The optimal ate pairing over the Barreto-Naehrig curve via parallelizing elliptic nets

Abstract

In this paper, we discuss the optimal ate pairing over Barreto-Naehrig (BN) curves. First, we give an explicit formula for computing this pairing via elliptic nets associated to the twist curves. Second, we consider parallel algorithms to calculate elliptic nets for computing this pairing. Finally, we evaluate the costs of our parallel algorithms.