Hierarchical identity-based encryption without key delegation in decryption

Hierarchical Identity-Based Encryption (HIBE) is a generalisation of Identity- Based Encryption (IBE) which mirrors an organisational hierarchy. However, when the user decrypts a ciphertext encrypted to a hierarchical identity, he/she should know the exact hierarchical identity in order to run the delegate algorithm to get the secret key corresponding to the target hierarchical identity if the hierarchical identity linked with his/her key is a prefix of the target hierarchical identity. In this paper, we consider a new concept called HIBE without key delegation in decryption. In such HIBE systems, the user can decrypt the ciphertext directly without running the delegate algorithm even if his hierarchical identity is only a prefix of the target hierarchical identity. We present two HIBE systems, which are proven secure in the standard model under the decision BDH and l-BDHE assumptions, respectively. Both systems have the same decryption efficiency in pairing, compared with BB1-HIBE system and BBG-HIBE system, respectively.