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 refle...
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