Generating Pairing-Friendly Elliptic Curves Using Parameterized Families

抄録

A new method is proposed for the construction of pairing-friendly elliptic curves. For any fixed embedding degree, it can transform the problem to solving equation systems instead of exhaustive searching, thus it's more targeted and efficient. Via this method, we obtain various families including complete families, complete families with variable discriminant and sparse families. Specifically, we generate a complete family with important application prospects which has never been given before as far as we know.