Related papers: Differentially low uniform permutations from known…

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion,…

Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using…

Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that…

We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…

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 a XOR-based alternating block cipher the plaintext is masked by a sequence of layers each performing distinct actions: a highly nonlinear permutation, a linear transformation, and the bitwise key addition. When assessing resistance…

It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…

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…

Very recently, a new concept called multiplicative differential and the corresponding $c$-differential uniformity were introduced by Ellingsen et al. A function $F(x)$ over finite field $\mathrm{GF}(p^n)$ to itself is called…

A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…

Extending the notion of bounded variation, a function $u \in L_c^1(\mathbb R^n)$ is of bounded fractional variation with respect to some exponent $\alpha$ if there is a finite constant $C \geq 0$ such that the estimate \[ \biggl|\int u(x)…

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,…

$ n-$cycle permutation polynomials with small n have the advantage that their compositional inverses are efficient in terms of implementation. These permutation polynomials have significant applications in cryptography and coding theory. In…

We contruct two classes of Zalcman-type domains, on which the Bergman distance functions have certain pre-described boundary behaviors. Such examples also lead to generalizations of uniformly perfectness in the sense of Pommerenke. These…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

In the literature, there are many results about permutation polynomials over finite fields. However, very few permutations of vector spaces are constructed although it has been shown that permutations of vector spaces have many applications…

This paper introduces a compact and secure 16-bit substitution box (S-box) designed over the composite field $\F_{(((2^2)^2)^2)^2}$, optimized for both hardware efficiency and cryptographic robustness. The proposed S-box decomposes…

This paper is continuation of the study of the 1-box pattern in permutations introduced by the authors in \cite{kitrem4}. We derive a two-variable generating function for the distribution of this pattern on 132-avoiding permutations, and…

We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each…

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…