Optimization of reconfigurable SM2 algorithm over prime filed

Bin LI; Qinglei ZHOU; Xiaojie CHEN; Feng FENG

doi:10.11959/j.issn.1000-436x.2022043

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Optimization of reconfigurable SM2 algorithm over prime filed

Papers | 更新时间：2024-06-05

- Optimization of reconfigurable SM2 algorithm over prime filed
- Journal on Communications Vol. 43, Issue 3, Pages: 30-41(2022)
- 作者机构：
  
  1. 郑州大学计算机与人工智能学院，河南郑州 450001
  2. 数学工程与先进计算国家重点实验室，河南郑州 450001
- 作者简介：
- 基金信息：
  
  The National Key Research and Development Program of China(2016YFB0800100);The National Key Research and Development Program of China(2016YFB0800101);The National Natural Science Foundation of China(61572444)
- DOI：10.11959/j.issn.1000-436x.2022043
  CLC： TP309
- Online First：2022-03，
  
  Published：25 March 2022
- 稿件说明：
移动端阅览
Bin LI, Qinglei ZHOU, Xiaojie CHEN, et al. Optimization of reconfigurable SM2 algorithm over prime filed[J]. Journal on Communications, 2022, 43(3): 30-41.
DOI：

Bin LI, Qinglei ZHOU, Xiaojie CHEN, et al. Optimization of reconfigurable SM2 algorithm over prime filed[J]. Journal on Communications, 2022, 43(3): 30-41. DOI： 10.11959/j.issn.1000-436x.2022043.

摘要

针对SM2算法软件效率低、硬件实现资源利用率低、可扩展性差的问题，提出了一种可重构的素域SM2算法优化方法。通过对SM2算法的深入分析，从不同计算阶段和计算特点着手，分别采用KOA快速乘法、快速模约减和Barrett算法实现推荐或任意参数的模乘运算，并优化改进基为4的扩展欧几里得算法加速模逆运算。然后，在标准射影坐标系下以蒙哥马利方法提高点乘运算效率，并优化了点加和倍点数据流，将运算周期缩短至12个时钟。同时，在FPGA内部实现了快速的坐标系转换。最后，设计实现了多SM2的并行调度管理，满足日益多样化的应用需求。实验结果分析表明，所优化的SM2充分利用了FPGA的资源，缩短了点乘周期，每秒计算次数最多较CPU（Intel i5-8300）高352.48倍，提高了计算性能和可扩展性。

Abstract

Aiming at the problems of inefficient of software

low utilization of hardware resources and poor scalability of SM2 algorithm

a reconfigurable optimization method of SM2 algorithm over prime filed was proposed.Through in-depth analysis of the SM2 algorithm

starting from different computation stages and characteristics

respectively using KOA fast multiplication

fast modular reduction and Barrett algorithm to achieve recommended or arbitrary parameters of the modular multiplication operation

and the radix-4 extended Euclidean algorithm was optimized and improved to accelerate the modular inverse operation.Then

in the standard projective coordinate system

the Montgomery method was used to improve the efficiency of point multiplication

and the data flow of point addition and double point was optimized to shorten the operation cycle to 12 clocks.At the same time

fast coordinate system conversion was realized inside the FPGA.Finally

the parallel scheduling management of multi-SM2 was designed and implemented to meet the computational requirements of multiple applications.The experimental results show that the optimized SM2 makes full use of FPGA resources and shortens the cycle of point multiplication.The maximum number of calculations per second is 352.48 times higher than the CPU (Intel i5-8300)

which improves the performance and scalability.

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references

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