Constant Size Ciphertext HIBE in the Augmented Selective-ID Model and its Extensions

Abstract: at eurocrypt 2005, boneh, boyen and goh presented a constant-size ci- phertext hierarchical identity-based encryption (hibe) protocol. our main contribu- tion is to present a variant of the bbg-hibe. the new hibe is proved to be secure (without any degradation) in an extension of the s-id model (denoted the s+-id model) and the components of the identities are from zp,where p is a suitable large prime. the bbg-hibe is proved to be secure in the selective-id (s-id) security model and the components of the identities are from z *p.in the s+-id model the adversary is allowed to vary the length of the challenge identity whereas this is not allowed in the s-id model. the new hibe shares all the good features of the bbg-hibe. the drawback is that the public parameters and the private key are longer than that of the bbg-hibe. we also provide two more extensions of the basic constant-size ciphertext hibe. the first is a constant-size ciphertext hibe secure in the generalised selective-id model m2. the second one is a product construction composed of two hibes and a trade-o. is possible between the private key size and the ciphertext size.