An Analysis of the 𝒞 Class of Bent Functions

Abstract

Two (so-called C;D) classes of permutation-based bent Boolean functions were introduced by Carlet two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass D0). In this article, we look in more detail at theC class, and derive some existence and nonexistence results concerning the bent functions in the C class for many of the known classes of permutations over F2n. Most importantly, the existence results induce generic methods of constructing bent functions in classC which possibly do not belong to the completed Maiorana-McFarland class. The question whether the specic permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open.