Abstract. Often S-boxes are the only nonlinear component in a block cipher and as such play an important role in ensuring its resistance to cryptanalysis. Cryptographic properties and constructions of S-boxes have been studied for many years. The most common techniques for constructing S-boxes are: algebraic constructions, pseudo-random generation and a variety of heuristic approaches. Among the latter are the genetic algorithms. In this paper, a genetic algorithm working in a reversed way is proposed. Using the algorithm we can rapidly and repeatedly generate a large number of strong bijective S-boxes of each dimension from (8 × 8) to (16 × 16), which have sub-optimal properties close to the ones of S-boxes based on finite field inversion, but have more complex algebraic structure and possess no linear redundancy.

Some known localization results for hyperconvexity, tautness or kcompleteness of bounded domains in C n are extended to unbounded open sets in C n .

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 a reasonable search time.