High-Speed FPGA Implementation of SIKE Based on an Ultra-Low-Latency Modular Multiplier

The supersingular isogeny key encapsulation (SIKE) protocol, as one of the post-quantum protocol candidates, is widely regarded as the best alternative for curve-based cryptography. However, the long latency, caused by the serial large-degree isogeny computation which is dominated by modular multiplications, has made it less competitive than most popular post-quantum candidates. In this paper, we propose a high-speed and low-latency architecture for our recently presented optimized SIKE algorithm. Firstly, we design a new field arithmetic logic unit (FALU) with many algorithmic transformations and architectural optimizations. Especially, for the FALU, an extremely low-latency modular multiplier is devised based on a modified algorithm by fully parallelizing and highly optimizing the small-size multipliers and the reduction submodules. Secondly, we develop a compact control logic and update the instructions based on the benchmark provided in the newest SIKE library, fitting well with our design. Thirdly, an efficient memory access method is proposed by scheduling the input and output of the arithmetic logic unit (ALU) in two identical RAMs, which can significantly reduce the latency. Finally, we code the proposed architectures using the Verilog language and integrate them into the SIKE library. The implementation results on a Xilinx Virtex-7 FPGA show that for SIKEp751, our design only costs 9.3 Ens with a frequency of 155.8 MHz, about 2x faster than the state-of-the-art, and achieves the best area efficiency among existing works. Particularly, the modular multiplier merely needs 16 clock cycles, reducing the delay by nearly one order of magnitude with a small factor of increase in hardware resource.