8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign
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 compac...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024537?viewType=HTML |
| _version_ | 1797230938873135104 |
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| author | Mohammad Mazyad Hazzazi Amer Aljaedi Zaid Bassfar Misbah Rani Tariq Shah |
| author_facet | Mohammad Mazyad Hazzazi Amer Aljaedi Zaid Bassfar Misbah Rani Tariq Shah |
| author_sort | Mohammad Mazyad Hazzazi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T15:36:27Z |
| format | Article |
| id | doaj.art-85cea5f1af41408cbe1c6d7083a8d14a |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T15:36:27Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-85cea5f1af41408cbe1c6d7083a8d14a2024-04-02T01:32:09ZengAIMS PressAIMS Mathematics2473-69882024-03-0195109771099610.3934/math.20245378×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesignMohammad Mazyad Hazzazi 0Amer Aljaedi 1Zaid Bassfar 2Misbah Rani3Tariq Shah 41. Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia2. College of Computing and Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia3. Department of Information Technology, University of Tabuk, Tabuk 71491, Saudi Arabia4. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan4. Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanThis 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.https://www.aimspress.com/article/doi/10.3934/math.2024537?viewType=HTMLaesklein four group $ {v}_{4} $s-boxescartesian structurecartesian permutation$ {v}_{4}\times {v}_{4} $ |
| spellingShingle | 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 AIMS Mathematics aes klein four group $ {v}_{4} $ s-boxes cartesian structure cartesian permutation $ {v}_{4}\times {v}_{4} $ |
| title | 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign |
| title_full | 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign |
| title_fullStr | 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign |
| title_full_unstemmed | 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign |
| title_short | 8×8 S-boxes over Klein four-group and Galois field $ {GF}\left({2}^{4}\right) $: AES redesign |
| title_sort | 8 8 s boxes over klein four group and galois field gf left 2 4 right aes redesign |
| topic | aes klein four group $ {v}_{4} $ s-boxes cartesian structure cartesian permutation $ {v}_{4}\times {v}_{4} $ |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024537?viewType=HTML |
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