GPU-Based Implementation of 128-Bit Secure Eta Pairing over a Binary Field

Abstract

Abstract. Eta pairing on a supersingular elliptic curve over the binary field F 2 1223 used to offer 128-bit security, and has been studied extensively for efficient implementations. In this paper, we report our GPUbased implementations of this algorithm on an NVIDIA Tesla C2050 platform. We propose efficient parallel implementation strategies for multiplication, square, square root and inverse in the underlying field. Our implementations achieve the best performance when López-Dahab multiplication with four-bit precomputations is used in conjunction with one-level Karatsuba multiplication. We have been able to compute up to 566 eta pairings per second. To the best of our knowledge, ours is the fastest GPU-based implementation of eta pairing. It is about twice as fast as the only reported GPU implementation, and about five times as fast as the fastest reported single-core SIMD implementation. We estimate that the NVIDIA GTX 480 platform is capable of producing the fastest known software implementation of eta pairing.