a modified public key cryptography based on generalized lucas matrices

In this paper, we propose a generalized lucas matrix (a recursive matrix of higher order) obtained from the generalized fibonacci sequences. we obtain their algebraic properties such as direct inverse calculation, recursive nature, etc. then, we propose a modified public key cryptography using the generalized lucas matrices as a key element that optimizes the keyspace construction complexity. furthermore, we establish a key agreement for encryption-decryption with a combination of the terms of generalized lucas sequences under the residue operation.