Fully Secure Functional Encryption with General Relations from the Decisional Linear Assumption

This paper presents a fully secure functional encryption scheme for a wide class of relations, that are specified by non-monotone access structures combined with inner-product relations. The security is proven under a standard assumption, the decisional linear (DLIN) assumption, in the standard model. The proposed functional encryption scheme covers, as special cases, (1) key-policy, ciphertext-policy and unified-policy (of key and ciphertext policies) attribute-based encryption with non-monotone access structures, and (2) (hierarchical) predicate encryption with inner-product relations and functional encryption with non-zero inner-product relations. ∗An extended abstract was presented at Advances in Cryptology – CRYPTO 2010, LNCS 6223, pages 191-208. This is the full paper.