Research And Realization Of The Elliptic Curve Cryptography

Nowdays information has been booming becaue of the development of computer technology. It has become an important part of our modern society. The imformation security has become an international issue. There are many ways to protect the information. Cryptography is one of them. It provids many algorithms and protocals to meet many prectical needs. In this paper, elleiptic curve cyrptography was discussed. Elliptic curve cryptography is a kind of public key cryptography based on the elliptic curve discrete logarithm problem. It is safer and faster than the other algorithm. Now the research of elliptic curve theory is the key point of the cryptography. So the research of elliptic curve in this paper has an important value.Elliptic Curve Cryptography (ECC) systems, which are a series of public-key systems based on elliptic-curve discrete logarithm problem, are presented first by Miller and Koblitz independenty. ECC system makes use of the finite group of elliptic curve on the finite field instead of finite cyclic group used in the discrete logarithm problem. The theory of ECC is being studied a lot and it is the focus of the cryptography and the industrial estate, especially the technique of the implementation of ECC.In this thesis, the meaning of the information technology is discussed firstly, then we analyze the classical cryptography algoritham. After that, the mathematics base of elliptic curve cryptosytems are introduced, especially the theory of the finite field. As for some algorithms, we also give out the program of reliazation. And then we analy the discrete logarithm problem and the attacks of ECC. In the third part, we discusse the details of the ECC and the software realization. A new embedding algorithm is proposed; we also give out our experiment data of every part. In the forth part, we discuss the software realization of ECC, explain the details of every part, such as the generation of the key, plaintext embedding and so on. In the fifth part, we associate the elliptic curve cryptography with remote control system and proposed a mode of identity realization and the data cryption.In the last part of this thesis, we sumrize the whole paper, point out the work we have done. At the same time, the exsit problems of the ECC are given out, Then it further provides the prospect of ECC with the development of the reckon technics, network technics, optimization technics, mathematical theory and computer software and hardware.