Signatures in hierarchical certificateless cryptography: Efficient constructions and provable security

Many efforts have been devoted in recent years to constructing secure schemes in certificateless cryptography. The aim is to eliminate the key escrow problem of identity-based cryptography. However, most of the work takes place 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. To incorporate the advantages of both types of cryptosystems, in this paper 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, our proposal is secure and scalable.