Paper 2017/556 Original: eprint.iacr.org/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($p^q$).
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2017-06-08: last updated
- 2017-06-08: published
- Short URL
- https://ia.cr/2017/556
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}