A novel public key cryptography based on generalized Lucas matrices
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908801126367232 |
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| author | Prasad, Kalika Mahato, Hrishikesh Kumari, Munesh |
| author_facet | Prasad, Kalika Mahato, Hrishikesh Kumari, Munesh |
| contents | In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further, we have proposed a modified public key cryptography using these matrices as keys in Affine cipher and key agreement for encryption-decryption with the combination of terms of generalized Lucas sequences under residue operations. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers(parameters) need to be exchanged, which reduces the time complexity as well as space complexity of the key transmission and has a large key-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_08156 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A novel public key cryptography based on generalized Lucas matrices Prasad, Kalika Mahato, Hrishikesh Kumari, Munesh Cryptography and Security Discrete Mathematics Combinatorics Number Theory 11T71, 11B39, 94A60, 14G50, 68P30 E.3; G.2.1 In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further, we have proposed a modified public key cryptography using these matrices as keys in Affine cipher and key agreement for encryption-decryption with the combination of terms of generalized Lucas sequences under residue operations. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers(parameters) need to be exchanged, which reduces the time complexity as well as space complexity of the key transmission and has a large key-space. |
| title | A novel public key cryptography based on generalized Lucas matrices |
| topic | Cryptography and Security Discrete Mathematics Combinatorics Number Theory 11T71, 11B39, 94A60, 14G50, 68P30 E.3; G.2.1 |
| url | https://arxiv.org/abs/2202.08156 |