Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography

Arslan Shafique (), Kashif Hesham Khan, Mohammad Mazyad Hazzazi, Ismail Bahkali, Zaid Bassfar and Mujeeb Ur Rehman
Additional contact information
Arslan Shafique: Department of Electrical Engineering, Riphah International University, Islamabad 46000, Pakistan
Kashif Hesham Khan: Department of Computer Science, RMIT University, Melbourne 3001, Australia
Mohammad Mazyad Hazzazi: Department of Mathematics, College of Science, King Khalid University, Abha 61421, Saudi Arabia
Ismail Bahkali: Department of Information Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Zaid Bassfar: Department of Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia
Mujeeb Ur Rehman: School of Science, Technology and Health, York St. John University, York YO31 7EX, UK

Mathematics, 2023, vol. 11, issue 10, 1-25

Abstract: Substitution boxes are the key factor in symmetric-key cryptosystems that determines their ability to resist various cryptanalytic attacks. Creating strong substitution boxes that have multiple strong cryptographic properties at the same time is a challenging task for cryptographers. A significant amount of research has been conducted on S-boxes in the past few decades, but the resulting S-boxes have been found to be vulnerable to various cyberattacks. This paper proposes a new method for creating robust S-boxes that exhibit superior performance and possess high scores in multiple cryptographic properties. The hybrid S-box method presented in this paper is based on Chua’s circuit chaotic map, two-dimensional cellular automata, and an algebraic permutation group structure. The proposed 16 × 16 S-box has an excellent performance in terms of security parameters, including a minimum nonlinearity of 102, the absence of fixed points, the satisfaction of bit independence and strict avalanche criteria, a low differential uniformity of 5, a low linear approximation probability of 0.0603, and an auto-correlation function of 28. The analysis of the performance comparison indicates that the proposed S-box outperforms other state-of-the-art S-box techniques in several aspects. It possesses better attributes, such as a higher degree of inherent security and resilience, which make it more secure and less vulnerable to potential attacks.

Keywords: chaos theory; cyberattacks; substitution boxes; data security (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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