EA and CCZ equivalence of functions over GF(2 n )

Abstract

EA-equivalence classes and the more general CCZ-equiva- lence classes of functions over GF(2 n ) each preserve APN and AB properties desirable for S-box functions. We show that they can be related to subsets c[T] and g[T] of equivalence classes [T] of transversals, respectively, thus clarifying their relationship and providing a new approach to their study. We derive a formula which characterises when two CCZ-equivalent functions are EA-inequivalent. © 2008 Springer-Verlag Berlin Heidelberg.