Related papers: Classification of $(q,q)$-biprojective APN functio…

In this paper, we establish a lower bound on the total number of inequivalent APN functions on the finite field with $2^{2m}$ elements, where $m$ is even. We obtain this result by proving that the APN functions introduced by Pott and the…

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In this paper, we study monomial GAPN functions for…

In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis.…

Recently, a new concept called multiplicative differential cryptanalysis and the corresponding $c$-differential uniformity were introduced by Ellingsen et al.~\cite{Ellingsen2020}, and then some low differential uniformity functions were…

In a prior paper [14], along with P. Ellingsen, P. Felke and A. Tkachenko, we defined a new (output) multiplicative differential, and the corresponding c-differential uniformity, which has the potential of extending differential…

Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…

In a recent work, Beierle, Brinkmann and Leander presented a recursive tree search for finding APN permutations with linear self-equivalences in small dimensions. In this paper, we describe how this search can be adapted to find many new…

APN functions play a fundamental role in cryptography against attacks on block ciphers. Several families of quadratic APN functions have been proposed in the recent years, whose construction relies on the existence of specific families of…

In this paper disprove a conjecture by Pal and Budaghyan (DCC, 2024) on the existence of a family of APN permutations, but showing that if the field's cardinality $q$ is larger than~$9587$, then those functions will never be APN. Moreover,…

We present two infinite families of APN functions where the degree of the field is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which…

In a recent paper, it is shown that functions of the form $L_1(x^3)+L_2(x^9)$, where $L_1$ and $L_2$ are linear, are a good source for construction of new infinite families of APN functions. In the present work we study necessary and…

We present an infinite family of quadratic APN functions on a finite field of dimension over GF(2) divisible by 3.

In this paper, we obtain a $(p,\nu)$-extension of the Whittaker function $M_{\kappa,\mu}(z)$ by using the extended confluent hypergeometric function of the first kind $\Phi_{p,\nu}(b;c;z)$ introduced in Parmar et al. [J. Classical Anal. 11…

We provide the necessary and sufficient conditions for a generalized Nevanlinna function $Q$ ($Q\in N_{\kappa }\left( \mathcal{H} \right)$) to be a Weyl function (also known as a Weyl-Titchmarch function). We also investigate an important…

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…

Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with…

We consider exceptional APN functions on ${\bf F}_{2^m}$, which by definition are functions that are not APN on infinitely many extensions of ${\bf F}_{2^m}$. Our main result is that polynomial functions of odd degree are not exceptional,…

In "Self-adjoint Operators as Functions I: Lattices, Galois Connections, and the Spectral Order" [arXiv:1208.4724], it was shown that self-adjoint operators affiliated with a von Neumann algebra N can equivalently be described as certain…

In this paper, two new classes of perfect nonlinear functions over $\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the…