Open Access

ARTICLE

Mordell Elliptic Curve Based Design of Nonlinear Component of Block Cipher

Hafeez ur Rehman^1,*, Tariq Shah¹, Mohammad Mazyad Hazzazi², Ali Alshehri³, Bassfar Zaid⁴

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

* Corresponding Author: Hafeez ur Rehman. Email:

Computers, Materials & Continua 2022, 73(2), 2913-2930. https://doi.org/10.32604/cmc.2022.028765

Received 16 February 2022; Accepted 14 April 2022; Issue published 16 June 2022

Abstract

Elliptic curves (ECs) are deemed one of the most solid structures against modern computational attacks because of their small key size and high security. In many well-known cryptosystems, the substitution box (S-box) is used as the only nonlinear portion of a security system. Recently, it has been shown that using dynamic S-boxes rather than static S-boxes increases the security of a cryptosystem. The conferred study also extends the practical application of ECs in designing the nonlinear components of block ciphers in symmetric key cryptography. In this study, instead of the Mordell elliptic curve (MEC) over the prime field, the Galois field has been engaged in constructing the S-boxes, the main nonlinear component of the block ciphers. Also, the proposed scheme uses the coordinates of MEC and the operation of the Galois field to generate a higher number of S-boxes with optimal nonlinearity, which increases the security of cryptosystems. The proposed S-boxes resilience against prominent algebraic and statistical attacks is evaluated to determine its potential to induce confusion and produce acceptable results compared to other schemes. Also, the majority logic criteria (MLC) are used to assess the new S-boxes usage in the image encryption application, and the outcomes indicate that they have significant cryptographic strength.

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Keywords

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