Classification of 6 x 6 S-boxes Obtained by Concatenation of RSSBs

KAVUT S., Baloglu S.

5th International Workshop on Lightweight Cryptography for Security and Privacy (LightSec), Cappadocia, Turkey, 20 - 21 September 2016, vol.10098, pp.110-127 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 10098
  • Doi Number: 10.1007/978-3-319-55714-4_8
  • City: Cappadocia
  • Country: Turkey
  • Page Numbers: pp.110-127
  • Middle East Technical University Affiliated: Yes


We give an efficient exhaustive search algorithm to enumerate 6x6 bijective S-boxes with the best known nonlinearity 24 in a class of S-boxes that are symmetric under the permutation tau (x) = (x(0), x(2), x(3), x(4), x(5), x(1)), where x = (x(0), x(1), ... , x(5)). is an element of F-2(6). Since any S-box S : F-2(6)-> F-2(6) in this class has the property that S(tau (x)) = tau (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.