Parallelizing the Weil and Tate Pairings

Abstract

In the past year, the speed record for pairing implementations on desktop-class machines has been broken several times. The speed records for asymmetric pairings were set on a single processor. In this paper, we describe our parallel implementation of the optimal ate pairing over Barreto-Naehrig (BN) curves that is about 1.23 times faster using two cores of an Intel Core i5 or Core i7 machine, and 1.45 times faster using 4 cores of the Core i7 than the state-of-the-art implementation on a single core. We instantiate Hess's general Weil pairing construction and introduce a new optimal Weil pairing tailored for parallel execution. Our experimental results suggest that the new Weil pairing is 1.25 times faster than the optimal ate pairing on 8-core extensions of the aforementioned machines. Finally, we combine previous techniques for parallelizing the eta pairing on a supersingular elliptic curve with embedding degree 4, and achieve an estimated 1.24-fold speedup on an 8-core extension of an Intel Core i7 over the previous best technique.