Changing almost perfect nonlinear functions on affine subspaces of small codimensions

TL;DR

This paper investigates how to modify almost perfect nonlinear (APN) functions on affine subspaces to generate new APN functions, providing criteria for such modifications and establishing inequivalence of some new functions.

Contribution

It introduces algebraic criteria for modifying APN functions on affine subspaces and demonstrates the creation of inequivalent APN functions through these modifications.

Findings

Criteria for modifications that preserve APN properties

Construction of new APN functions inequivalent to original ones

Enhanced understanding of APN function structure

Abstract

In this article, we study algebraic decompositions and secondary constructions of almost perfect nonlinear (APN) functions. In many cases, we establish precise criteria which characterize when certain modifications of a given APN function yield new ones. Furthermore, we show that some of the newly constructed functions are extended-affine inequivalent to the original ones.