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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Arslan Shafique & Kashif Hesham Khan & Mohammad Mazyad Hazzazi & Ismail Bahkali & Zaid Bassfar & Mujeeb Ur Rehman, 2023. "Chaos and Cellular Automata-Based Substitution Box and Its Application in Cryptography," Mathematics, MDPI, vol. 11(10), pages 1-25, May.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2322-:d:1148417
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    References listed on IDEAS

    as
    1. B. B. Cassal-Quiroga & E. Campos-Cantón, 2020. "Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, March.
    2. Yin, Ruming & Yuan, Jian & Wang, Jian & Shan, Xiuming & Wang, Xiqin, 2009. "Designing key-dependent chaotic S-box with larger key space," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2582-2589.
    Full references (including those not matched with items on IDEAS)

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