Faster Fp-arithmetic for Cryptographic Pairings on Barreto-Naehrig Curves

This paper describes a new method to speed up Fp-arithmetic for Barreto-Naehrig (BN) curves. We explore the characteristics of the modulus defined by BN curves and choose curve parameters such that Fp multiplication becomes more efficient. The proposed algorithm uses Montgomery reduction in a polynomial ring combined with a coefficient reduction phase using a pseudo-Mersenne number. With this algorithm, the performance of pairings on BN curves can be significantly improved, resulting in a factor 5.4 speed-up compared with the state-of-the-art hardware implementations. Using this algorithm, we implemented a pairing processor in hardware, which runs at 204 MHz and finishes one ate and R-ate pairing computation over a 256-bit BN curve in 4.22 ms and 2.91 ms, respectively.