Signatures in hierarchical certificateless cryptography: Efficient constructions and provable security

Recent years, lots of efforts have been devoted to construct secure schemes in certificateless cryptography which eliminates the key escrow problem in identity-based cryptography. However, most of them are designed in traditional certificateless cryptography which suffers from the single-point problem. Hierarchical cryptography exploits a practical security model to mirror the organizational hierarchy in the real world and hence can eliminate the single-point problem. In this paper, to incorporate the advantages of both types of cryptosystems, we instantiate hierarchical certificateless cryptography by formalizing the notion of hierarchical certificateless signatures. A concrete hierarchical certificateless signature scheme is also proposed. The security of our scheme is proven under the computational Diffie-Hellman assumption. As to efficiency, our scheme has constant complexity, regardless of the depth of the hierarchy. Therefore, the proposal is secure and practical for scalable applications.