Paper 2017/556
Multiplication and Division over Extended Galois Field GF($p^q$): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF($p^q$).
Sankhanil Dey and Ranjan Ghosh
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.
Note: To Sankhanil Dey and Ranjan Ghosh Dear authors, Please use basic Latex commands in the abstract, e.g., $p^q$. Why do you capitalize some words in the abstract such as Multiplication and Algorithm? What is BPD €q ? Please justify in the paper the time complexity of your algorithms. Can you justify correctness of your algorithms? Thanks, From, Sasha Boldyreva ePrint co-Editor
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Galois FieldFinite fieldIrreducible Polynomials (IPs)Monic IPs.
- Contact author(s)
- sankhanil12009 @ gmail com
- History
- 2017-06-08: received
- Short URL
- https://ia.cr/2017/556
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/556,
author = {Sankhanil Dey and Ranjan Ghosh},
title = {Multiplication and Division over Extended Galois Field {GF}($p^q$): A new Approach to find Monic Irreducible Polynomials over any Galois Field {GF}($p^q$).},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/556},
year = {2017},
url = {https://eprint.iacr.org/2017/556}
}
