Constructing pairing-friendly elliptic curves using factorization of cyclotomic polynomials

Abstract

The problem of constructing pairing-friendly elliptic curves has received a lot of attention. To find a suitable field for the construction we propose a method to find a polynomial u(x), by the method of indeterminate coefficients, such that Φ k (u(x)) factors. We also refine the algorithm by Brezing and Weng using a factor of Φ k (u(x)). As a result, we produce new families of parameters using our algorithm for pairing-friendly elliptic curves with embedding degree 8, and we compute some explicit curves as numerical examples. © Springer-Verlag Berlin Heidelberg 2008.