基于FPGA的SM9倍点运算快速实现
Fast Implementation of SM9 Multi-Point Operation Based on FPGA
摘要
Abstract
The SM9 algorithm is an elliptic curve-based public key cryptography released by the State Cryptography Administration.Nevertheless,the algorithm's double-point operations involve a significant amount of computation time.This study optimized the point multiplication operation in the SM9 algorithm on an FPGA platform by utilizing the Jacobian weighted projective coordinate system combined with the characteristics of BN curves.It also employed the non-adjacent form(NAF)representation to improve computational parameters,reduce the number of point addition algorithm operations,and achieve a fast hardware implementation method for the SM9 algorithm.Experimental results show that the proposed method improves the efficiency of double-point operations by 37%and increases the efficiency of the SM9 signature algorithm by approximately 13.1%.关键词
SM9/FPGA/Jacobian加重射影坐标系/倍点运算Key words
SM9/FPGA/Jacobian weighted projective coordinate system/point doubling operation分类
信息技术与安全科学引用本文复制引用
梅峰,马钰,周峰,李子臣..基于FPGA的SM9倍点运算快速实现[J].密码学报（中英文）,2025,12(3):576-585,10.基金项目
国家自然科学基金(61370188) （61370188）
北京市教委科研计划(KM202010015009,KM202110015004,KM202310015002) （KM202010015009,KM202110015004,KM202310015002）
北京印刷学院博士启动金项目(27170120003/020,27170122006) （27170120003/020,27170122006）
北京印刷学院科研创新团队项目(Eb202101) （Eb202101）
北京印刷学院校内学科建设项目(21090121021) （21090121021）
北京印刷学院重点教改项目(22150121033/009) （22150121033/009）
北京印刷学院科研基础研究一般项目(Ec202201) （Ec202201）
北京市高等教育学会 2022 年立项面上课题(MS2022093)National Natural Science Foundation of China(61370188) （MS2022093）
Beijing Municipal Education Commission Scientific Research Project(KM202010015009,KM202110015004,KM202310015002) （KM202010015009,KM202110015004,KM202310015002）
Beijing Institute of Graphic Communication Doctoral Funding Project(27170120003/020,27170122006) （27170120003/020,27170122006）
Beijing Institute of Graphic Communica-tion Research Innovation Team Project(Eb202101) （Eb202101）
Intramural Discipline Construction Project of Beijing Institute of Graphic Communication(21090121021) （21090121021）
Key Educational Reform Project of Beijing Institute of Graphic Communica-tion(22150121033/009) （22150121033/009）
General Research Project of Basic Research of Beijing Institute of Graphic Communication(Ec202201) （Ec202201）
General Research Project of Beijing Association of Higher Education in 2022(MS2022093) （MS2022093）
