Anonymous HIBE: Compact construction over prime-order groups

We present an anonymous hierarchical identity based encryption (HIBE) scheme that not only achieves constant-size ciphertext, but also works in bilinear groups with prime order. In contrast to our work, all previous anonymous HIBE schemes either have ciphertext size linear in the depth of the hierarchy or work in bilinear groups with a composite order. Our construction is more efficient than previous schemes in terms of ciphertext size and decryption cost.We give provable security of our construction, consisting of confidentiality and anonymity, without random oracles. To gain anonymity, we introduce a novel and simple method called "double exponent" technique, which gives an anonymous HIBE scheme more compact than the result at CRYPTO2006. Our method is quite general in that it works on both symmetric and asymmetric bilinear maps. The simple method might also be of independent interest to gain anonymity of attributes in constructing searchable encryption schemes on encrypted data.