A High-Performance Universal FPGA Implementation for PM and DPM Based on Differential Addition Chain

Point multiplication (PM) and double point multiplication (DPM) are fundamental essential operations in elliptic curve cryptography (ECC). This paper presented a novel and versatile architecture for PM and DPM based on the differential addition chain. The execution pattern of PM and DPM is uniform to resist side-channel attacks. The datapath and modular operation units are shared by PM and DPM to optimize the utilization of hardware resources. The pipeline stages are carefully designed, leading to a compact timing schedule for PM and DPM. The architecture has been implemented on Virtex-7, supporting ${GF}(2^{163})$, ${GF}(2^{283})$ and ${GF}(2^{571})$. The implementation results indicate that the proposed design achieves 5.7%, 8.7% and 23.6% performance improvements over existing works.