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As a special cryptographical tool, designated verifier signature scheme (DVS) is a signature scheme which provides authentication of a message without providing a non-repudiation property of traditional signature. Thus, designated verifier signature scheme plays an important role in copyright protection. However, most of existing schemes include hash functions to realize security proof and the security of most existing schemes is only proven in the random oracle model. However, security in random oracle model doesn't imply the security in the real world. In this paper, we proposed an efficient Designated verifier signature scheme without random oracle and show that the security of the scheme is tightly related to Strong Diffie-Hellman assumption. The prominent advantage of the scheme is that the pairing operation and hash function are not involved in signing phase, the size of signature is 480 bits. Thus the scheme is very efficient.