MDS Block Hankel-like Rhotrices using Conjugate Elements and Self-Dual Bases of Finite Fields

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¹Shalini Gupta*, ²Ruchi Narang, ³Mansi Harish and ⁴Neetu Dhiman

Bulletin of Pure and Applied Sciences

Section – E – Mathematics & Statistics

Vol. 41E, No.2, July-December 2022.P.184-198

DOI: 10.5958/2320-3226.2022.00025.X

Original Article

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Categories: 41E(2), JUL-DEC 2022, BPAS-Mathmatics & Statics

Description

MDS Block Hankel-like Rhotrices using Conjugate Elements and Self-Dual Bases of Finite Fields

¹Shalini Gupta*, ²Ruchi Narang, ³Mansi Harish and ⁴Neetu Dhiman

Author’s Affiliation:

^1,2,3Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, Himachal Pradesh 171005, India.

⁴University Institute of Technology, Himachal Pradesh University, Shimla, Himachal Pradesh 171005, India.

¹Email: shalini.garga1970@gmail.com, ²Email: ruchinarang8878@gmail.com, ³Email: mansihverma16@gmail.com

⁴Email: dhimanneetu.278@gmail.com

*Corresponding Author: Shalini Gupta, Department of Mathematics & Statistics, Himachal Pradesh University, Shimla, Himachal Pradesh 171005, India.

E-mail: shalini.garga1970@gmail.com

How to cite this article: Gupta S., Narang R., Harish M., Dhiman N. (2022). MDS Block Hankel- like Rhotrices using Conjugate Elements and Self-Dual Bases of Finite Fields. Bull. Pure Appl. Sci. Sect. E Math. Stat. 41E(2), 184-198.

Received on 25.08.2022/ Revised on 19.10.2022/ Accepted on 30.11.2022

Online First Published on Dec 15, 2022 at https://www.bpasjournals.com/

Abstract

Maximum Distance Separable (MDS) matrices offer ideal diffusion properties and are of great importance in design of block ciphers and hash functions. A rhotrix as defined by Sani is a coupled matrix which when used in a cryptosystem provides double security. Many authors constructed MDS Rhotrices over finite fields using matrices which are cryptographically significant. Hankel matrices have wide range of applications in engineering, coding theory and cryptography. In the present paper, we define block rhotrix and block Hankel- like rhotrix. Further, we construct MDS block Hankel-like rhotrices using self-dual basis and conjugate elements of . KEYWORDS: Finite Fields, MDS Rhotrix, Block Rhotrix, Hankel matrix, Hankel Rhotrix, Block Hankel- like Rhotrix.