Introducing Ramanujan's Class Polynomials in the Generation of Prime Order Elliptic Curves

TL;DR

This paper introduces Ramanujan's class polynomials as a new tool for efficiently generating prime order elliptic curves via the CM-method, outperforming existing polynomial classes.

Contribution

It presents a novel application of Ramanujan class polynomials in elliptic curve construction and demonstrates their superior efficiency over traditional polynomial classes.

Findings

Ramanujan class polynomials outperform Weber and other polynomials in efficiency.

Experimental and theoretical comparisons show improved performance.

The method simplifies prime order elliptic curve generation.

Abstract

In this paper, we propose the use of Ramanujan class of polynomials for the construction of prime order elliptic curves using the CM-method. We compare (theoretically and experimentally) the efficiency of using this new class against the use of the Weber, $M_{D,l}(x)$ and $M_{D,p_1,p_2}(x)$ polynomials and show that they clearly outweigh all of them in the generation of prime order elliptic curves.