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 …

The differential spectrum of a cryptographic function is of significant interest for estimating
the resistance of the involved vectorial function to some variances of differential …

In this paper, we investigate the power functions $ F (x)= x^ d $ over the finite field $\mathbb
{F} _ {2^{4n}} $, where $ n $ is a positive integer and $ d= 2^{3n}+ 2^{2n}+ 2^{n}-1$. It is …

Recently, a new concept called multiplicative differential was introduced by Ellingsen et al.
Inspired by this pioneering work, power functions with low c-differential uniformity were …

Motivated by a recent work of Zhang and Yan on the $ c $-differential spectrum of some
power functions over finite fields, we further study an AP $ c $ N function and express its $ c …

In this paper, we give some new low differential uniformity of some power functions defined
on finite fields with odd characteristic. As corollaries of the uniformity, we obtain two families …

Permutation polynomials over finite fields are fundamental objects as they are used in
various theoretical and practical applications in cryptography, coding theory, combinatorial …

Very recently, a new concept called multiplicative differential and the corresponding c-
differential uniformity were introduced by Ellingsen et al.(IEEE Trans. Inform. Theory 66 (9) …

Abstract Let F (x)= x 2 2 k+ 2 k+ 1 be a power function over the finite field GF (2 n), where k is
a positive integer and n= 4 k. It is known by a recent result of Bracken and Leander that F (x) …

Let $ F $ be a finite field, let $ f $ be a function from $ F $ to $ F $, and let $ a $ be a nonzero
element of $ F $. The discrete derivative of $ f $ in direction $ a $ is $\Delta_a f\colon F\to F …