Paper 2020/1609
A new method for secondary constructions of vectorial bent functions
Amar Bapić and 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, EAinequivalent 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.
Metadata
 Available format(s)
 Publication info
 Preprint. MINOR revision.
 Keywords
 Bent functionsVectorial bent functionsAlgebraic degreeEA equivalenceCCZ equivalenceMaximal number of bent components
 Contact author(s)
 amar bapic @ famnit upr si
 History
 20201227: received
 Short URL
 https://ia.cr/2020/1609
 License

CC BY
BibTeX
@misc{cryptoeprint:2020/1609, author = {Amar Bapić and Enes Pasalic}, title = {A new method for secondary constructions of vectorial bent functions}, howpublished = {Cryptology ePrint Archive, Paper 2020/1609}, year = {2020}, note = {\url{https://eprint.iacr.org/2020/1609}}, url = {https://eprint.iacr.org/2020/1609} }