Open Access

ARTICLE

Nonlinear Components of a Block Cipher over Eisenstein Integers

by Mohammad Mazyad Hazzazi¹, Muhammad Sajjad², Zaid Bassfar³, Tariq Shah^2,*, Ashwag Albakri⁴

1 Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia
2 Department of Mathematics, Quaid-I-Azam University, Islamabad, 45320, Pakistan
3 Department of Information Technology, University of Tabuk, Tabuk, 71491, Saudi Arabia
4 Department of Computer Science, College of Computer Science & Information Technology, Jazan University, Jazan, 45142, Saudi Arabia

* Corresponding Author: Tariq Shah. Email:

Computers, Materials & Continua 2023, 77(3), 3659-3675. https://doi.org/10.32604/cmc.2023.039013

Received 07 January 2023; Accepted 14 April 2023; Issue published 26 December 2023

Abstract

In block ciphers, the nonlinear components, also known as substitution boxes (S-boxes), are used with the purpose to induce confusion in cryptosystems. For the last decade, most of the work on designing S-boxes over the points of elliptic curves, chaotic maps, and Gaussian integers has been published. The main purpose of these studies is to hide data and improve the security levels of crypto algorithms. In this work, we design pair of nonlinear components of a block cipher over the residue class of Eisenstein integers (EI). The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters. However, in the same way, by taking three fixed parameters only one S-box is obtained through a prime field-dependent Elliptic curve (EC), chaotic maps, and Gaussian integers. The newly designed pair of S-boxes are assessed by various tests like nonlinearity, bit independence criterion, strict avalanche criterion, linear approximation probability, and differential approximation probability.

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Keywords

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