A Note on Rotation Symmetric S-boxes

Abstract

This paper is twofold. The first is devoted to study a class of quadratic rotation symmetric S-boxes (RSSBs) which was presented by Gao G, et al., Constructions of quadratic and cubic rotation symmetric bent functions, IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4908–4913, 2012, by decomposing a class of cubic rotation symmetric bent functions. The authors obtain its nonlinearity and differential uniformity of such class of S-boxes. In particular, the compositional inversion of the class of rotation symmetric S-boxes is also presented. Then the authors introduce a steepest-descent-like search algorithm for the generation of RSSBs. The algorithm finds 5,6,7,8-bit RSSBs with very good cryptographic properties which can be applied in designing cryptographical algorithms.