Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes
This paper proposes to present a novel group theoretic approach of improvising the cryptographic features of substitution-boxes. The approach employs a proposed finite Abelian group of order 3720 with three generators and six relations. The pre and post-action of the new Abelian group on some nonlin...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9007348/ |
| _version_ | 1818853413088133120 |
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| author | Muhammad Awais Yousaf Hanan Alolaiyan Musheer Ahmad Muhammad Dilbar Abdul Razaq |
| author_facet | Muhammad Awais Yousaf Hanan Alolaiyan Musheer Ahmad Muhammad Dilbar Abdul Razaq |
| author_sort | Muhammad Awais Yousaf |
| collection | DOAJ |
| description | This paper proposes to present a novel group theoretic approach of improvising the cryptographic features of substitution-boxes. The approach employs a proposed finite Abelian group of order 3720 with three generators and six relations. The pre and post-action of the new Abelian group on some nonlinear schemes is analyzed and investigated. It has been found that post-action is competent to construct substitution-boxes whose cryptographic strengths are quite better compared to them before the group action. The S-box strength improvisation has been perceived on multiple performance parameters including nonlinearity, differential uniformity, bits independent criteria, linear approximation probability, and auto-correlation functions along with the satisfaction of strict avalanche criteria. The suitability of proposed improved S-box is tested for image encryption applications under the majority logic criterions and differential analyses. The conducted statistical investigations demonstrated the proficiency of anticipated group action approach and its suitability for cryptographic usages. |
| first_indexed | 2024-12-19T07:36:25Z |
| format | Article |
| id | doaj.art-73112082be4a444191fa2f0f85d30926 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-19T07:36:25Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-73112082be4a444191fa2f0f85d309262022-12-21T20:30:35ZengIEEEIEEE Access2169-35362020-01-018397813979210.1109/ACCESS.2020.29758809007348Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear SchemesMuhammad Awais Yousaf0https://orcid.org/0000-0002-3507-9367Hanan Alolaiyan1https://orcid.org/0000-0002-7845-7751Musheer Ahmad2https://orcid.org/0000-0002-4915-9325Muhammad Dilbar3https://orcid.org/0000-0002-9048-4090Abdul Razaq4https://orcid.org/0000-0002-1898-4082Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, King Saud University, Riyadh, Saudi ArabiaDepartment of Computer Engineering, Jamia Millia Islamia, New Delhi, IndiaDepartment of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, PakistanThis paper proposes to present a novel group theoretic approach of improvising the cryptographic features of substitution-boxes. The approach employs a proposed finite Abelian group of order 3720 with three generators and six relations. The pre and post-action of the new Abelian group on some nonlinear schemes is analyzed and investigated. It has been found that post-action is competent to construct substitution-boxes whose cryptographic strengths are quite better compared to them before the group action. The S-box strength improvisation has been perceived on multiple performance parameters including nonlinearity, differential uniformity, bits independent criteria, linear approximation probability, and auto-correlation functions along with the satisfaction of strict avalanche criteria. The suitability of proposed improved S-box is tested for image encryption applications under the majority logic criterions and differential analyses. The conducted statistical investigations demonstrated the proficiency of anticipated group action approach and its suitability for cryptographic usages.https://ieeexplore.ieee.org/document/9007348/Substitution-boxgroup actionAbelian groupimage encryption |
| spellingShingle | Muhammad Awais Yousaf Hanan Alolaiyan Musheer Ahmad Muhammad Dilbar Abdul Razaq Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes IEEE Access Substitution-box group action Abelian group image encryption |
| title | Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes |
| title_full | Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes |
| title_fullStr | Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes |
| title_full_unstemmed | Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes |
| title_short | Comparison of Pre and Post-Action of a Finite Abelian Group Over Certain Nonlinear Schemes |
| title_sort | comparison of pre and post action of a finite abelian group over certain nonlinear schemes |
| topic | Substitution-box group action Abelian group image encryption |
| url | https://ieeexplore.ieee.org/document/9007348/ |
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