On Constructing Prime Order Elliptic Curves Suitable for Pairing-Based Cryptography

Abstract

Since Boneh and Franklin implemented the Identity Based Encryption in 2001, a number of novel schemes have been proposed based on bilinear pairings, which have been widely used in the scenario of blockchain. The elliptic curves with low embedding degree and large prime-order subgroup (a.k.a pairing-friendly elliptic curves) are the basic components for such schemes, where prime order elliptic curves are most frequently used in practice. In this paper, a systematic method is utilized to find all the possible prime order families, then it is shown that all the existing constructions can be explained via our method. We further give the evidence that it’s unlikely to produce extra families.