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

Muhammad Sajjad1,*, 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: email

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

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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Cite This Article

M. Sajjad, T. Shah and R. J. Serna, "Designing pair of nonlinear components of a block cipher over gaussian integers," Computers, Materials & Continua, vol. 75, no.3, pp. 5287–5305, 2023.



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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