A Cellular Automata Driven Image Encryption System

Efficient pseudorandom number generation is critical for a wide variety of applications in science and engineering. Stochastic optimization, Monte Carlo simulation, and modern encryption schemes are all fundamentally dependent upon reliable sources of pseudorandom data (Vattulainen). Encryption, in particular, demands the highest quality pseudorandom numbers as the encryption power of a given symmetric cryptosystem is highly dependent upon how difficult it is for current analytical methods to find structure in pseudorandom data. Further, as analytical techniques evolve, data which was previously classified as “random” becomes unusable as its underlying structure can be at least partially detected. Thus, there is an ever-evolving search for novel forms of “randomness” generation to fuel the increasing demand for faster, stronger, and more efficient cryptosystems. The aim of this thesis is to design, implement, and study a two-dimensional cellular automaton and demonstrate its potential to serve as the basis for an image specific symmetric cryptosystem. To achieve this, a totalistic cellular automaton rule derived from digital root analysis is iteratively computed on a toroidal surface. The surface is seeded with a single initial condition and the computational feedback dynamics are studied. The motivating concept is to vary the system parameters in order to push the automaton to a critical point at which a small change in the object parameter(s) will elicit a large change in the output. Such transition points are known to produce data that is highly interdependent and thus likely to be difficult to unwind via cryptanalysis. The model is written in the programming language Netlogo in order to generate testable streams of data. The focus is on demonstrating the viability of an image encryption scheme rather than on high efficiency. In practical applications, efficiency would be gained by implementation in a more basic language or possibly even an integrated circuit designed specifically for this image encryption protocol.