Open Access

ARTICLE

Design of Nonlinear Components Over a Mordell Elliptic Curve on Galois Fields

Hafeez ur Rehman^1,*, Tariq Shah¹, Amer Aljaedi², Mohammad Mazyad Hazzazi³, Adel R. Alharbi²

1 Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
2 College of Computing and Information Technology, University of Tabuk, Tabuk, 71491, Saudi Arabia
3 Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

* Corresponding Author: Hafeez ur Rehman. Email:

Computers, Materials & Continua 2022, 71(1), 1313-1329. https://doi.org/10.32604/cmc.2022.022224

Received 31 July 2021; Accepted 02 September 2021; Issue published 03 November 2021

Abstract

Elliptic curve cryptography ensures more safety and reliability than other public key cryptosystems of the same key size. In recent years, the use of elliptic curves in public-key cryptography has increased due to their complexity and reliability. Different kinds of substitution boxes are proposed to address the substitution process in the cryptosystems, including dynamical, static, and elliptic curve-based methods. Conventionally, elliptic curve-based S-boxes are based on prime field but in this manuscript; we propose a new technique of generating S-boxes based on mordell elliptic curves over the Galois field . This technique affords a higher number of possibilities to generate S-boxes, which helps to increase the security of the cryptosystem. The robustness of the proposed S-boxes against the well-known algebraic and statistical attacks is analyzed to classify its potential to generate confusion and achieve up to the mark results compared to the various schemes. The majority logic criterion results determine that the proposed S-boxes have up to the mark cryptographic strength.

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Keywords

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