High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves

Abstract

This paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto-Naehrig elliptic curve. Our library is able to compute the optimal ate pairing over a 254-bit prime field double-struck F signp, in just 2.33 million of clock cycles on a single core of an Intel Core i7 2.8GHz processor, which implies that the pairing computation takes 0.832msec. We are able to achieve this performance by a careful implementation of the base field arithmetic through the usage of the customary Montgomery multiplier for prime fields. The prime field is constructed via the Barreto-Naehrig polynomial parametrization of the prime p given as, p=36t4+36t3+24t2+6t+1, with t=2 62-254+244. This selection of t allows us to obtain important savings for both the Miller loop as well as the final exponentiation steps of the optimal ate pairing. © 2010 Springer-Verlag Berlin Heidelberg.