FPGA Implementations of Pairing using Residue Number System and Lazy Reduction

Recently, a lot of progress has been made in the implementation of pairings in both hardware and software. In this paper, we present two FPGA-based high speed pairing designs using the Residue Number System and lazy reduction. We show that by combining RNS, which is naturally suitable for parallel architectures, and lazy reduction, which performs one reduction for multiple multiplications, the speed of pairing computation in hardware can be largely increased. The results show that both designs achieve higher speed than previous designs. The fastest version computes an optimal ate pairing at 126-bit security level in 0.573 ms, which is 2 times faster than all previous hardware implementations at the same security level. © 2011 International Association for Cryptologic Research.