相关论文: Two Classes of Power Mappings with Boomerang Unifo…

We consider the boomerang uniformity of an infinite class of (locally-APN) power maps and show that its boomerang uniformity over the finite field $\F_{2^n}$ is $2$ and $4$, when $n \equiv 0 \pmod 4$ and $n \equiv 2 \pmod 4$, respectively.…

In this paper, we study the boomerang spectrum of the power mapping $F(x)=x^{k(q-1)}$ over ${\mathbb F}_{q^2}$, where $q=p^m$, $p$ is a prime, $m$ is a positive integer and $\gcd(k,q+1)=1$. We first determine the differential spectrum of…

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…

Recently, several studies have shown that when $q\equiv3\pmod{4}$, for certain choices of $r$, the function $F_r(x)=x^r+x^{r+\frac{q-1}{2}}$ defined over $\Fq$ is locally-APN and has boomerang uniformity at most~$2$. In this paper, we…

In this paper, we investigate the differential and boomerang properties of a class of binomial $F_{r,u}(x) = x^r(1 + u\chi(x))$ over the finite field $\mathbb{F}_{p^n}$, where $r = \frac{p^n+1}{4}$, $p^n \equiv 3 \pmod{4}$, and $\chi(x) =…

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…

We discuss the second-order differential uniformity of vectorial Boolean functions. The closely related notion of second-order zero differential uniformity has recently been studied in connection to resistance to the boomerang attack. We…

Let $f(x)=x^{s(p^m-1)}$ be a power mapping over $\mathbb{F}_{p^n}$, where $n=2m$ and $\gcd(s,p^m+1)=t$. In \cite{kpm-1}, Hu et al. determined the differential spectrum and boomerang spectrum of the power function $f$, where $t=1$. So what…

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…

In this paper, for an odd prime $p$, the differential spectrum of the power function $x^{\frac{p^k+1}{2}}$ in $\mathbb{F}_{p^n}$ is calculated. For an odd prime $p$ such that $p\equiv 3\bmod 4$ and odd $n$ with $k|n$, the differential…

Recent studies on binomials of the form $F_r(x) = x^r(1 + \chi(x))$ over $\mathbb{F}_{p^n}$ have shown that these functions can exhibit very low boomerang uniformity. In this paper, we focus on the specific behavior of such binomials in…

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…

In this paper, we present infinite families of permutations of $\mathbb{F}_{2^{2n}}$ with high nonlinearity and boomerang uniformity $4$ from generalized butterfly structures. Both open and closed butterfly structures are considered. It…

Let $\mathbb{F}_q$ be a finite field, and let $F \in \mathbb{F}_q [X]$ be a polynomial with $d = \text{deg} \left( F \right)$ such that $\gcd \left( d, q \right) = 1$. In this paper we prove that the $c$-Boomerang uniformity, $c \neq 0$, of…

Feistel Boomerang Connectivity Table (FBCT) is an important cryptanalytic technique on analysing the resistance of the Feistel network-based ciphers to power attacks such as differential and boomerang attacks. Moreover, the coefficients of…

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…

We study a class of general quadrinomials over the field of size $2^{2m}$ with odd $m$ and characterize conditions under which they are permutations with the best boomerang uniformity, a new and important parameter related to…

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…

We investigate mappings $F = (f_1, f_2) \colon \mathbb{R}^2 \to \mathbb{R}^2 $ where $ f_1, f_2 $ are bivariate normal densities from the perspective of singularity theory of mappings, motivated by the need to understand properties of…

The Feistel Boomerang Connectivity Table (FBCT) was proposed as the feistel counterpart of the Boomerang Connectivity Table. The entries of the FBCT are actually related to the second-order zero differential spectrum. Recently, several…