On the c-differential spectrum of power functions over finite fields

TL;DR

This paper explores the c-differential spectrum of power functions over finite fields, providing new properties and applying them to analyze specific functions, leading to the discovery of a new class of APcN functions.

Contribution

It introduces properties of the c-differential spectrum and applies them to analyze power functions, resulting in the identification of a new class of APcN functions.

Findings

Properties of the c-differential spectrum are established.

Analysis of specific power functions' c-differential spectra.

A new class of APcN functions is constructed.

Abstract

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 constructed. Wang et al. defined the c-differential spectrum of a power function [27]. In this paper, we present some properties of the c-differential spectrum of a power function. Then we apply these properties to investigate the c-differential spectra of some power functions. A new class of APcN function is also obtained.