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An Analysis of the C Class of Bent Functions

Mandal B., Gangopadhyay S., Stănică P., Pasalic E.

Fundamenta Informaticae

2016

Vol. 146, nr 3

271--292

Two (so-called C;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 D0). In this article, we look in more detail at the C 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 class C 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.