Several classes of 0-APN power functions over $\mathbb{F}_{2^n}$

TL;DR

This paper introduces new infinite classes of 0-APN power functions over finite fields, expanding understanding of their structure and inequivalence to known functions, with computational verification for small cases.

Contribution

It proposes several new infinite classes of 0-APN power functions over finite fields, demonstrating their inequivalence to known functions and explaining previously unexplained exponents.

Findings

New infinite classes of 0-APN power functions identified.

These functions are CCZ-inequivalent to existing known functions.

Computational verification for small field sizes confirms the results.

Abstract

Recently, the investigation of Partially APN functions has attracted a lot of attention. In this paper, with the help of resultant elimination and MAGMA, we propose several new infinite classes of 0-APN power functions over $\mathbb{F}_{2^{n}}$. By the main result in [4], these $0$-APN power functions are CCZ-inequivalent to the known ones. Moreover, these infinite classes of 0-APN power functions can explain some exponents for $1\leq n\leq11$ which are not yet ``explained" in the tables of Budaghyan et al. [3].