The $c$-differential spectrum of $x\mapsto x^{\frac{p^n+1}{2}}$ in finite fields of odd characteristics

TL;DR

This paper analyzes the $c$-differential spectrum of a specific power map over finite fields of odd characteristic, providing detailed results for all $c eq 1$ using combinatorial and number theory methods.

Contribution

It computes the detailed $c$-differential spectrum of the map $x o x^{(p^n+1)/2}$ over finite fields for all $c eq 1$, extending known results.

Findings

Explicit $c$-differential spectrum for the map in finite fields

New combinatorial and number theory techniques applied

Complete characterization for all $c eq 1$

Abstract

In the paper, we concentrate on the map $x\mapsto x^{\frac{p^n+1}{2}}$ on $\mathbb{F}_{p^n}$ and using combinatorial and number theory techniques, we compute its detailed $c$-differential spectrum for all values of $c\neq 1$ (the spectrum for $c=1$ is known).