A new public key cryptography using generalized Fibonacci matrices

Abstract

This work presents a new public key cryptography encryption-decryption scheme based on generalized Fibonacci matrices and the Hill cipher. This scheme proposes using Fibonacci sequences under prime modulo for key establishment. This scheme exchanges the key matrix X = Mθp of order p × p for encryption and decryption. As an alternative to a key matrix, our scheme only requires the exchange of a pair of numbers (p,θ), resulting in a small key space and reduced time and space complexity. We also implemented our scheme with the help of java script and established better security.

Keywords

• cryptography
• hill cipher
• fibonacci sequence
• generalized fibonacci matrices
• key exchange elgamal