Abstract. We give an efficient exhaustive search algorithm to enumerate 6×6 bijective S-boxes with the best known nonlinearity 24 in a class of S-boxes that are symmetric under the permutation τ(x) = (x_o,x_2,x_3,x_4, x_5,x_1), where x = (x_o, x_1,... ,X_5) ϵ F_2~6. Since any S-box S : F_2~6 →F_2~6 in this class has the property that S(τ(x)) = τ(S(x)) for all x, it can be considered as a construction obtained by the concatenation of 5 x 5 rotation-symmetric S-boxes (RSSBs). The size of the search space, i.e., the number of S-boxes belonging to the class, is 2~(61.28). By performing our algorithm, we find that there exist 2~(37.56) S-boxes with nonlinearity 24 and among them the number of differentially 4-uniform ones is 2~(33.99), which indicates that the concatenation method provides a rich class in terms of high nonlinearity and low differential uniformity. Moreover, we classify those S-boxes achieving the best possible trade-off between nonlinearity and differential uniformity within the class with respect to absolute indicator, algebraic degree, and transparency order.
展开▼
