Paper 2014/801

Reversed Genetic Algorithms for Generation of Bijective S-boxes with Good Cryptographic Properties

Georgi Ivanov, Nikolay Nikolov, and Svetla Nikova

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 $(8 \times 8)$ to $(16 \times 16)$, 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.