Study On Fast Implementation Alogrithms And Key Techniques For Elliptic Curve And Pairing-based Crytography

With the development of network technology and the wide application of technologies such as cloud computing,big data,and Internet of Things,society has entered the era of informationization.Information security has become more and more important.Cryptography is the core and supporting technology of information security,and the application of cryptography plays an irreplaceable role in the healthy development of social informatization.In the information age,with the continuous expansion of data scale,the huge number of users,massive data scale and high concurrent processing performance put forward higher requirements for cryptographic operation encryption and decryption speed,digital signature speed and other performance indicators.Only the cryptographic operation with higher performance can minimize the performance loss caused by the cryptographic operation in the business system,so as to prevent the cryptographic technology from becoming the bottleneck of social development in the information age.This paper focuses on the optimal implementation algorithm and key technology of elliptic curve cryptography and proposes a new optimization algorithm of elliptic curve scalar multiplication and bilinear pair cryptography,based on which a high-performance cryptographic chip is implemented.Finally,a new application mode of elliptic curve cryptography is designed for mobile Internet,which is convenient for the application and popularization of elliptic curve cryptography algorithm.The main achievements are as follows:First,the optimization algorithm and implementation of elliptic curve scalar multiplication.In this paper,a new optimization algorithm of elliptic curve scalar multiplication is proposed,which considers both area and performance,and reduces the consumption of resources while ensuring high performance.Specifically,according to the properties of special primes of elliptic curve cryptography,a high-speed modular multiplier supporting four-stage pipelining is designed.it takes only seven clock cycles to complete one modular multiplication,and it can support four modular multiplications at the same time without increasing resources.A parallel architecture is designed based on modular multiplier,and a parallel point addition and doubling algorithm is designed by analyzing correlation and other operations,which completes the high-speed implementation of point addition and multiplication.Based on the previous work,an improved sliding window method is adopted to realize the scalar multiplication of elliptic curve,which can effectively resist side channel attacks while improving the performance of scalar multiplication.To verify the optimization algorithm proposed in this paper,we have carried out experiments on the Kintex-7 FPGA platform of Xilinx Company.On this platform,it takes 13652 cycles to complete a total of 22938 LUTs,for one scalar multiplication,the running time is about 0.15ms,and the throughput can reach 2.31 Mbps.The experimental results show that the optimization algorithm proposed in this paper is real and effective and is better than other similar optimization algorithms.Second,the optimization algorithm and implementation of cipher based on bilinear pair.This paper proposes a fast optimization algorithm for the digital signature scheme based on bilinear pairs,which can greatly improve the performance of the digital signature algorithm.Specifically,this paper uses the Miller algorithm to calculate bilinear pairs;on this basis,through the mechanism of pre-calculation and dynamic storage,a fast bilinear pairwise exponentiation algorithm is designed to achieve the purpose of accelerating digital signature.To verify the optimization algorithm proposed in this paper,we have carried out experiments on the Kintex-7 FPGA platform of Xilinx Company.Experimental results show that the algorithm can improve the performance of the algorithm by about 3 times at the cost of adding a small amount of storage space.Third,the design and system implementation of distributed collaborative signature algorithm.In this paper,based on the digital signature standard of elliptic curve cryptosystem,relying on the technology of key segmentation and signature proxy,a new distributed cooperative signature algorithm is designed and developed.The algorithm has the following advantages:the signature private key will not appear in any process in the form of plaintext to ensure absolute security;distributed collaborative signature requires both parties to sign at the same time,and neither party can complete the signature alone.The security is further improved;the protocol is simple and convenient,only two interactions are needed to complete the complete signature,and the implementation is simple and convenient.Based on the distributed cooperative signature algorithm,this paper designs a mobile phone shield signature verification system which is suitable for mobile terminals(mobile phones).Under the condition of convenient application,the system does not reduce the security of the signature private key,and is convenient for the popularization and application of elliptic curve cryptography algorithm in mobile Internet.Fourth,the implementation and verification of cryptographic security chip.In order to facilitate the promotion and use of cryptographic algorithms,this paper designs and implements a high-performance password security chip suitable for cloud computing,big data and other environments.The chip mainly provides high-performance cryptographic algorithms,and the cryptographic algorithm module in the chip is based on the fast cryptographic implementation algorithm proposed in this paper.In the process of the design and implementation of the chip,the cryptographic algorithm is first simulated and verified by FGPA,and then integrated into the overall design of the chip.In the production stage of the chip,SMIC is chosen as the contract factory and the manufacturing process is 55nm CMOS process.At present,the chip has been successfully trial-produced in a small batch,using BGA324 packaging,the working frequency is 400MHz,and the current of the chip is about 2-2.5A in normal operation.Finally,the measured performance of SM2 digital signature algorithm can reach 400000 times per second,and the performance of SM9 signature algorithm can reach 1000 times per second,which reaches the international and domestic leading level,and meets the application requirements of cloud computing,big data and other high-performance scenarios.