面向移动设备的国密SM2高效实现研究

张吉鹏; 黄军浩; 于璇; 刘哲

doi:10.12263/DZXB.20221419

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面向移动设备的国密SM2高效实现研究

学术论文 | 更新时间：2025-12-11

- 面向移动设备的国密SM2高效实现研究
- Research on Efficient Implementation of SM2 for Mobile Devices
- 电子学报 2023年51卷第12期页码：3437-3443
- 作者机构：
  
  1.南京航空航天大学计算机科学与技术学院,江苏南京 211106
  2.香港浸会大学,香港 999077
  3.北京师范大学-香港浸会大学联合国际学院,广东珠海 519087
  4.之江实验室,浙江杭州 311101
- 作者简介：
  
  [ "张吉鹏男，1999年3月出生于山东省济宁市.现为南京航空航天大学博士生.研究方向为公钥密码算法、后量子密码算法、密码工程.E-mail: jp-zhang@outlook.com" ]
  [ "黄军浩男，1995年11月出生于广东省化州市.现为香港浸会大学、北京师范大学香港浸会大学联合国际学院博士生.研究方向为公钥密码算法、后量子密码算法、密码工程. E-mail: huangjunhao@uic.edu.cn" ]
  [ "刘哲（通讯作者）男，1986年12月出生于山东省济宁市，国家海外高层次人才，现任之江实验室基础理论研究院副院长.曾获得教育部高校计算机专业优秀教师奖、《麻省理工科技评论》中国区“35岁以下科技创新35人”、阿里巴巴达摩院青橙奖、中国密码学会密码创新奖一等奖等荣誉.长期从事信息安全领域的研究，在IACR CHES、ACM CCS、IEEE S&P等顶级安全会议和IEEE TC、IEEE TDSC、IEEE TIFS等顶级安全期刊发表学术论文160多篇. E-mail: zhe.liu@zhejianglab.com" ]
- 基金信息：
  
  国家重点研发计划(2020AAA0107703);国家自然科学基金(62132008);霍英东教育基金(171057);江苏省杰出青年基金(BK20220075)
- DOI：10.12263/DZXB.20221419
  中图分类号： TP309
- 收稿：2022-12-21，
  
  修回：2023-07-31，
  
  纸质出版：2023-12-25
- 稿件说明：
移动端阅览
张吉鹏,黄军浩,于璇等.面向移动设备的国密SM2高效实现研究[J].电子学报,2023,51(12):3437-3443.

ZHANG Ji-peng,HUANG Jun-hao,YU Xuan,et al.Research on Efficient Implementation of SM2 for Mobile Devices[J].ACTA ELECTRONICA SINICA,2023,51(12):3437-3443.
张吉鹏,黄军浩,于璇等.面向移动设备的国密SM2高效实现研究[J].电子学报,2023,51(12):3437-3443. DOI： 10.12263/DZXB.20221419.

ZHANG Ji-peng,HUANG Jun-hao,YU Xuan,et al.Research on Efficient Implementation of SM2 for Mobile Devices[J].ACTA ELECTRONICA SINICA,2023,51(12):3437-3443. DOI： 10.12263/DZXB.20221419.

摘要

SM2的优化实现在x86-64架构上已经得到了充分的研究，但在ARMv8-A架构上的优化仍不充分，为此本工作提出了以下优化方案：针对SM2的模

与模

乘法/平方运算，充分利用

与

的数值特点优化了蒙哥马利模乘；针对模

与模

求逆运算，推导并实现了更快的基于费马小定理的模逆算法；针对固定点与非固定点标量乘法，分别实现了宽度为7与5的窗口算法；针对签名生成过程中

的计算，用一个模

加/减法替换一个模

乘法.将上述优化技术集成到OpenSSL（3.0.0-beta1）中后，在华为云鲲鹏920计算平台上的测试表明，SM2签名性能提升8.7倍；SM2验签性能提升3.5倍.在移动设备树莓派4平台上，SM2的签名性能提高9.7倍；验签性能提高3.4倍.

Abstract

SM2 has been fully studied on x86-64 architecture

but its optimization on ARMv8-A architecture is inadequate. In this work

we propose the following optimizations to fill this gap: for the modular multiplication/squaring of

and

in SM2

we optimize Montgomery modular multiplication/squaring by leveraging the numerical characteristics of

and

; for the modular inversion of

and

in SM2

we derive and implement a faster modular inversion algorithm based on Fermat's little theorem; for fixed-point and unknown-point scalar multiplication

we implement window algorithms with a window width of 7 and 5

respectively; for the calculation of

during the signature generation process

we replace a modular multiplication of

with a cheaper modular addition/subtraction of

. After integrating the optimizations mentioned above into OpenSSL (3.0.0-beta1)

the benchmark on the HUAWEI Cloud Kunpeng 920 computing platform shows that the performance of SM2 signature generation is accelerated by 8.7 times; the performance of SM2 signature verification is accelerated by 3.5 times. Meanwhile

on the mobile device Raspberry Pi 4 platform

the performance of SM2 signature generation is accelerated by 9.7 times; the

performance of SM2 signature verification is accelerated by 3.4 times.

关键词

Keywords

references

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