The design of S-boxes by simulated annealing

Abstract

Substitution boxes (S-boxes) are important components in many modern-day symmetric key ciphers. Their study has attracted a great deal of attention over many years. The emergence of a variety of cryptosystem attacks has shown that substitutions must be designed with great care. Some general criteria such as high non-linearity and low autocorrelation have been proposed (providing some protection against attacks such as linear cryptanalysis and differential cryptanalysis). The design of appropriate S-boxes is a difficult task: several criteria must be traded off and the design space is huge. There has been little application of evolutionary search to the development of S-boxes. In this paper we show how a cost function that has found excellent single-output Boolean functions can be generalised to provide improved results for small S-boxes.