## Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / Galois Field, Finite field, Irreducible Polynomials (IPs), Monic IPs.

Date: received 7 Jun 2017

Contact author: sankhanil12009 at gmail com

Available format(s): PDF | BibTeX Citation

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

Short URL: ia.cr/2017/556

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