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This paper introduces a public-key cryptosystem based on elliptic curves which is proved to be semantically secure under CCA-2 (Adaptive Chosen Ciphertext Attack) attacks. This system is an analogue of Cramer-Shoup system over elliptic curves.Its security relies only on the hardness of the Elliptic Curve Decision Diffie-Hellman (ECDDH) problem. We want to use this protocol to show