8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign

Mohammad Mazyad Hazzazi; Amer Aljaedi; Zaid Bassfar; Misbah Rani; Tariq Shah; Mohammad Mazyad Hazzazi; Amer Aljaedi; Zaid Bassfar; Misbah Rani; Tariq Shah

doi:10.3934/math.2024537

AIMS Mathematics

2024, Volume 9, Issue 5: 10977-10996. doi: 10.3934/math.2024537

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Research article

8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
2.
College of Computing and Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia
3.
Department of Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia
4.
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

Received: 09 December 2023 Revised: 17 February 2024 Accepted: 26 February 2024 Published: 20 March 2024
MSC : 68P25, 68U15

This research paper is supplemented with a unique formation to design state-of-the-art S-boxes. The invented approach is simple but has the capability of creating confusion in our newly proposed algorithm. Our core planned work refined the method of already designed S-boxes to accomplish more compact ones. Various structures were merged here, namely affine transformation, fractional linear transformation, structure of Klein four-group, and the algebraic structures of the Galois fields, $ GF\left({2}^{4}\right) $ and $ GF\left({2}^{8}\right). $ These structures were utilized to synthesize newly $ 1600 $ robust S-boxes. Besides, we discussed encryption steps of AES with these newly generated S-boxes. We highlighted some specific characteristics, performance of parameter's improvement, and their utilization. Nonlinear properties were mainly set to inspect the behavior of I/O bits and could apply image encryption. Then, the performance of proposed S-boxes and newly structured AES was tested in comparison with other prevailing S-boxes.
- AES,
- Klein four group $ {V}_{4} $,
- S-boxes,
- Cartesian structure,
- Cartesian permutation,
- $ {V}_{4}\times {V}_{4} $
Citation: Mohammad Mazyad Hazzazi, Amer Aljaedi, Zaid Bassfar, Misbah Rani, Tariq Shah. 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign[J]. AIMS Mathematics, 2024, 9(5): 10977-10996. doi: 10.3934/math.2024537

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Abstract

This research paper is supplemented with a unique formation to design state-of-the-art S-boxes. The invented approach is simple but has the capability of creating confusion in our newly proposed algorithm. Our core planned work refined the method of already designed S-boxes to accomplish more compact ones. Various structures were merged here, namely affine transformation, fractional linear transformation, structure of Klein four-group, and the algebraic structures of the Galois fields, $ GF\left({2}^{4}\right) $ and $ GF\left({2}^{8}\right). $ These structures were utilized to synthesize newly $ 1600 $ robust S-boxes. Besides, we discussed encryption steps of AES with these newly generated S-boxes. We highlighted some specific characteristics, performance of parameter's improvement, and their utilization. Nonlinear properties were mainly set to inspect the behavior of I/O bits and could apply image encryption. Then, the performance of proposed S-boxes and newly structured AES was tested in comparison with other prevailing S-boxes.

References

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