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An Algorithm to Find the Irreducible Polynomials Over Galois Field GF(pm)

by J K M Sadique Uz Zaman, Sankhanil Dey, Ranjan Ghosh
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 109 - Number 15
Year of Publication: 2015
Authors: J K M Sadique Uz Zaman, Sankhanil Dey, Ranjan Ghosh
10.5120/19266-1012

J K M Sadique Uz Zaman, Sankhanil Dey, Ranjan Ghosh . An Algorithm to Find the Irreducible Polynomials Over Galois Field GF(pm). International Journal of Computer Applications. 109, 15 ( January 2015), 24-29. DOI=10.5120/19266-1012

@article{ 10.5120/19266-1012,
author = { J K M Sadique Uz Zaman, Sankhanil Dey, Ranjan Ghosh },
title = { An Algorithm to Find the Irreducible Polynomials Over Galois Field GF(pm) },
journal = { International Journal of Computer Applications },
issue_date = { January 2015 },
volume = { 109 },
number = { 15 },
month = { January },
year = { 2015 },
issn = { 0975-8887 },
pages = { 24-29 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume109/number15/19266-1012/ },
doi = { 10.5120/19266-1012 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:44:53.948034+05:30
%A J K M Sadique Uz Zaman
%A Sankhanil Dey
%A Ranjan Ghosh
%T An Algorithm to Find the Irreducible Polynomials Over Galois Field GF(pm)
%J International Journal of Computer Applications
%@ 0975-8887
%V 109
%N 15
%P 24-29
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Irreducible Polynomials over GF(pm) and the multiplicative inverses under it are important in cryptography. Presently the method of deriving irreducible polynomials of a particular prime modulus is very primitive and time consuming. In this paper, in order to find all irreducible polynomials, be it monic or non-monic, of all prime moduli p with all its order m, a fast deterministic computer algorithm based on an algebraic method producing a (m×m) matrix is proposed. The maximum number of terms in each column of the matrix is 2j where j is the column index.

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Index Terms

Computer Science
Information Sciences

Keywords

Extended Finite field Finite field Galois field GF(73) Irreducible polynomial Multiplicative inverse.

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