Sadmir Kudin

University of Primorska | UP · Department of Applied Natural Sciences

Recently, the construction of bent functions that belong to the so-called \(\mathcal {C}\) class and are provably outside the completed Maiorana-McFarland (\({\mathscr{M}}\)) class, introduced by Carlet almost three decades ago, has been addressed in several works. The main method for proving the class membership is based on a sufficient (but not n...

Two new classes of bent functions derived from the Maiorana–McFarland (M) class, so-called C and D, were introduced by Carlet (1994) two decades ago. The difficulty of satisfying their defining conditions was emphasized in Mandal et al. (2016). In a recent work Zhang et al. (2017) a set of efficient sufficient conditions for specifying bent functio...

For a function f:{−1,1}n→{−1,1} the relationship between the sum of its linear Fourier coefficients f̂(i) (defined by f̂(i)≔12n∑x∈{−1,1}nf(x)xi for i=1,2,…,n and x=(x1,…,xn)) and its degree d is a problem in theoretical computer science related to social choice. In that regard, in 2012, O’Donnell conjectured that ∑i=1nf̂(i)≤dd−1⌊d−12⌋21−d. In 2020,...

Correlation immunity (CI) of Boolean functions is an important concept relevant both in the design of nonlinear combiners and for the protection against side-channel cryptanalysis to name a few applications. In this article we give further simplification of the proofs of some known characterizations of these functions, including some new results re...