An Analysis of the π Class of Bent Functions
Bimal Mandal, Pantelimon StΔnicΔ, Sugata Gangopadhyay, Enes PaΕ‘aliΔ Β· Fundamenta Informaticae Β· 2016
Two (so-called π, D) classes of permutation-based bent Boolean functions were introduced by Carlet [4] two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass π 0 ). In this article, we look in more detail at the π class, and derive some existence and nonexistence results concerning the bent functions in the π class for many of the known classes of permutations over π½ 2 n . Most importantly, the existence results induce generic methods of constructing bent functions in class π which possibly do not belong to the completed Maiorana-McFarland class. The question whether the specific permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open.