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A toolbox for simple finite field operation

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A toolbox for simple finite field operation


Samuel Cheng (view profile)


13 Sep 2011 (Updated )

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

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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
% create gf class of 3^2

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

% compute rank

% compute inverse
inva = gf9.inv(a)

% Check inverse

% matrix divide

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

% compute summation

% compute subtraction

% compute dot multiplication

% compute dot division

% 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];



MATLAB release MATLAB 7.11 (R2010b)
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Comments and Ratings (3)
02 Jan 2015 hajer

hajer (view profile)

when i try run the code there are problem in rank function
and what is mean obj

30 Aug 2012 Samuel Cheng

Samuel Cheng (view profile)

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

Comment only
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]?

Comment only
14 Sep 2011 1.1

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 1.3

Added new functionality to manipulate polynomials.

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