Related papers: $C$-differentials, multiplicative uniformity and (…

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially-4 uniform function called…

Functions with low $c$-differential uniformity were proposed in $2020$ and attracted lots of attention, especially the P$c$N and AP$c$N functions, due to their applications in cryptography. The objective of this paper is to study P$c$N and…

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…

Here, we give a complete description of the c-Boomerang Connectivity Table for the Gold function over finite fields of even characteristic, by using double Weil sums. In the process we generalize a result of Boura and Canteaut (IACR Trans.…

Boolean functions with good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. In this paper, we propose a large class of weightwise perfectly…

We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform…

Conformal Test Martingales (CTMs) are a standard method within the Conformal Prediction framework for testing the crucial assumption of data exchangeability by monitoring deviations from uniformity in the p-value sequence. Although…

We study the characteristic polynomial of random permutation matrices following some measures which are invariant by conjugation, including Ewens' measures which are one-parameter deformations of the uniform distribution on the permutation…

In this paper, we present several new constructions of differentially 4-uniform permutations over $\F_{2^{2m}}$ by modifying the values of the inverse function on some subsets of $\F_{2^{2m}}$. The resulted differentially 4-uniform…

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…

Let ${\mathcal P}_k$ denote the set of all algebraic polynomials of degree at most $k$ with real coefficients. Let ${\mathcal P}_{n,k}$ be the set of all algebraic polynomials of degree at most $n+k$ having exactly $n+1$ zeros at $0$. Let…

A unitary divisor $c$ of a positive integer $n$ is a positive divisor of $n$ that is relatively prime to $\displaystyle{\frac{n}{c}}$. For any integer $k$, the function $\sigma_k^*$ is a multiplicative arithmetic function defined so that…

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…

Let $\mathbb{F}_q$ be a finite field of characteristic $p$. In this paper we prove that the $c$-Boomerang Uniformity, $c \neq 0$, for all permutation monomials $x^d$, where $d > 1$ and $p \nmid d$, is bounded by $d^2$. Further, we utilize…

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…

Maximum nonlinear functions on finite fields are widely used in cryptography because the coordinate functions have large distance to linear functions. More precisely, the Hamming distance to the characteristic functions of hyperplanes is…

In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function…

For any complex number $c$, let $\sigma_c\colon\mathbb N\rightarrow\mathbb C$ denote the divisor function defined by $\sigma_c(n)=\displaystyle{\sum_{d|n}d^c}$ for all $n\in\mathbb N$, and define $R(c)=\{\sigma_c(n)\in\mathbb C\colon…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

We develop criteria to guarantee uniqueness of the C$^*$-norm on a *-algebra $\mathcal{B}$. Nontrivial examples are provided by the noncommutative algebras of $\mathcal{C}$-valued functions $\mathcal{S}_J^\mathcal{C}(\mathbb{R}^n)$ and…