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In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities…
Let $q$ be an odd prime power with $q\equiv 3\ ({\rm{mod}}\ 4)$. In this paper, we study the differential and boomerang properties of the function $F_{2,u}(x)=x^2\big(1+u\eta(x)\big)$ over $\mathbb{F}_{q}$, where $u\in\mathbb{F}_{q}^*$ and…
In this paper, we explicitly construct a large class of symmetric Boolean functions on $2k$ variables with algebraic immunity not less than $d$, where integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary…
It was shown by Boukerrou et al.~[IACR Trans. Symmetric Cryptol. 1 (2020), 331--362] that the $F$-boomerang uniformity (which is the same as the second-order zero differential uniformity in even characteristic) of perfect nonlinear…
This paper deals with Niho functions which are one of the most important classes of functions thanks to their close connections with a wide variety of objects from mathematics, such as spreads and oval polynomials or from applied areas,…
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second…
We investigate the existence of Boolean degree $d$ functions on the Grassmann graph of $k$-spaces in the vector space $\mathbb{F}_q^n$. For $d=1$ several non-existence and classification results are known, and no non-trivial examples are…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
We give some classes of power maps with low $c$-differential uniformity over finite fields of odd characteristic, {for $c=-1$}. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect $c$-nonlinear…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
The notion of $c$-differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect $c$-nonlinear functions in terms of difference sets in some quasigroups was…
We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…
Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their varied applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear…
The Feistel Boomerang Connectivity Table ($\rm{FBCT}$), which is the Feistel version of the Boomerang Connectivity Table ($\rm{BCT}$), plays a vital role in analyzing block ciphers' ability to withstand strong attacks, such as boomerang…
In this paper, we prove that nonnegative polyharmonic functions on the upper half space satisfying a conformally invariant nonlinear boundary condition have to be the "\emph{polynomials} plus \emph{bubbles}" form. The nonlinear problem is…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as, e.g., BD- or CD-regularity. For certain composite-type…
A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be…
Algebraic immunity of Boolean function $f$ is defined as the minimal degree of a nonzero $g$ such that $fg=0$ or $(f+1)g=0$. Given a positive even integer $n$, it is found that the weight distribution of any $n$-variable symmetric Boolean…
We show that certain determinantal functions of multiple matrices, when summed over the symmetries of the cube, decompose into functions of the original matrices. These are shown to be true in complete generality; that is, no properties of…