Welcome to the resource topic for 2020/1609
Title:
A new method for secondary constructions of vectorial bent functions
Authors: Amar Bapić, Enes Pasalic
Abstract:In 2017, Tang et al. have introduced a generic construction for bent functions of the form f(x)=g(x)+h(x), where g is a bent function satisfying some conditions and h is a Boolean function. Recently, Zheng et al. generalized this result to construct large classes of bent vectorial Boolean function from known ones in the form F(x)=G(x)+h(X), where G is a bent vectorial and h a Boolean function. In this paper we further generalize this construction to obtain vectorial bent functions of the form F(x)=G(x)+\mathbf{H}(X), where \mathbf{H} is also a vectorial Boolean function. This allows us to construct new infinite families of vectorial bent functions, EA-inequivalent to G, which was used in the construction. Most notably, specifying \mathbf{H } (x)=\mathbf{h} (Tr_1^n(u_1x),\ldots,Tr_1^n(u_tx)), the function \mathbf{h} :\mathbb{F}_2^t \rightarrow \mathbb{F}_{2^t} can be chosen arbitrary which gives a relatively large class of different functions for a fixed function G. We also propose a method of constructing vectorial (n,n)-functions having maximal number of bent components.
ePrint: https://eprint.iacr.org/2020/1609
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