The Design And Implement Of The Elliptic Curve Cryptography Engine

In this paper, an elliptic curve cryptography engine is designed and implemented. The whole engine is composed of serven modules: the protocols, the opetations on the curve, the symmetric cryptography, the digital digest, the keys database, the keys exportation, the keys management. Besides the analysis and the design, there are some other works done in this paper. Firstly, the mathematics background of the elliptic curve cryptography is introduced. Then, the study of the operations on the curve is implemented, including the field operations and the point operations. An improvement of the algorithm of the multiplication of two big numbers is given. The algorithm of point multiplication is analysized and an improvement of this algorithm is given too. Secondly, it provides the schemes of producing and validating the field parameters, producing the ephemeral key pair and validating the public key, etc. Meanwhile, a flexible design of the symmetric cryptography module and the digital digest module is given. By changing the value of the arguments, it can be freely to choose different algorithms without changing the programs. Finally, based on the three kinds of basic protocols, some derivated protocols are provided, including the protocol of miscellaneous encryption without chaning the shared point and the protocol of simplified encrypting and signing. An optimized algorithm of the key derivation function is given also.It is more efficient and has shorter keys with the same strength compared with the RSA engine. So it can be used widely in the e-commerce, the secure instant messaging, the secure e-mail, etc.