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Due to more overhead of asymmetric cryptosystems, traditionally, the symmetric cryptosystem is used to encrypt long messages. In case of symmetric cryptosystems, it creates the problem of key management. So to encrypt long messages, we usually, take the help of both symmetric and asymmetric cryptosystems. In this paper, we proposed an asymmetric cryptosystem for encrypting long messages, which is not only efficient but also secure. In consideration of the aspect of efficiency and computation, our proposed scheme uses elliptic curve cryptosystem.