New cryptographic applications of boolean function equivalence classes

In this paper we investigate several issues for equivalence classes of Boolean functions which are interesting for cryptology. As well as reviewing the established concepts, we present three new applications of these ideas. Firstly we propose a novel yet natural extension to the existing transform based equivalence class distinguishing algorithm, which can provide improved performance. Secondly, making novel use of the class graph notion, we completely explain the required conditions for high nonlinearity in the concatenation construction of Boolean functions. Finally, we use the linear class graph to comment on algebraic attacks by defining all the equivalence classes possible for the important set of annihilating functions. This approach provides a new solution to the problem of finding (and avoiding) low degree annihilators.