Alexandr A. Polujan

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20192026

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6 papers · 1 filter

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…

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…

math.CO2019

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…

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

Vectorial Negabent Concepts: Similarities, Differences, and Generalizations

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

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