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A toolbox for simple finite field operation

version 1.3 (10.9 KB) by

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

Updated

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).

% 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

% 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)

hajer

hajer (view profile)

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

Samuel Cheng

Valentina

Valentina (view profile)

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!