Paper 2011/540 Original: eprint.iacr.org/2011/540 ↗

Efficient Implementation of the $\eta_T$ Pairing on GPU

Abstract

Recently, efficient implementation of cryptographic algorithms on graphics processing units (GPUs) has attracted a lot of attention in the cryptologic research community. In this paper, we deal with efficient implementation of the $\eta_T$ pairing on supersingular curves over finite fields of characteristics 3. We report the performance results of implementations on NVIDIA GTX 285, GTX 480, Tesla C1060, and Tesla C2050 graphics cards. We have implemented $\eta_T$ pairing in three different ways, namely, one pairing by one thread (Implementation~\Rmnum{1}), one pairing by multiple threads (Implementation~\Rmnum{2}), and multiple pairings by multiple threads in a bitsliced fashion (Implementation~\Rmnum{3}). The timing for Implementation~\Rmnum{3} on a single GTX 285 is 1.47, 8.15, and 140.7~milliseconds for $\eta_T$ pairing over $\mathbb{F}_{3^{97}}$, $\mathbb{F}_{3^{193}}$, and $\mathbb{F}_{3^{509}}$, respectively. On a single GTX 480, the throughput performance of Implementation~\Rmnum{3} is 33710, 4970, and 332 $\eta_T$ pairings per second over $\mathbb{F}_{3^{97}}$, $\mathbb{F}_{3^{193}}$, and $\mathbb{F}_{3^{509}}$, respectively. To the best of our knowledge, this is the first implementation of $\eta_T$ pairing on GPU. Furthermore, it is currently the software implementation that achieves the highest single-chip throughput for $\eta_T$ pairing.