Related papers: A Generalization of APN Functions for Odd Characte…
We adapt (over $\mathbb{F}_2$) the general notions of multiplicative function, Dirichlet convolution and Inverse. We get some interesting results, namely necessary conditions for an odd binary polynomial to be perfect. Note that we are…
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…
Constructing permutation polynomials over finite fields, particularly those with simple algebraic structure in multiple variables, is a fundamental problem with applications in cryptography and coding theory. Recently, Li and Kaleyski (IEEE…
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…
We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along…
We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…
Recently, the investigation of Partially APN functions has attracted a lot of attention. In this paper, with the help of resultant elimination and MAGMA, we propose several new infinite classes of 0-APN power functions over…
We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…
We determine a connection between the weight of a Boolean function and the total weight of its first-order derivatives. The relationship established is used to study some cryptographic properties of Boolean functions. We establish a…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
All almost perfect nonlinear (APN) permutations that we know to date admit a special kind of linear self-equivalence, i.e., there exists a permutation $G$ in their CCZ-equivalence class and two linear permutations $A$ and $B$, such that $G…
In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these…
In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3\in\mathbb{F}_{2^n}$ with $n=2m$ such that $f(x) = {x}^{3\cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$ is an…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite…
Recently, the Walsh spectrum and boomerang properties of special power functions have aroused widespread research interest, owing to their important applications in cryptography and information security. In particular, locally-APN functions…
We prove a necessary condition for some polynomials of Kasami degree to be APN over F_{q^n} for large n.
We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0 and -(r-1)+t<s,…