Linear Cellular Automata as Discrete Models for Generating Cryptographic Sequences

Abstract

This work shows that a wide class of cryptographic sequences, the so-called interleaved sequences, can be generated by means of linear multiplicative polynomial cellular automata. In fact, this type of one-dimensional linear 90/150 cellular automata can be devised as generators of pseudo-random sequences. Moreover, these linear automata generate all the solutions of a type of difference equations with constant coefficients. Interleaved sequences are just particular solutions of such equations. In this way, linear discrete models based on cellular automata realize many popular nonlinear sequence generators of current application in stream ciphers. Thus, cryptographic sequence generators conceived and designed originally as complex nonlinear models can be easily written in terms of simple linear equivalents.