Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Kölsch, Lukas"'
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
Autor:
Kölsch, Lukas
In this article, we present two new constructions for semifields of order $p^{2m}$. Together, the constructions unify and generalize around a dozen distinct semifield constructions, including both the oldest known construction by Dickson and the larg
Externí odkaz:
http://arxiv.org/abs/2405.09068
Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct irreducible polynomials of large composite degrees from irreducible po
Externí odkaz:
http://arxiv.org/abs/2402.14613
Autor:
Kölsch, Lukas
APN functions play a big role as primitives in symmetric cryptography as building blocks that yield optimal resistance to differential attacks. In this note, we consider a recent extension of a biprojective APN family by G\"olo\u{g}lu defined on $\ma
Externí odkaz:
http://arxiv.org/abs/2402.11329
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
Autor:
Kölsch, Lukas
This work presents a real-time dynamic pricing framework for future electricity markets. Deduced by first-principles analysis of physical, economic, and communication constraints within the power system, the proposed feedback control mechanism ensure
Externí odkaz:
https://library.oapen.org/handle/20.500.12657/58901
Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this end, we d
Externí odkaz:
http://arxiv.org/abs/2208.03884
Autor:
Göloğlu, Faruk, Kölsch, Lukas
We investigate the isotopy question for Taniguchi semifields. We give a complete characterization when two Taniguchi semifields are isotopic. We further give precise upper and lower bounds for the total number of non-isotopic Taniguchi semifields, pr
Externí odkaz:
http://arxiv.org/abs/2207.13497
Autor:
Göloğlu, Faruk, Kölsch, Lukas
Two important problems on almost perfect nonlinear (APN) functions are the enumeration and equivalence problems. In this paper, we solve these two problems for any biprojective APN function family by introducing a strong group theoretic method for th
Externí odkaz:
http://arxiv.org/abs/2111.04197
Autor:
Göloğlu, Faruk, Kölsch, Lukas
We show that the number of non-isotopic commutative semifields of odd order $p^{n}$ is exponential in $n$ when $n = 4t$ and $t$ is not a power of $2$. We introduce a new family of commutative semifields and a method for proving isotopy results on com
Externí odkaz:
http://arxiv.org/abs/2109.04923