A novel public key cryptography based on generalized Lucas matrices
Cryptography and Security
2026-02-03 v1 Discrete Mathematics
Combinatorics
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2202.08156,
title = {A novel public key cryptography based on generalized Lucas matrices},
author = {Kalika Prasad and Hrishikesh Mahato and Munesh Kumari},
journal= {arXiv preprint arXiv:2202.08156},
year = {2026}
}
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14pages