Efficiently CCA Secure HIBE Schemes under Double Models with Constant Ciphersize

Identity-based encryption schemes simplify the problem of the management and maintenance of digital certificates in the PKI environment. If the number of identities is large enough in a KGC (key generation center) domain, a single KGC will be a bottleneck of computation and communication. HIBE (Hierarchical identity-based encryption) has been introduced to solve this problem. For the present HIBEs, the size of public parameters is large and is twice as the number of hierarchy, and the analysis method is unique. Most of the existing HIBEs are either proved secure under RO (random oracle) model, or complicated and proved secure under standard mode. This paper further investigates both efficient and provably secure HIBE schemes with small public key size under multi-models. The size of public parameters of the proposed scheme is small and is independent of bit representation of an identity, and is about the same size as the number of hierarchy. The proposed scheme also has the advantage of constant size of cipher text, which is composed of 4 group elements. At last, the proposed scheme is proved sID-IND-CCA secure under both RO and standard models based on the standard DBDH problem. Investigations on the method of cryptographic scheme design and proof of security under multi-models can improve the confidence on its security.