Evolving S-boxes based on cellular automata with genetic programming

Abstract

The design of cryptographically strong Substitution Boxes (S-boxes) is an interesting problem from both a cryptographic perspective as well as the combinatorial optimization one. Here we introduce the concept of evolving cellular automata rules that can be then translated into S-boxes. With it, we are able to find optimal S-boxes for sizes from $4 \times 4$ up to $7 \times 7$. As far as we know, this is the first time a heuristic approach is able to find optimal S-boxes for sizes larger than $4$.