Constructing pairing-friendly curves with variable CM discriminant

Abstract

A new algorithm is proposed for the construction of Brezing- Weng-like elliptic curves such that polynomials defining the CM discrim- inant are linear. Using this construction, new families of curves with variable discriminants and embedding degrees of k∈{8, 16, 20, 24}, which were not covered by Freeman, Scott, and Teske [9], are presented. Our result is useful for constructing elliptic curves with larger and more exible discriminants. © 2012 The Korean Mathematical Society.