On Equivalence of Known Families of APN Functions in Small Dimensions

TL;DR

This paper computationally analyzes and catalogs CCZ-inequivalent APN functions from known families in small dimensions, aiding in the classification and comparison of these functions.

Contribution

It provides a comprehensive list of CCZ-inequivalent APN functions for dimensions 6 to 11, simplifying equivalence checking against known families.

Findings

Identified CCZ-inequivalent APN functions in small dimensions

Provided a list of functions with simplest coefficients from each class

Facilitated easier CCZ-equivalence testing for future research

Abstract

In this extended abstract, we computationally check and list the CCZ-inequivalent APN functions from infinite families on $\mathbb{F}_2^n$ for n from 6 to 11. These functions are selected with simplest coefficients from CCZ-inequivalent classes. This work can simplify checking CCZ-equivalence between any APN function and infinite APN families.