A practical certificateless signature scheme

In Asiacrypt'03, Al-Riyami and Paterson introduced the concept of certificateless public key cryptography (CLPKC). CLPKC is a paradigm to solve the inherent key escrow problem suffered by identity-based cryptography (IBC). In this paper we propose a practical certificateless signature (CLS) scheme based on bilinear pairings. Three pairing computations can be used in the verification algorithm of our scheme, in contrast to at least four pairing in the verification phase of previous provably secure CLS schemes. In addition, only one pairing which is precomputable can be saved in the sign algorithm. The security of the proposed scheme can be proved to be equivalent to the Inverse Computational Diffie-Hellman problem and q-Strong Diffie-Hellman problem in the random oracle model.