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

TL;DR

This paper introduces multiple new infinite classes of 0-APN power functions over finite fields, expanding the understanding of APN functions with potential cryptographic applications, and demonstrates their inequivalence to existing functions.

Contribution

The paper presents novel infinite classes of 0-APN power functions over _{2^n} using multivariate methods and resultants, showing they are CCZ-inequivalent to known functions.

Findings

New infinite classes of 0-APN power functions identified

Functions are proven CCZ-inequivalent to existing ones

Methodology involves multivariate approach and resultant elimination

Abstract

The investigation of partially APN functions has attracted a lot of research interest recently. In this paper, we present several new infinite classes of 0-APN power functions over $\mathbb{F}_{2^n}$ by using the multivariate method and resultant elimination, and show that these 0-APN power functions are CCZ-inequivalent to the known ones.