Cryptographically Strong S-Boxes Generated by Modified Immune Algorithm

S-boxes play an important role in ensuring the resistance of block ciphers against cryptanalysis as often they are their only nonlinear components. The cryptographic properties of S-boxes and a variety of constructions have been studied extensively over the past years. Techniques for S-box generation include algebraic constructions, pseudo-random generation and heuristic approaches. The family of artificial immune algorithms is a particular example of a heuristic approach. In this paper we propose an S-box generation technique using a special kind of artificial immune algorithm, namely the clonal selection algorithm, combined with a slightly modified hill climbing method for S-boxes. Using this special algorithm we generate large sets of highly nonlinear bijective S-boxes of low differential uniformity in very reasonable search time.