Cryptographic Properties and Applications of Bipermutive Cellular Automata


Bipermutive Cellular Automata (BCA) are defined by local rules which have a simple combinatorial characterization. It has been shown that BCA satisfy several definitions of chaotic systems (Devaney-chaos, Mixing-chaos and Expansive-chaos), and are thus of interest for cryptographic applications, in particular for pseudorandom number generation. In this talk, we consider BCA local rules with respect to their cryptographic properties, showing how their nonlinearity, resiliency and algebraic degree can be determined by studying the corresponding generating functions. We then report some results on the heuristic optimization of the cryptographic properties of BCA using various soft computing techniques. Finally, we show how the surjectivity of BCA can be employed to design a perfect and ideal secret sharing scheme, pointing out some possible future developments to improve its access structure.

Salle de ConfĂ©rence, Laboratoire d’Informatique, Signaux et Systèmes de Sophia Antipolis (I3S), France