On constructing families of pairing-friendly elliptic curves with variable discriminant

Abstract

In [10] Freeman, Scott and Teske consider three types of families: complete, sparse and complete with variable discriminant. A general method for constructing complete families is due to Brezing and Weng. In this note we generalize this method to construct families of the latter two types. As an application, we find variable-discriminant families for a few embedding degrees, which improve the previous best ρ-values of families given in [10]. © 2011 Springer-Verlag.