A novel public key cryptography based on generalized Lucas matrices

TL;DR

This paper introduces a new public key cryptography scheme utilizing generalized Lucas matrices, which are linked to generalized Fibonacci sequences, offering efficient key exchange with reduced transmission overhead.

Contribution

It proposes a novel cryptographic method based on generalized Lucas matrices, enhancing security and efficiency over traditional schemes.

Findings

Reduces key transmission size by exchanging only parameters.

Provides a large key-space for enhanced security.

Demonstrates improved time and space complexity in key exchange.

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.