Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q).

Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, West Bengal, India
DOI
10.7287/peerj.preprints.3259v1
Subject Areas
Cryptography, Scientific Computing and Simulation, Security and Privacy
Keywords
Cryptography, Irreducible Polynomials, Monic IPs
Copyright
© 2017 Dey et al.
Licence
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
Cite this article
Dey S, Ghosh R. 2017. Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q). PeerJ Preprints 5:e3259v1

Abstract

Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.

Author Comment

It is an Original Work