Vectorial bent functions in odd characteristic and their components
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Date
2020
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
Bent functions in odd characteristic can be either (weakly) regular or non-weakly regular. Furthermore one can distinguish between dual-bent functions, which are bent functions for which the dual is bent as well, and non-dual bent functions. Whereas a weakly regular bent function always has a bent dual, a non-weakly regular bent function can be either dual-bent or non-dual-bent. The classical constructions (like quadratic bent functions, Maiorana-McFarland or partial spread) yield weakly regular bent functions, but meanwhile one knows constructions of infinite classes of non-weakly regular bent functions of both types, dual-bent and non-dual-bent. In this article we focus on vectorial bent functions in odd characteristic. We first show that mostp-ary bent monomials and binomials are actually vectorial constructions. In the second part we give a positive answer to the question if non-weakly regular bent functions can be components of a vectorial bent function. We present the first construction of vectorial bent functions of which the components are non-weakly regular but dual-bent, and the first construction of vectorial bent functions with non-dual-bent components.
Description
Keywords
Vectorial Bent Functions, Finite-Fields, Constructions, Bounds
Journal or Series
Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences
WoS Q Value
Q3
Scopus Q Value
Q1
Volume
12
Issue
5
