A new application to cryptology using generalized Jacobsthal matrices, inner product and self-adjoint operator

Abstract

In this paper, we first examine the properties of the matrices of the generalized [Formula: see text]-step Jacobsthal sequence, and we develop a public key cryptosystem using key exchange based on the relationship between inner product and orthogonality. Then we create encryption and decryption algorithms using this key exchange, self-adjoint operator, and generalized [Formula: see text]-step Jacobsthal sequence, and we provide a detailed example of how encryption and decryption algorithms work. Finally, a security strength and complexity analysis of these algorithms will be made.