An efficient S-box design scheme for image encryption based on the combination of a coset graph and a matrix transformer

Asima Razzaque; Abdul Razaq; Sheikh Muhammad Farooq; Ibtisam Masmali; Muhammad Iftikhar Faraz; Asima Razzaque; Abdul Razaq; Sheikh Muhammad Farooq; Ibtisam Masmali; Muhammad Iftikhar Faraz

doi:10.3934/era.2023137

Electronic Research Archive

2023, Volume 31, Issue 5: 2708-2732. doi: 10.3934/era.2023137

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An efficient S-box design scheme for image encryption based on the combination of a coset graph and a matrix transformer

1.
Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Hofuf, Saudi Arabia
2.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
3.
Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
4.
College of Mechanical Engineering, King Faisal University Al-Ahsa Hofuf, Saudi Arabia

Received: 07 January 2023 Revised: 23 February 2023 Accepted: 01 March 2023 Published: 10 March 2023

Modern block ciphers deal with the development of security mechanisms to meet the security needs in several fields of application. The substitution box, which is an important constituent in block ciphers, necessarily has sufficient cryptographic robustness to counter different attacks. The basic problem with S-box design is that there is no evident pattern in its cryptographic properties. This study introduces a new mathematical algorithm for developing S-box based on the modular group coset graphs and a newly invented mathematical notion "matrix transformer". The proficiency of the proposed S-box is assessed through modern performance evaluation tools, and it has been observed that the constructed S-box has almost optimal features, indicating the effectiveness of the invented technique.
- coset graphs for the modular group,
- cryptography,
- block cipher,
- S-box,
- matrix transformer,
- security of the cryptosystem,
- image encryption
Citation: Asima Razzaque, Abdul Razaq, Sheikh Muhammad Farooq, Ibtisam Masmali, Muhammad Iftikhar Faraz. An efficient S-box design scheme for image encryption based on the combination of a coset graph and a matrix transformer[J]. Electronic Research Archive, 2023, 31(5): 2708-2732. doi: 10.3934/era.2023137

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Abstract

Modern block ciphers deal with the development of security mechanisms to meet the security needs in several fields of application. The substitution box, which is an important constituent in block ciphers, necessarily has sufficient cryptographic robustness to counter different attacks. The basic problem with S-box design is that there is no evident pattern in its cryptographic properties. This study introduces a new mathematical algorithm for developing S-box based on the modular group coset graphs and a newly invented mathematical notion "matrix transformer". The proficiency of the proposed S-box is assessed through modern performance evaluation tools, and it has been observed that the constructed S-box has almost optimal features, indicating the effectiveness of the invented technique.

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