# Dembowski-Ostrom polynomials and reversed Dickson polynomials

## TL;DR

This paper classifies Dembowski-Ostrom polynomials formed from reversed Dickson polynomials and monomials over finite fields, analyzing their planarity using algebraic curve point bounds, with implications for cryptography and coding theory.

## Contribution

It provides a classification of Dembowski-Ostrom polynomials from reversed Dickson polynomials and studies their planarity using a Weil bound variant.

## Key findings

- Classification of Dembowski-Ostrom polynomials achieved
- Identification of planar polynomials among them
- Applications in cryptography and coding theory discussed

## Abstract

We discuss the problem of classifying Dembowski-Ostrom polynomials from the composition of reversed Dickson polynomials of arbitrary kind and monomials over finite fields of odd characteristic. Moreover, by using a variant of the Weil bound for the number of points of affine algebraic curves over finite fields, we discuss the planarity of all such Dembowski-Ostrom polynomials. Planar Dembowski-Ostrom polynomials have applications in many areas including cryptography and coding theory.