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Certificateless public-key cryptosystem" is a new and attractive paradigm, which avoids the inherent key escrow property in identity-based public-key cryptosystems, and does not need expensive certificates as in the public key infrastructure. A strong security model for certificateless public key encryption was established by Al-Riyami and Paterson in 2003. In this paper, we first present a security model for certificateless public-key signature schemes, and then propose an efficient construction based on bilinear pairings. The security of the proposed scheme can be proved to be equivalent to the computational Diffie-Hellman problem in the random oracle model with a tight reduction.

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