Abstract: Certificateless cryptography eliminates the key escrow problem inherent in identity-based cryptosystems and avoids the complex certificate managerment problem in traditional certificate-based public-key cryptosystems,so it achieves the best advantages of them．Signcryption is a cryptographic primitive that could achieve authentication and confidentiality simultaneously by combining digital signature and public key encryption,while it has lower computational cost than signing and encryption respectively．In this paper,a provably secure certificateless signcryption scheme was proposed,which requires only two bilinear pairing operation in the unsigncryption phase and is much more efficient than the existing ones．In the last,we proved it satisfies indistinguishability against adaptive chosen ciphertext attack and existential unforgeability against adaptive chosen message and identity attack by using the complexity assumptions in the random oracle model.

Key words: Certificateless cryptography,Signcryption,Provable security,Random oracle model