Enhancing the robustness of block ciphers through a graphical S-box evolution scheme for secure multimedia applications

Abdul Razaq; Muhammad Mahboob Ahsan; Hanan Alolaiyan; Musheer Ahmad; Qin Xin; Abdul Razaq; Muhammad Mahboob Ahsan; Hanan Alolaiyan; Musheer Ahmad; Qin Xin

doi:10.3934/math.20241681

AIMS Mathematics

2024, Volume 9, Issue 12: 35377-35400. doi: 10.3934/math.20241681

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Enhancing the robustness of block ciphers through a graphical S-box evolution scheme for secure multimedia applications

1.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan, abdul.razaq@ue.edu.pk
2.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan, ahsanmahboob1983@gmail.com
3.
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia, holayan@ksu.edu.sa
4.
Department of Computer Engineering, Jamia Millia Islamia, New Delhi 110025, India, musheer.cse@gmail.com
5.
Faculty of Science and Technology, University of the Faroe Islands, Vestara Bryggja 15, Faroe Islands, Denmark, qinx@setur.fo

Received: 01 September 2024 Revised: 30 November 2024 Accepted: 03 December 2024 Published: 18 December 2024
MSC : 20D35, 94A60

Block ciphers are essential for the secure exchange of data and communication, as they are one of the primary components of network security systems. Modern-day block ciphers are most significantly reliant on substitution-boxes (S-boxes). In essence, the security of these cryptosystems is contingent upon the quality of the S-box that is implemented. Robustness and assurance of the security competency necessary to block ciphers are provided by the cryptographically strong S-boxes. A novel coset graph-based algebraic method was proposed to evolve a robust and efficient S-box in order to address the challenges of strong S-box generation. To begin, the vertices of coset graphs for two Galois fields and a bijective function were employed to generate an initial S-box of sufficient cryptographic strength. Afterwards, a permutation group of large order enhances the robustness of the initial S-box, ensuring its resistance against various cryptanalytic attacks. The proposed method's efficacy was verified by comparing the attributes of our S-box with those of S-boxes that have been recently investigated. Furthermore, the proposed S-box was used for image encryption. The outcome of the majority logic criterion (MLC) criteria, differential analysis, and histogram test demonstrates the suitability of the proposed S-box for secure multimedia applications in the results.
- substitution-box,
- Galois fields,
- coset graphs,
- block ciphers,
- image encryption
Citation: Abdul Razaq, Muhammad Mahboob Ahsan, Hanan Alolaiyan, Musheer Ahmad, Qin Xin. Enhancing the robustness of block ciphers through a graphical S-box evolution scheme for secure multimedia applications[J]. AIMS Mathematics, 2024, 9(12): 35377-35400. doi: 10.3934/math.20241681

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Abstract

Block ciphers are essential for the secure exchange of data and communication, as they are one of the primary components of network security systems. Modern-day block ciphers are most significantly reliant on substitution-boxes (S-boxes). In essence, the security of these cryptosystems is contingent upon the quality of the S-box that is implemented. Robustness and assurance of the security competency necessary to block ciphers are provided by the cryptographically strong S-boxes. A novel coset graph-based algebraic method was proposed to evolve a robust and efficient S-box in order to address the challenges of strong S-box generation. To begin, the vertices of coset graphs for two Galois fields and a bijective function were employed to generate an initial S-box of sufficient cryptographic strength. Afterwards, a permutation group of large order enhances the robustness of the initial S-box, ensuring its resistance against various cryptanalytic attacks. The proposed method's efficacy was verified by comparing the attributes of our S-box with those of S-boxes that have been recently investigated. Furthermore, the proposed S-box was used for image encryption. The outcome of the majority logic criterion (MLC) criteria, differential analysis, and histogram test demonstrates the suitability of the proposed S-box for secure multimedia applications in the results.

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