Six Subfamilies of Implementation-Friendly Barreto-Naehrig Curves

In this paper, we depict in detail six subfamilies of implementation-friendly Barreto-Naehrig (BN) elliptic curves by choosing six special congruency classes of the curve-finding search parameter. These curves have small curve constants, support efficient tower extension options of finite field required in fast pairing implementation and have obvious generators for the bilinear cycle group G1. The detailed description will supply the implementor with more choices of suitable BN curves.