Code covered by the BSD License  

Highlights from
A toolbox for simple finite field operation

Be the first to rate this file! 22 Downloads (last 30 days) File Size: 10.9 KB File ID: #32872

A toolbox for simple finite field operation

by

 

13 Sep 2011 (Updated )

This is a toolbox providing simple operations (+,-,*,/,.*,./,inv) for finite field.

| Watch this File

File Information
Description

This toolbox can handle simple operations (+,-,*,/,.*,./,inv) of GF(p^n) for any p and n. Examples are given below (also documented in gf_test.m).

If you find any bug or have any concern/comment, please contact me.

% setup path
java_path_setup;
% create gf class of 3^2
gf9=gf(3,2);

%%%%
% Eg. 1
a=[2 1;1 0]

% compute rank
gf9.rank(a)

% compute inverse
inva = gf9.inv(a)

% Check inverse
a_times_ainva=gf9.mult(a,inva)

% matrix divide
gf9.div(a,a)

%%%%%
% Eg. 2
b=[1 2 1;1 0 1];
c=[1 1 0;2 1 1];

% compute summation
gf9.add(b,c)

% compute subtraction
gf9.sub(b,c)

% compute dot multiplication
gf9.dmult(b,c)

% compute dot division
gf9.ddiv(b,c)

% output the primitive polynomial
gf9.return_primitive_polynomial % x^2 + 1

% show polynomial representation
gf9.return_poly_representation(5) % x + 2

%%%%
% Eg. 3

% manipulating polynomials.

a=[1 2 1 1];
b=[1 3 1];

gf9.conv(a,b)

[q,rem]=gf9.deconv(a,b)

MATLAB release MATLAB 7.11 (R2010b)
Tags for This File   Please login to tag files.
Please login to add a comment or rating.
Comments and Ratings (2)
30 Aug 2012 Samuel Cheng

@Valentina's comments, I have added functions for multiplying and dividing polynomials.

01 Aug 2012 Valentina

Hi Samuel,
I'm trying to use this code to perform some AES operations... What I need is e.g. to define a polynomial which can have a max degree = 7, with coefficients 0 and 1. (i.e., over GF(2)), and then compute its inverse modulo a poly of degree 8, again with binay coeffs. I can't figure out how to declare the gf, which in your example is gf9=gf(3,2); and then how do i define the poly? what does the 2 line matrix in your example mean, a=[2 1;1 0]?
Thanks!

Updates
14 Sep 2011

Oops, found two silly bugs. First, an error check condition was corrected.

Second, I guess it is probably the safest to run a separate script to setup path and so I extracted that part out.

04 Sep 2012

Added new functionality to manipulate polynomials.

Contact us