Practical Inner Product Encryption with Constant Private Key

Inner product encryption, first introduced by Katz et al., is a type of predicate encryption in which a ciphertext and a private key correspond to an attribute vector and a predicate vector, respectively. Only if the attribute and predicate vectors satisfy the inner product predicate will the decryption in this scheme be correct. In addition, the ability to use inner product encryption as an underlying building block to construct other useful cryptographic primitives has been demonstrated in the context of anonymous identity-based encryption and hidden vector encryption. However, the computing cost and communication cost of performing inner product encryption are very high at present. To resolve this problem, we introduce an efficient inner product encryption approach in this work. Specifically, the size of the private key is only one G element and one Zp element, and decryption requires only one pairing computation. The formal security proof and implementation result are also demonstrated. Compared with other state-of-the-art schemes, our scheme is the most efficient in terms of the number of pairing computations for decryption and the private key length.