Alexandr A. Polujan

activity

20192026

most citedCubic bent functions outside the completed Maiorana-McFarland class

26 citations · 34 across the 12 of their papers we have counts for

collaborators

13 papers

math.HO2026

Bent Functions and the Completed Maiorana-McFarland Class

Enes Pasalic, Alexandr Polujan, Fengrong Zhang +1

In this article, we survey some fundamental results and recent advances in the design and analysis of Boolean bent functions from the perspective of their relation to the completed…

cs.NE2025

On Counts and Densities of Homogeneous Bent Functions: An Evolutionary Approach

Claude Carlet, Marko Ðurasevic, Domagoj Jakobovic +3

Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions…

math.CO2025

Permutations satisfying $(P_{1})$ and $(P_{2})$ properties and $ℓ$ -optimal bent functions

Sadmir Kudin, Enes Pasalic, Alexandr Polujan +1

An important classification of permutations over $F_{2}^{m}$ , suitable for constructing Maiorana-McFarland bent functions on $F_{2}^{m} \times F_{2}^{m}$ with the un…

math.CO2025

Almost Maiorana-McFarland bent functions

Sadmir Kudin, Enes Pasalic, Alexandr Polujan +2

In this article, we study bent functions on $F_{2}^{2 m}$ of the form $f (x, y) = x \cdot ϕ (y) + h (y)$ , where $x \in F_{2}^{m - 1}$ and $y \in F_{2}^{m + 1}$ , which…

math.CO2025

Changing almost perfect nonlinear functions on affine subspaces of small codimensions

Hiroaki Taniguchi, Alexandr Polujan, Alexander Pott +1

In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which chara…

cs.IT2024

When does a bent concatenation not belong to the completed Maiorana-McFarland class?

Sadmir Kudin, Enes Pasalic, Alexandr Polujan +1

Every Boolean bent function $f$ can be written either as a concatenation $f = f_{1} ∣∣ f_{2}$ of two complementary semi-bent functions $f_{1}, f_{2}$ ; or as a concatenation $f=f_1||f_2||f_3||f_…

math.CO2024★ 1 cited

Vectorial Negabent Concepts: Similarities, Differences, and Generalizations

Nurdagül Anbar, Sadmir Kudin, Wilfried Meidl +2

In Pasalic et al., IEEE Trans. Inform. Theory 69 (2023), 2702--2712, and in Anbar, Meidl, Cryptogr. Commun. 10 (2018), 235--249, two different vectorial negabent and vectorial bent…

math.CO2023

Bent functions satisfying the dual bent condition and permutations with the $(A_{m})$ property

Alexandr Polujan, Enes Pasalic, Sadmir Kudin +1

The concatenation of four Boolean bent functions $f = f_{1} ∣∣ f_{2} ∣∣ f_{3} ∣∣ f_{4}$ is bent if and only if the dual bent condition $f_{1}^{*} + f_{2}^{*} + f_{3}^{*} + f_{4}^{*} = 1$ is satisfied. However, to…

cs.IT2023

Design and analysis of bent functions using $M$ -subspaces

Enes Pasalic, Alexandr Polujan, Sadmir Kudin +1

In this article, we provide the first systematic analysis of bent functions $f$ on $F_{2}^{n}$ in the Maiorana-McFarland class $MM$ regarding the origin and cardin…

cs.IT2020

Linear codes and incidence structures of bent functions and their generalizations

Wilfried Meidl, Alexandr A. Polujan, Alexander Pott

In this paper we consider further applications of $(n, m)$ -functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson the…

cs.IT2020

Vanishing Flats: A Combinatorial Viewpoint on the Planarity of Functions and Their Application

Shuxing Li, Wilfried Meidl, Alexandr Polujan +3

For a function $f$ from $F_{2}^{n}$ to $F_{2}^{n}$ , the planarity of $f$ is usually measured by its differential uniformity and differential spectrum. In this paper, we p…

cs.IT2020★ 7 cited

On design-theoretic aspects of Boolean and vectorial bent functions

Alexandr Polujan, Alexander Pott

There are two construction methods of designs from $(n, m)$ -bent functions, known as translation and addition designs. In this paper we analyze, which equivalence relation for Boole…

math.CO2019★ 26 cited

Cubic bent functions outside the completed Maiorana-McFarland class

Alexandr Polujan, Alexander Pott

In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ vari…

Bent Functions and the Completed Maiorana-McFarland Class

On Counts and Densities of Homogeneous Bent Functions: An Evolutionary Approach

Permutations satisfying (P1​) and (P2​) properties and ℓ-optimal bent functions

Almost Maiorana-McFarland bent functions

Changing almost perfect nonlinear functions on affine subspaces of small codimensions

When does a bent concatenation not belong to the completed Maiorana-McFarland class?

Vectorial Negabent Concepts: Similarities, Differences, and Generalizations

Bent functions satisfying the dual bent condition and permutations with the (Am​) property

Design and analysis of bent functions using M-subspaces

Linear codes and incidence structures of bent functions and their generalizations

Vanishing Flats: A Combinatorial Viewpoint on the Planarity of Functions and Their Application

On design-theoretic aspects of Boolean and vectorial bent functions

Cubic bent functions outside the completed Maiorana-McFarland class

Permutations satisfying $(P_{1})$ and $(P_{2})$ properties and $ℓ$ -optimal bent functions

Bent functions satisfying the dual bent condition and permutations with the $(A_{m})$ property

Design and analysis of bent functions using $M$ -subspaces