Certificateless cryptography is introduced to eliminate certificate management in traditional public key cryptography and key escrow problem in identity-based cryptography. In this paper, an efficient certificateless signature scheme is proposed. It has the following advantages. First, pairing operations in signing phrase are eliminated and only two pairing operations are involved in verifying phrase, the signature length is also reduced to 160 bits. Second, user's public key is bound with his/her private key, so public key replacement attack can hardly be implemented. Last, the scheme is proven secure against existential forgery of adaptively chosen message attack in random oracle model.
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