Binary Synchronization of Complex Dynamics in Cellular Automata and its Applications in Compressed Sensing and Cryptography

Abstract

Complex dynamics of the type used in random number generators may emerge in elementary cellular automata with properly designed structures and cells. This chapter reviews recent results in quantifying the complexity of the dynamics in cellular automata with an emphasis on the recently discovered phenomenon called binary synchronization. It allows that two cellular automata systems with the same structure will synchronize (the receiver will duplicate the n-dimensional state vector of the transmitter) receiving only a single bit stream, produced by the output of a single cell of the transmitter cellular automaton. The decoding of this stream is possible only when the structure of the cellular automata (encryption key) is known. It is shown how the key space may be increased using various methods (e.g. using hybrid models or perturbing the cellular network model into a small-worlds model). Applications in cryptography, spread spectrum communications, and compressed sensing are reviewed. Some particularities for the implementation of such cellular automata systems in FPGA technologies are provided.