Some More Functions That Are Not APN Infinitely Often. The Case of Kasami exponents

TL;DR

This paper establishes a necessary condition for certain Kasami degree polynomials to be APN over large finite fields, advancing understanding of their cryptographic properties.

Contribution

It introduces a new necessary condition for Kasami degree polynomials to be APN, expanding theoretical knowledge in finite field cryptography.

Findings

Identifies a necessary condition for APN property in Kasami degree polynomials

Provides theoretical insights into the behavior of these polynomials over large fields

Enhances criteria for cryptographic function analysis

Abstract

We prove a necessary condition for some polynomials of Kasami degree to be APN over F_{q^n} for large n.