Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation
This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour i...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8868884 |
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| author | Musheer Ahmad Eesa Al-Solami |
| author_facet | Musheer Ahmad Eesa Al-Solami |
| author_sort | Musheer Ahmad |
| collection | DOAJ |
| description | This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. The standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box. The simulation and comparison results demonstrate the effectiveness of proposed method for the construction of cryptographically sound S-boxes. |
| format | Article |
| id | doaj-art-e33b59730fb44cc8bec866132da8e72e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e33b59730fb44cc8bec866132da8e72e2025-02-03T01:28:26ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/88688848868884Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes GenerationMusheer Ahmad0Eesa Al-Solami1Department of Computer Engineering, Jamia Millia Islamia, New Delhi 110025, IndiaDepartment of Information Security, University of Jeddah, Jeddah 21493, Saudi ArabiaThis paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. The standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box. The simulation and comparison results demonstrate the effectiveness of proposed method for the construction of cryptographically sound S-boxes.http://dx.doi.org/10.1155/2020/8868884 |
| spellingShingle | Musheer Ahmad Eesa Al-Solami Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation Complexity |
| title | Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation |
| title_full | Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation |
| title_fullStr | Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation |
| title_full_unstemmed | Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation |
| title_short | Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation |
| title_sort | improved 2d discrete hyperchaos mapping with complex behaviour and algebraic structure for strong s boxes generation |
| url | http://dx.doi.org/10.1155/2020/8868884 |
| work_keys_str_mv | AT musheerahmad improved2ddiscretehyperchaosmappingwithcomplexbehaviourandalgebraicstructureforstrongsboxesgeneration AT eesaalsolami improved2ddiscretehyperchaosmappingwithcomplexbehaviourandalgebraicstructureforstrongsboxesgeneration |