Paper 2020/365 Original: eprint.iacr.org/2020/365 ↗
A New Algorithm to Find Monic Irreducible Polynomials over Extended Galois field GF prime p and extension q using Positional Arithmetic
Abstract
Search for monic irreducible polynomials (IPs) over extended Galois field GF(p^q) for a large value of the prime moduli p and a large extension to the Galois Field q is a well needed solution in the field of cryptography. In this paper a new algorithm to obtain monic IPs over extended Galois field GF(p^q) for the large values of p and q is introduced. Here in this paper the positional arithmetic is used to multiply all possible two monic elemental polynomials (EPs) with their Galois field number (GFN) to generate all the monic reducible polynomials (RPs). All the monic RPs are cancelled out from the list of monic basic polynomials (BPs) leaving behind all the monic IPs. Time complexity analysis of the said algorithm is also executed that ensures the algorithm to be less time consuming.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2020-04-02: last updated
- 2020-04-02: published
- Short URL
- https://ia.cr/2020/365
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2020/365,
author = {Sankhanil Dey and Amlan Chakrabarti and Ranjan Ghosh},
title = {A New Algorithm to Find Monic Irreducible Polynomials over Extended Galois field GF prime p and extension q using Positional Arithmetic},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/365},
year = {2020},
url = {https://eprint.iacr.org/2020/365}
}