Research of elliptic curve cryptosystem

In this paper, the concepts of elliptic curve and their related knowledge are introduced briefly. Then,three focuses on the elliptic curve in the present are given:fast algorithm of point add of elliptic curve cryptosystem, analysis of elliptic curve cryptosystem in the security,generation of secure elliptic curve. At last, a kind of typical example of elliptic curve cryptosystem is raised. As a summary, the status of the elliptic curve cryptosystem and the problems that this cryptosystem face now are reflected. And the newest development in this area are covered.