Constant Size Hierarchical Identity-Based Encryption Tightly Secure in the Full Model without Random Oracles

We present a new hierarchical identity-based encryption (HIBE) system where the cipher text size as well as the decryption cost are independent of the hierarchy depth. Most interestingly, our scheme is fully secure in the standard model and has a tight security reduction. The underlying assumption of our system is a variant of Boneh et al.´s decisional bilinear Diffie-Hellman exponent assumption, which has been used to construct several elegant cryptosystems. Our assumption is new and non-standard. However, it is worth noting that, unlike those used in some (H)IBE systems, our assumption is fixed and does not become stronger as the hierarchy depth or the number of the private key queries increases.