Fast Software Implementation Research Of SM9

SM9 is an Identity-Based Cryptography(IBC)with independent intellectual property rights of the People’s Republic of China,which is based on the Public Key Infrastructure(PKI).A cryptographic system developed on the basis of PKI,the main purpose is to solve the problem that PKI needs to exchange a large number of digital certificates in specific security applications.The current effective IBC scheme depends on the calculation of bilinear pairs.As a relatively complex algebraic operation,the computational efficiency of bilinear pairs limits the practicability of IBC.Therefore,designing an efficient calculation method of bilinear pairs is of great significance to improve the overall performance and efficiency of SM9.The basic operations of bilinear based on elliptic curve are carried out in finite domain,and modular reduction is a time-consuming operation in finite domain computation.The calculation method based on lazyreduction can effectively reduce the number of modular reduction in finite domain computation.so as to obtain high performance.Based on the above principles,this paper designs a finite domain calculation method based on lazy-reduction which accords with the SM9 tower extension structure,and combines this method with the research basis of existing literature to propose a software fast calculation method of SM9 bilinear pairs.Based on the above calculation methods,the experimental part of this paper uses C to implement SM9 standard cryptographic protocol and an extension protocol,and tests the correctness and performance of the signature protocol and the extension protocol in SM9.The algorithm and test program are written based on the open-source big number arithmetic library GMP,and the test parameters are in accordance with the SM9 Identification cryptographic Algorithm Part 5:Parameter definition.According to the experimental results,the average time of calculating single SM9 algorithm bilinear pairing on Intel(R)Core(TM)i5-6300U 2.4GHz processor platform is 2.782 ms,1.846 ms on Intel(R)Core(TM)i7-6700k 4.0GHz processor platform,and 0.993 ms on Intel(R)Core(TM)i9-12900k 3.19GHz processor platform.The calculation results of SM9 cryptographic protocol and extension protocol are correct,the computational efficiency is superior to that of similar algorithms.