Symmetric Encryption Algorithms in a Polynomial Residue Number System
In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multipli...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/4894415 |
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| _version_ | 1849686064322576384 |
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| author | I. Yakymenko M. Karpinski R. Shevchuk M. Kasianchuk |
| author_facet | I. Yakymenko M. Karpinski R. Shevchuk M. Kasianchuk |
| author_sort | I. Yakymenko |
| collection | DOAJ |
| description | In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem. |
| format | Article |
| id | doaj-art-bb805d9abcd84d78a45ff5f507ca264b |
| institution | DOAJ |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-bb805d9abcd84d78a45ff5f507ca264b2025-08-20T03:22:52ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/4894415Symmetric Encryption Algorithms in a Polynomial Residue Number SystemI. Yakymenko0M. Karpinski1R. Shevchuk2M. Kasianchuk3Department of Cyber SecurityDepartment of Cyber SecurityDepartment of Computer ScienceDepartment of Cyber SecurityIn this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem.http://dx.doi.org/10.1155/2024/4894415 |
| spellingShingle | I. Yakymenko M. Karpinski R. Shevchuk M. Kasianchuk Symmetric Encryption Algorithms in a Polynomial Residue Number System Journal of Applied Mathematics |
| title | Symmetric Encryption Algorithms in a Polynomial Residue Number System |
| title_full | Symmetric Encryption Algorithms in a Polynomial Residue Number System |
| title_fullStr | Symmetric Encryption Algorithms in a Polynomial Residue Number System |
| title_full_unstemmed | Symmetric Encryption Algorithms in a Polynomial Residue Number System |
| title_short | Symmetric Encryption Algorithms in a Polynomial Residue Number System |
| title_sort | symmetric encryption algorithms in a polynomial residue number system |
| url | http://dx.doi.org/10.1155/2024/4894415 |
| work_keys_str_mv | AT iyakymenko symmetricencryptionalgorithmsinapolynomialresiduenumbersystem AT mkarpinski symmetricencryptionalgorithmsinapolynomialresiduenumbersystem AT rshevchuk symmetricencryptionalgorithmsinapolynomialresiduenumbersystem AT mkasianchuk symmetricencryptionalgorithmsinapolynomialresiduenumbersystem |