Reversibility of a Family of 2D Cellular Automata Hybridized by Diamond and Cross Rules Over Finite Fields and an Application to Visual Cryptography

Abstract

This article studies the behavior of Iwo-dimensional finite cellular automata defined by two special family of rules under null boundary condition. The rule matrices of these families of two-dimensional hybrid cellular automata composed by diamond and cross rules respectively over the finite field F-p(p prime) are established. Further, explicit formulae that gives the rank of these rule matrices are provided. Hence, we are able to determine the reversibility of these cellular automata. Finally, we conclude by presenting an application of this family to pseudo random number generators applied to visual cryptography.