Open Access

ARTICLE

Designing Pair of Nonlinear Components of a Block Cipher over Gaussian Integers

Muhammad Sajjad^1,*, Tariq Shah¹, Robinson Julian Serna²

1 Department of Mathematics, Quaid-I-Azam University, Islamabad, 45320, Pakistan
2 Escuela de Matemáticas y Estadística, Universidad Pedagógica y Tecnológica de Colombia, Tunja, 150003, Columbia

* Corresponding Author: Muhammad Sajjad. Email:

Computers, Materials & Continua 2023, 75(3), 5287-5305. https://doi.org/10.32604/cmc.2023.035347

Received 17 August 2022; Accepted 24 October 2022; Issue published 29 April 2023

Abstract

In block ciphers, the nonlinear components, also known as substitution boxes (S-boxes), are used with the purpose of inducing confusion in cryptosystems. For the last decade, most of the work on designing S-boxes over the points of elliptic curves 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 Gaussian integers (GI). The fascinating features of this structure provide S-boxes pair at a time by fixing three parameters. But the prime field dependent on the Elliptic curve (EC) provides one S-box at a time by fixing three parameters and . 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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