiply that by itself i times, again each time taking the result modulo f. * Construct x^(2^w)^i modulo f. That will be a polynomial of maximum degree n-1
* with coefficients in GF(2^w). You construct that polynomial by starting with x
When you're done, you need to "subtract" x -- since addition = subtraction = * and doubling it w times, each time taking the result modulo f. Then you
XOR, that means XOR x. * multiply that by itself i times, again each time taking the result modulo f.
*
Now, find the GCD of that last polynomial and f, using Euclid's algorithm. If * When you're done, you need to "subtract" x -- since addition = subtraction =
the GCD is not one, then f is reducible. If it is not reducible for each of * XOR, that means XOR x.
those i, then it is irreducible. *
* Now, find the GCD of that last polynomial and f, using Euclid's algorithm. If
In this code, I am using a gf_general_t to represent elements of GF(2^w). This * the GCD is not one, then f is reducible. If it is not reducible for each of
is so that I can use base fields that are GF(2^64) or GF(2^128). * those i, then it is irreducible.
*
I have two main procedures. The first is x_to_q_to_i_minus_x, which calculates * In this code, I am using a gf_general_t to represent elements of GF(2^w). This
x^(2^w)^i - x, putting the result into a gf_general_t * called retval. * is so that I can use base fields that are GF(2^64) or GF(2^128).
*
The second is gcd_one, which takes a polynomial of degree n and a second one * I have two main procedures. The first is x_to_q_to_i_minus_x, which calculates
of degree n-1, and uses Euclid's algorithm to decide if their GCD == 1. * x^(2^w)^i - x, putting the result into a gf_general_t * called retval.
*
These can be made faster (e.g. calculate x^(2^w) once and store it). * The second is gcd_one, which takes a polynomial of degree n and a second one
* of degree n-1, and uses Euclid's algorithm to decide if their GCD == 1.
*
* These can be made faster (e.g. calculate x^(2^w) once and store it).
*/ */
#include "gf_complete.h" #include "gf_complete.h"

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gf_rand.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_rand.c -- Random number generator. * gf_rand.c -- Random number generator.
*/ */

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gf_time.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_time.c * gf_time.c
* *
* Performs timing for gf arithmetic * Performs timing for gf arithmetic

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gf_unit.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_unit.c * gf_unit.c
* *
* Performs unit testing for gf arithmetic * Performs unit testing for gf arithmetic

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gf_w128.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w128.c * gf_w128.c
* *
* Routines for 128-bit Galois fields * Routines for 128-bit Galois fields

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gf_w16.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w16.c * gf_w16.c
* *
* Routines for 16-bit Galois fields * Routines for 16-bit Galois fields

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gf_w32.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w32.c * gf_w32.c
* *
* Routines for 32-bit Galois fields * Routines for 32-bit Galois fields

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gf_w4.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w4.c * gf_w4.c
* *
* Routines for 4-bit Galois fields * Routines for 4-bit Galois fields

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gf_w64.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w64.c * gf_w64.c
* *
* Routines for 64-bit Galois fields * Routines for 64-bit Galois fields

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gf_w8.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_w8.c * gf_w8.c
* *
* Routines for 8-bit Galois fields * Routines for 8-bit Galois fields

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gf_wgen.c
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/* /*
* GF-Complete: A Comprehensive Open Source Library for Galois Field Arithmetic
* James S. Plank, Ethan L. Miller, Kevin M. Greenan,
* Benjamin A. Arnold, John A. Burnum, Adam W. Disney, Allen C. McBride.
*
* gf_wgen.c * gf_wgen.c
* *
* Routines for Galois fields for general w < 32. For specific w, * Routines for Galois fields for general w < 32. For specific w,