Two Kinds of Division Polynomials For Twisted Edwards Curves

TL;DR

This paper introduces two types of division polynomials for twisted Edwards curves that precisely identify their n-torsion points and provides insights into their coefficients to facilitate computation.

Contribution

It presents two novel division polynomials for twisted Edwards curves that characterize n-torsion points and explores their coefficients for computational advantages.

Findings

Division polynomials characterize n-torsion points.

Coefficients of these polynomials can aid in computations.

Two distinct types of division polynomials are introduced.

Abstract

This paper presents two kinds of division polynomials for twisted Edwards curves. Their chief property is that they characterise the $n$-torsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation.