MNT Elliptic Curves with Non-Prime Order

TL;DR

This paper introduces a method for generating generalized MNT elliptic curves with non-prime order, expanding on previous work that focused on prime order curves, thus broadening the applicability of pairing-friendly elliptic curves.

Contribution

It presents a novel approach for constructing pairing-friendly elliptic curves whose order is the product of two primes, extending the existing MNT curve generation methods.

Findings

New method for generating generalized MNT curves

Curves with non-prime order constructed successfully

Potential applications in cryptography enhanced

Abstract

Miyaji, Nakabayashi, and Takano proposed the algorithm for the construction of prime order pairing-friendly elliptic curves with embedding degrees $k=3,4,6$. We present a method for generating generalized MNT curves. The order of such pairing-friendly curves is the product of two prime numbers.