Research And Implementation Of Elliptic Curve Cryptography-based Payment System

Along with the development of the electronic commerce, the research of safe electronic payment becomes a hotspot. There are two protocols in electronic payment, the SSL protocol and the SET protocol. The system of electronic payment based on SSL protocol costs low and has some advantage while the system based on SET protocol uses the public key encryption, information digest, data signature as well as dual data signature etc, and so the later one has more obvious advantages. It provides authentication of participants and insures the confidentiality, integrity of information and disavowal and makes whole payment process safer. The constituters of the SET protocol make elliptic curve cryptosystem as default public cryptosystem. How to improve elliptic curve system performance efficiency is the research topic of elliptic curve cryptosystem.After the study of elliptic curve cryptosystem, this paper puts forward fast scalar multiplication algorithm and researches on payment system based on elliptic curve cryptosystem. The main work in this paper is showed as follows:Firstly, this paper researches the mathematics foundation of the elliptic curve cryptosystem and analyzes the related calculation algorithm of elliptic curve cryptosystem. Based on the limited field arithmetic and the elliptic curve arithmetic, this paper analyzes the run- time efficiency and safety of elliptic curve cryptosystem. It studies the method of elliptic curve selection, elliptic curve data signature as well as the process of elliptic curve key agreement and elliptic curve encryption. It also describes the related algorithm.Secondly, the paper studies the key factor scalar multiplication which influences the run-time efficiency of elliptic curve cryptosystem, and then puts forward two fast scalar multiplication algorithms. The paper converts coordinate system of Finite Abelian Group which is made up of point set on elliptic curve and point-addition operation. It researches the algorithm of standard projection coordinate system and Jacobian projection coordinate system respectively and also analyzes their run-time efficiency. It researches binary number system and non-adjacent form algorithm of finite field, and puts forward two fast scalar multiplication algorithms - fixed base scalar multiplication as well as three bits non-adjacent form algorithm, and applies them to ECDSA and ECDH, and then analyzes the run-time efficiency of ECDSA and ECDH. Lastly, it verifies the two algorithms and compares them.Finally, the paper analyzes and designs the payment system. It mainly realizes the fast scalar multiplication algorithm..