Efficient Implementation of the etaT Pairing on GPU

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 ηT 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 ηT pairing in three different ways, namely, one pairing by one thread (Implementation I), one pairing by multiple threads (Implementation II), and multiple pairings by multiple threads in a bitsliced fashion (Implementation III). The timing for Implementation III on a single GTX 285 is 1.47, 8.15, and 140.7 milliseconds for ηT pairing over F397 , F3193 , and F3509 , respectively. On a single GTX 480, the throughput performance of Implementation III is 33710, 4970, and 332 ηT pairings per second over F397 , F3193 , and F3509 , respectively. To the best of our knowledge, this is the first implementation of ηT pairing on GPU. Furthermore, it is currently the software implementation that achieves the highest single-chip throughput for ηT pairing.