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

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 $c\ne 1$ (the spectrum for $c=1$ is known).