基于FPGA的SM9数字签名算法的快速实现
Fast Implementation of SM9 Digital Signature Algorithm Based on FPGA
DOI: 10.12677/csa.2025.154086, PDF,    国家自然科学基金支持
作者: 梅 峰, 李子臣*：北京印刷学院信息工程学院，北京
关键词: SM9；R-ate对；蒙哥马利模乘；滑动窗口算法；SM9； R-ate Pairing； Montgomery Modular Multiplication； Sliding Window Algorithm
摘要: SM9算法是由我国推出的基于双线性对的标识密码算法，其中使用的R-ate双线性对在计算效率上优于Weil对和Tate对，但在实际应用中仍有不足。针对上述问题，为了提升SM9中双线性对的计算效率，提出了一种在FPGA平台上使用滑动窗口改进R-ate对运算的方法。该方法以蒙哥马利模乘为基础改进扩域模逆运算并通过滑动窗口算法优化R-ate双线性对运算中的Miller循环部分。同时根据蒙哥马利模乘特性减少椭圆曲线上点运算计算量提升签名算法运算效率。仿真结果表明，采用该方法可以将SM9中R-ate对的运算效率提升约18.46%，对SM9签名算法效率提升约为13.55%。
Abstract: SM9 algorithm is an identity-based cryptographic algorithm based on bilinear pairing introduced by our country, in which the R-ate pairing used is better than Weil pairing and Tate pairing in terms of computational efficiency, but it still has deficiencies in practical applications. To improve the computational efficiency of the bilinear pairing in SM9, a method was proposed to improve the R-ate pairing operation by using a sliding window on the FPGA platform. The method was based on the Montgomery modular multiplication to enhance the modular inverse operation in the twelfth extension field and optimize the Miller loop in the R-ate pairing operation through the sliding window algorithm. At the same time, the computational efficiency of the signature algorithm was improved by reducing the number of point operations on elliptic curves according to the Montgomery modular multiplication property. Simulation results showed that this method could improve the computational efficiency of R-ate pairing in SM9 by approximately 18.46%, and the efficiency of the SM9 signature algorithm by approximately 13.55%.
文章引用：梅峰, 李子臣. 基于FPGA的SM9数字签名算法的快速实现[J]. 计算机科学与应用, 2025, 15(4): 134-144. https://doi.org/10.12677/csa.2025.154086

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