On the construction of irreducible polynomials over finite fields via prime degree endomorphisms of elliptic curves

TL;DR

This paper introduces a method to construct irreducible polynomials over finite fields using endomorphisms of elliptic curves of prime degree, providing a new algebraic approach.

Contribution

It presents an iterative construction technique leveraging elliptic curve endomorphisms of prime degree to generate irreducible polynomials over finite fields.

Findings

New algebraic method for polynomial construction

Utilizes endomorphisms of elliptic curves of prime degree

Potential applications in coding theory and cryptography

Abstract

In this paper we present an iterative construction of irreducible polynomials over finite fields based upon repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.