In this paper， we showed the theory of elliptic curve， discrete logarithm problem (DLD)， elliptic curve discrete logarithm problem (EDLP)， discrete logarithm generator and EIGamal cryptosystem and elliptic cryptosystem. After that work， we proposed an elliptic curve cryptosystem on the base of discrete logarithm generator. The security of the proposed cryptosystem depend on the intractability of EDLP. At present no one seems to have a subexponential time algorithm for EDLP. So the proposed cryptosystem have the sufficient security.
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