An Update on Known Invariants of Vectorial Boolean Functions

Abstract

Almost Perfect Nonlinear functions are of great practical importance for cryptography as they provide optimum resistance to differential cryptanalysis. Due to the large number of such functions, they are classified up to CCZ-equivalence, which leaves this resistance to differential cryptanalysis invariant. Deciding the equivalence of two given functions from the definition is computationally difficult. We summarize computational results on some properties that remain invariant under CCZ-equivalence for the known APN functions, including more than 8000 new CCZ-inequivalent functions that have previously never been considered with respect to these invariants. Knowing these invariants greatly facilitates the classification of APN functions, since different values of these invariants immediately imply that two functions are CCZ-inequivalent.