Solving linear difference equations by means of cellular automata

Abstract

In this work, it is shown that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are binary sequences with application in cryptography. In this sense, we propose CA-based linear models that realize the solutions of difference equations as well as behave as cryptographic keystream generators. Due to the simple transition rules that govern these CA, the implementation of such models is quite easy. Some illustrative examples complete the work. © 2007 Springer-Verlag Berlin Heidelberg.