Efficient (Hierarchical) inner-product encryption tightly reduced from the decisional linear assumption

This paper proposes an inner-product encryption (IPE) scheme, which achieves selectively fully-attribute-hiding security in the standard model almost tightly reduced from the decisional linear (DLIN) assumption, and whose ciphertext is almost the shortest among the existing (weakly/fully) attribute-hiding IPE schemes, i.e., it consists of n + 4 elements of G and 1 element of Gr for a prime-order symmetric bilinear group (G, Gr), where n is the dimension of attribute/predicate vectors. We also present a variant of the proposed IPE scheme that enjoys shorter public and secret keys with preserving the security. A hierarchical IPE (HIPE) scheme can be realized that has short ciphertexts and selectively fully-attribute-hiding security almost tightly reduced from the DLIN assumption.