Determinants and Permanents of Hessenberg Matrices with Perrin’s Bivariate Complex Polynomials and Its Application

Abstract

In this paper, we define some n x n Hessenberg matrices and then we obtain determinants and permanents of their matrices that give the odd and even terms of bivariate complex Perrin polynomials. Moreover, we use our results to apply the application cryptology area. We discuss the Affine-Hill method over complex numbers by improving our matrix as the key matrix and present an experimental example to show that our method can work for cryptography.