Bent functions

Constructions of (vectorial) bent functions outside the completed Maiorana–McFarland class

Two new classes of bent functions derived from the Maiorana–McFarland ($\\mathcal{M}$) class, so-called $\\mathcal{C}$ and $\\mathcal{D}$, were introduced by Carlet (1993) almost three decades ago. In Zhang (2020) sufficient conditions for specifying …

Two secondary constructions of bent functions without initial conditions

In this article, we propose two secondary constructions of bent functions without any conditions on initial bent functions employed by these methods. It is shown that both methods generate bent functions that belong to the generalized …

Permutations without linear structures inducing bent functions outside the completed Maiorana-McFarland class

Recently, the construction of bent functions that belong to the so-called $\\mathcal{C}$ class and are provably outside the completed Maiorana-McFarland ($\\mathcal{M}$) class, introduced by Carlet almost three decades ago, has been addressed in …

A new method for secondary constructions of vectorial bent functions

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. (Discret Math 344:112473, 2021) …

Constructions of balanced Boolean functions on even number of variables with maximum absolute value in autocorrelation spectra $<2^{{n/2}^{\star}}$

The autocorrelation properties of Boolean functions are closely related to the Shannon’s concept of diffusion and can be accompanied with other cryptographic criteria (such as high nonlinearity and algebraic degree) for ensuring an overall robustness …

Vectorial bent functions weakly/strongly outside the completed Maiorana–McFarland class

Two new classes of bent functions derived from the Maiorana–McFarland ($\\mathcal{M}$) class, so-called $\\mathcal{C}$ and $\\mathcal{D}$, were introduced by Carlet (1994) two decades ago. The difficulty of satisfying their defining conditions was …

Characterization of Basic 5-Value Spectrum Functions Through Walsh-Hadamard Transform

The first and the third authors recently introduced a spectral construction of plateaued and of 5-value spectrum functions. In particular, the design of the latter class requires a specification of integers $\\{W(u)\\colon u \\in {F}_2^n\\}$, where …