Related papers: $C$-differentials, multiplicative uniformity and (…
This paper makes the first bridge between the classical differential/boomerang uniformity and the newly introduced $c$-differential uniformity. We show that the boomerang uniformity of an odd APN function is given by the maximum of the…
Only three classes of Almost Perfect Nonlinear (for short, APN) power functions over odd characteristic finite fields have been investigated in the literature, and their differential spectra were determined. The differential uniformity of…
Permutations over $F_{2^{2k}}$ with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well…
This paper introduces {\em truncated inner $c$-differential cryptanalysis}, a technique that enables the practical application of $c$-differential uniformity to block ciphers. While Ellingsen et al. (IEEE Trans. Inf. Theory, 2020)…
Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential…
Building upon the observation that the newly defined~\cite{EFRST20} concept of $c$-differential uniformity is not invariant under EA or CCZ-equivalence~\cite{SPRS20}, we showed in~\cite{SG20} that adding some appropriate linearized…
While the classical differential uniformity ($c=1$) is invariant under the CCZ-equivalence, the newly defined \cite{EFRST20} concept of $c$-differential uniformity, in general is not invariant under EA or CCZ-equivalence, as was observed in…
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,…
Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a $4$-differential uniform permutation function. Recently, in \cite{Li19} it was shown that this swapped version of the…
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 Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall…
Differentially 4-uniform permutations on $\gf_{2^{2k}}$ with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred…
Let $\gf_{p^n}$ denote the finite field containing $p^n$ elements, where $n$ is a positive integer and $p$ is a prime. The function $f_u(x)=x^{\frac{p^n+3}{2}}+ux^2$ over $\gf_{p^n}[x]$ with $u\in\gf_{p^n}\setminus\{0,\pm1\}$ was recently…
Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes respect to differential attacks. Power functions of the form $F(x)=x^d$ with low differential uniformity have been…
We introduce a new concept, the APN-defect, which can be thought of as measuring the distance of a given function $G:\mathbb{F}_{2^n} \rightarrow \mathbb{F}_{2^n}$ to the set of almost perfect nonlinear (APN) functions. This concept is…
Permutation polynomials over finite fields are fundamental objects as they are used in various theoretical and practical applications in cryptography, coding theory, combinatorial design, and related topics. This family of polynomials…
Starting with the multiplication of elements in $\mathbb{F}_{q}^2$ which is consistent with that over $\mathbb{F}_{q^2}$, where $q$ is a prime power, via some identification of the two environments, we investigate the $c$-differential…
The study of Boolean functions with low $c$-differential uniformity has become recently an important topic of research. However, in odd characteristic case, there are not many results on the ($c$-)differential uniformity of functions that…
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…
The $c$-differential uniformity is recently proposed to reflect resistance against some variants of differential attack. Finding functions with low $c$-differential uniformity is attracting attention from many researchers. For even…