Adaptively attribute-hiding (hierarchical) inner product encryption

This paper proposes the first (practical) inner product encryption (IPE) scheme that is adaptively secure and fully attribute-hiding (attribute-hiding in the sense of the definition by Katz, Sahai and Waters), while the existing (practical) IPE schemes are either fully attribute-hiding but selectively secure or adaptively secure but weakly attribute-hiding. The proposed IPE scheme is proven to be adaptively secure and fully attributehiding under the decisional linear assumption in the standard model. The IPE scheme is comparably as efficient as the existing (practical) attributehiding IPE schemes. We also present a variant of the proposed IPE scheme with the same security that achieves shorter public and secret keys. A hierarchical IPE scheme can be constructed that is also adaptively secure and fully attribute-hiding under the same assumption. In this paper, we extend the dual system encryption technique by Waters into a more general manner, in which new forms of ciphertext and secret keys are employed and new types of information theoretical tricks are introduced along with several forms of computational reduction.