一种SM9算法R-ate对的快速实现方法  

A Fast Implementation of R-ate Pairing in SM9 Algorithm

作　　者：胡芯忆 何德彪 彭聪 罗敏[1] 黄欣沂 HU Xin-Yi;HE De-Biao;PENG Cong;LUO Min;HUANG Xin-Yi(Key Laboratory of Aerospace Information Security and Trusted Computing,Ministry of Education,School of Cyber Science and Engineering,Wuhan University,Wuhan 430072,China;Artificial Intelligence Thrust,Information Hub,The Hong Kong University of Science and Technology(Guangzhou),Guangzhou 511455,China)

机构地区：[1]武汉大学国家网络安全学院空天信息安全与可信计算教育部重点实验室,武汉430072 [2]香港科技大学(广州)信息枢纽人工智能学域,广州511455

出　　处：《密码学报》2022年第5期936-948,共13页Journal of Cryptologic Research

基　　金：山东省重点研发计划(2020CXGC010115,2020CXGC010107);国家自然科学基金(62172307,U21A20466,62032005);湖北省自然科学基金(2020CFA052);湖北省重点研发计划(2020AEA013);武汉市科技计划项目(2020010601012187)。

摘　　要：SM9标识密码算法是一种基于双线性对的公钥密码算法.双线性对是SM9密码算法的核心运算部件,它的性能决定了SM9密码算法的性能.本文基于已有算法优化了十二次扩域的平方运算,设计了一种十二次扩域的等价转换方法,提出了一种面向椭圆曲线点乘的稀疏乘法,降低了有限域乘法数量,得到了一种SM9算法双线性对的快速软件实现方法.理论分析显示,本方法的计算复杂度低于现有的实现方法.实验结果显示,本方法计算一次SM9算法双线性对需要的时间为3.389毫秒.SM9 identity-based cryptographic algorithm is a pairing-based public key cryptographic algorithm. Bilinear pairing is one of the core computation units of SM9 cryptographic algorithms,which dominates the performance of SM9. This paper improves the squaring in the twelfth extension field based on existing algorithms, designs an equivalent conversion method of the twelfth extension field, presents sparse multiplication for elliptic curve point multiplication, decreases the counts of multiplication in the finite field, and achieves a fast software implementation of the pairing in SM9algorithms. Theoretical analysis shows that the computational complexity of the proposed method is lower than that of the best methods known so far. Experimental results show that this method takes3.389 ms to compute one pairing in SM9 algorithm.

关 键 词：SM9算法 双线性对 软件实现 R-ate对 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]