后量子签名算法Falcon的剩余数系统FPGA实现研究

Research on FPGA Implementation of Postquantum Signature Algorithm Falcon in RNS

作为后量子签名算法Falcon的核心部件,剩余数系统对算法的密钥生成模块中求解NTRU方程有重大意义。本文介绍了RNS的FPGA实现方法,深入研究其剩余数生成、循环群求逆模块以及剩余数还原模块,提出高效的硬件设计思路与结构,采用并行结构设计算法主体框架,利用循环迭代进行优化,并在芯片上进行综合,给出算法整体改进方案,实现剩余数系统在六轮升降环中的全部的应用,并进一步提高数据量,完成模数生成模块十轮升降环应用的硬件实现,算法整体使用较少的逻辑资源,并在运算速度上有进一步的提升。

As the core component of postquantum signature algorithm Falcon,Residual Number System(RNS)is of great significance for solving the NTRU equation in key generation module of algorithm.In this paper,FPGA implementation of RSN is introduced.Residual number generation,cyclic group in-version module and residual number reduction module are deeply studied.An efficient hardware design idea and structure is proposed,where main framework of the algorithm is designed using the parallel structure and cyclic iteration is adopted for optimization.Synthesis is performed on chip and an overall improvement scheme of the algorithm is presented.Applications of the RNS in 6-rounds lift ring are all realized and data volume is further increased.Hardware implementation of modular generation module application in 10-rounds lift ring is performed with less logical resource and higher operating speed.