Related papers: Non-Boolean almost perfect nonlinear functions on …
Perfect nonlinear functions from a finite group $G$ to another one $H$ are those functions $f: G \rightarrow H$ such that for all nonzero $\alpha \in G$, the derivative $d_{\alpha}f: x \mapsto f(\alpha x) f(x)^{-1}$ is balanced. In the case…
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…
In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a…
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…
A new almost perfect nonlinear function (APN) on the finite field GF(2^10) which is not equivalent to any of the previously known APN mappings is constructed. This is the first example of an APN mapping which is not equivalent to a power…
Let $G$, $H$ be finite groups and let $X$ be a finite $G$-set. $G$-perfect nonlinear functions from $X$ to $H$ have been studied in several papers. They have more interesting properties than perfect nonlinear functions from $G$ itself to…
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…
Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on. However APN…
The vectorial Boolean functions are employed in cryptography to build block coding algorithms. An important criterion on these functions is their resistance to the differential cryptanalysis. Nyberg defined the notion of almost perfect…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
We give a large family of almost perfect nonlinear (APN) permutations of finite vector spaces of every odd dimension divisible by three. We also give APN functions that are not bijective on even dimensions and related highly nonlinear…
In this paper we explore a connection between certain Almost Perfect Nonlinear Functions (APN functions) and relative difference sets. In particular, we show that the image set of certain 2-to-1 APN functions is a relative difference set.…
It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the…
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 associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
The main purpose of this paper is to describe the abelian part $\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the characteristic $p$ of $K$ and the non $p$-part of…
In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.
The target of this article is to discuss the concept of \textit{commuting probability} of finite groups which, in short, is a probabilistic measure of how abelian our group is. We shall compute the value of commuting probability for many…
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…
A set of quasi-uniform random variables $X_1,...,X_n$ may be generated from a finite group $G$ and $n$ of its subgroups, with the corresponding entropic vector depending on the subgroup structure of $G$. It is known that the set of entropic…