An analysis of the C class of bent functions

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Authors
Stănică, Pantelimon
Mandal, Bimal
Gangopadhyay, Sugata
Pasalic, Enes
Subjects
Boolean functions
bent functions
permutation polynomials
Advisors
Date of Issue
2015-06-14
Date
June 14, 2015
Publisher
Language
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 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.
Type
Preprint
Description
URI
https://hdl.handle.net/10945/48929
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
VSP award no. N62909-13-1-V105 (Department of the US Navy, ONR-Global)
Funding
VSP award no. N62909-13-1-V105 (Department of the US Navy, ONR-Global)
Format
20 p.
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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