Faster explicit formulae for computing pairings via elliptic nets and their parallel computation

Abstract

In this paper, we discuss computations of optimal pairings over some pairing-friendly curves and a symmetric pairing over supersingular curves via elliptic nets. We show that optimal pairings can be computed more efficiently if we use twists of elliptic curves and give formulae for computing optimal pairings via elliptic nets of these twist curves. Furthermore, we propose parallel algorithms for these pairings and estimate the costs of these algorithms in certain reasonable assumptions.