Journal on Communications ›› 2022, Vol. 43 ›› Issue (3): 30-41.doi: 10.11959/j.issn.1000-436x.2022043

• Papers • Previous Articles     Next Articles

Optimization of reconfigurable SM2 algorithm over prime filed

Bin LI1, Qinglei ZHOU1, Xiaojie CHEN2, Feng FENG1   

  1. 1 School of Computer and Artificial Intelligence, Zhengzhou University, Zhengzhou 450001, China
    2 State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
  • Revised:2022-02-08 Online:2022-03-25 Published:2022-03-01
  • Supported by:
    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)

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.

Key words: reconfigurable, SM2, FPGA, Montgomery point multiplication, fast modular multiplication

CLC Number: 

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