Affiliations: [a] Department of Mathematics, Indian Institute of Technology Roorkee, INDIA. [email protected] | [b] Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943-5216, USA. [email protected] | [c] Department of Computer Science and Engineering, Indian Institute of Technology Roorkee, INDIA. [email protected] | [d] University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies (Famnit), SLOVENIA. [email protected]
Correspondence:
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Address for correspondence: Department of Mathematics, Indian Institute of Technology Roorkee, INDIA.
Abstract: Two (so-called ๐, 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 ๐0). In this article, we look in more detail at the ๐ class, and derive some existence and nonexistence results concerning the bent functions in the ๐ class for many of the known classes of permutations over ๐ฝ2n. Most importantly, the existence results induce generic methods of constructing bent functions in class ๐ 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.
