Strongly full-hiding inner product encryption

Functional encryption (FE) is a noble cryptographic paradigm which enables delegation of computations on private sensitive data to external untrustworthy entities. In FE, it is possible to derive restricted decryption keys, also called functional keys, corresponding to specific functions from a master secret key. Such a functional key allows the evaluation of its associated functionality on encrypted data-items, but does not help to extract any additional information about the encrypted data. While confidentiality of the encrypted data is the prime security concern in FE, various scenarios of computation delegation, especially when the delegated functionalities themselves involve sensitive informations, privacy must also be ensured for the functions embedded within the issued functional keys. This paper presents a non-generic and simple private key FE scheme for the inner product functionality, also known as inner product encryption (IPE). In contrast to other similar constructions, our IPE scheme achieves the strongest indistinguishability-based notion of combined data and function privacy in the private key setting, termed as the full-hiding security, in the standard model without employing any heavy-duty cryptographic tool or non-standard complexity assumption. Our construction is built in the asymmetric bilinear pairing group setting of prime order. The security of our scheme is based on the well-studied Symmetric External Diffie-Hellman (SXDH) assumption.