An Authenticated Certificateless Public Key Encryption Scheme

In 2003, Al-Riyami and Paterson \cite{AP} proposed the certificateless public key cryptography(CL-PKC) which is intermediate between traditional certificated PKC and identity-based PKC. In this paper, we propose an authenticated certificateless public key encryption scheme. Our result improves their public key encryption scheme in efficiency and security. The security of the protocol is based on the hardness of two problems; the computational Diffie-Hellman problem(CDHP) and the bilinear Diffie-Hellman problem(BDHP). We also give a formal security model for both confidentiality and unforgeability, and then show that our scheme is provably secure in the random oracle model