The design of Substitution Boxes (S-boxes) with good cryptographic properties represents an interesting problem. In this paper, we investigate how to evolve cellular automata (CA) rules that can be then translated into S-boxes. We first prove some upper bounds for the nonlinearity and differential uniformity of S-boxes generated by CA rules. Next, we employ a heuristic technique called Genetic Programming in order to generate CA based S-boxes with good cryptographic properties. Finally, we use the same heuristic paradigm in order to investigate whether a certain S-box is obtainable by a single CA rule.
Note: work submitted to a journal