Elliptic Curve Public Key Cryptosystem And Application

Thesis introduce the history and current situation of Public Key Cryptosystems , and the application at present in information safety field, With the developing direction in the future. Discuss the Elliptic Curve Cryptosystems mainly. Proceed from general conclusion of algebra on the finite field, study this special algebra system of Elliptic Curve on the finite field, Discuss that sets up several theories of the Public Key Cryptosystems and the problems of implementation on it. Such as choose in the basis, prime parameter p, q, Parameter m of integer , the choosing of n. The sufficient safety Elliptic Curves based on different base field are chosen, including the basic points and orders are chosen. The scale of the key, Chosen of the encyption and decipher systems. Signature and verification systems, such as ECDSA etc , the discuss about key exchange systems such as Deffie-Hellman systeme, etc. This thesis also discussed several applications and information safety products of the Elliptic Curve Cryptosystems at the finite field too, Such as Digital Signature, the group Signature, the application in the smart card. Analysesd the current situation of the implemention of the attack of ECC system , proved that ECC is abundant and safey enough presently , Suitable for research and devolopment at present and applicate in normal communication.