New Perfect Nonlinear Functions over Finite Fields

TL;DR

This paper introduces a new class of perfect nonlinear functions over finite fields, expanding the known functions and demonstrating their inequivalence to existing ones, which has implications for cryptography.

Contribution

The paper presents a novel class of perfect nonlinear functions over finite fields and proves their inequivalence to all previously known functions.

Findings

New perfect nonlinear functions over $ ext{F}_{p^{2k}}$ for odd primes p

Proof that these functions are CCZ-inequivalent to existing ones

Advances understanding of nonlinear functions in finite field cryptography

Abstract

In this paper we present a new class of perfect nonlinear %Dembowski-Ostrom polynomials over $\mathbb{F}_{p^{2k}}$ for any odd prime $p$. In addition, we show that the new perfect nonlinear functions are CCZ-inequivalent to all the previously known perfect nonlinear functions in general.