Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Polujan, Alexandr"'
Autor:
Kölsch, Lukas, Polujan, Alexandr
We study combinatorial properties of plateaued functions. All quadratic functions, bent functions and most known APN functions are plateaued, so many cryptographic primitives rely on plateaued functions as building blocks. The main focus of our study
Externí odkaz:
http://arxiv.org/abs/2410.00611
In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of Boolean spac
Externí odkaz:
http://arxiv.org/abs/2407.14038
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 $f=f_1||f_2||f_3||f_4$ of four Boolean functions $f_1,f_2,f_3,f_4$, all of which are simul
Externí odkaz:
http://arxiv.org/abs/2404.16220
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-negabent concepts are introduced, which leads to seemingly contradict
Externí odkaz:
http://arxiv.org/abs/2402.05677
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 specify four bent functions satisfying this duality condition is in ge
Externí odkaz:
http://arxiv.org/abs/2310.10162
In this article, we provide the first systematic analysis of bent functions $f$ on $\mathbb{F}_2^{n}$ in the Maiorana-McFarland class $\mathcal{MM}$ regarding the origin and cardinality of their $\mathcal{M}$-subspaces, i.e., vector subspaces on whic
Externí odkaz:
http://arxiv.org/abs/2304.13432
Autor:
Kölsch, Lukas, Polujan, Alexandr
Publikováno v:
K\"olsch, L., Polujan, A. Value Distributions of Perfect Nonlinear Functions. Combinatorica (2023)
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions in the mos
Externí odkaz:
http://arxiv.org/abs/2302.03121
Publikováno v:
Discrete Mathematics, Volume 346, Issue 1, January 2023, 113157
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 theorem, by showing that linear codes of APN functions with the classical
Externí odkaz:
http://arxiv.org/abs/2012.06866
Autor:
Li, Shuxing, Meidl, Wilfried, Polujan, Alexandr, Pott, Alexander, Riera, Constanza, Stănică, Pantelimon
For a function $f$ from $\mathbb{F}_2^n$ to $\mathbb{F}_2^n$, the planarity of $f$ is usually measured by its differential uniformity and differential spectrum. In this paper, we propose the concept of vanishing flats, which supplies a combinatorial
Externí odkaz:
http://arxiv.org/abs/2006.01941
Autor:
Polujan, Alexandr, Pott, Alexander
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 Boolean bent functions, i.e. $(n,1)$-bent functions, and vectorial bent fun
Externí odkaz:
http://arxiv.org/abs/2003.12308