Efficient Implementation Of R-ate Bilinear Pairing Algorithm

Cryptography,as a means of protecting information,has been one of the hot topics in cryptology.In 2016,China's State Password Administration released the Chinese standard trade secret algorithm SM9.With the gradual deepening of research,the encryption technology based on bilinear pairing will play a vital role in all walks of life in the future.At present,however,there is still a certain gap between the computational efficiency of the bilinear pair encryption technology and the actual application requirements.Therefore,it is of great importance to explore and improve the efficiency of bilinear pairing algorithm.Under the guidance of SM9 standard,this thesis aims to reduce the computational complexity of R-ate bilinear computation,improve the efficiency of algorithm implementation and design an efficient encryption system.After a lot of theoretical analysis and experimental verification,some results are obtained as follows:1.According to the parameters given in the SM9 standard,the calculation of different levels is discussed in detail,and a detailed calculation method of the R-ate bilinear pairing encryption algorithm from top to bottom is given.It includes the basic arithmetic operation,the linear function and the last modular power part in the extended domain.2.A series of optimized algorithms is proposed to improve the efficiency of R-ate pairing algorithm,including NAF-based acceleration techniques,computations over montgomery and sparse multiplication under the twelve extension domain.3.On the basis of the above algorithm,a complete set of R-ate bilinear pairing calculation program is implemented with C language,and the program is transplanted to the SOC encryption system based on FPGA.After testing,this implementation can ensure the accuracy.At the same time,each cryptographic operation can be completed within 0.28 s,which has a higher advantage in terms of the execution efficiency.