Cryptology ePrint Archive: Report 2020/1125

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

Jing Tian and Bo Wu and Zhongfeng Wang

Abstract: 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 hard for practical applications. In this paper, we present a fast FPGA implementation for the SIKE by incorporating algorithmic transformations and architectural optimizations. Firstly, we introduce a novel data representation, which can facilitate faster and higher-parallel field arithmetic computing than prior arts. Secondly, an extremely low-latency modular multiplier is devised based on the new algorithm by fully parallelizing and highly optimizing the small-size multipliers and reduction modules. Thirdly, a compact control logic is developed based on the benchmark provided in the newest SIKE library, well fitting our arithmetic logic unit (ALU). 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 the SIKEp751, our design only costs 13.2 ms with a frequency of 138.9 MHz, about 2x faster than the state-of-the-art. 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.

Category / Keywords: implementation / Modular multiplication, supersingular isogeny key encapsulation (SIKE), elliptic curve cryptography (ECC), post-quantum cryptography (PQC), hardware implementation, FPGA.

Date: received 16 Sep 2020

Contact author: tianjing at nju edu cn

Available format(s): PDF | BibTeX Citation

Version: 20200921:081853 (All versions of this report)

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