On the semantic security of cellular automata based pseudo-random permutation using results from the Luby-Rackoff construction

This paper proposes a semantically secure construction of pseudo-random permutations using second-order reversible cellular automata. We show that the proposed construction is equivalent to the Luby- Racko model if it is built using non-uniform transition rules, and we prove that the construction is strongly secure if an adequate number of iterations is performed. Moreover, a corresponding symmetric block cipher is constructed and analysed experimentally in comparison with popular ciphers. Obtained results approve robustness and ecacy of the construction, while achieved performances overcome those of some existing block ciphers.