Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves.
Pu Duan, Shi Cui, Choong Wah Chan · 2005
Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose the idea of effective polynomial families for finding the curves through different kinds of Pell equations or special forms of D(x)V 2 (x). In addition, we discover some efficient families which can be used to build pairing-friendly elliptic curves over extension fields, e.g. Fp 2 and Fp 4.