# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1812.03594