Functional Encryption for Inner Product with Full Function Privacy

Functional encryption (FE) supports constrained decryption keys that allow decrypters to learn specific functions of encrypted messages. In numerous practical applications of FE, confidentiality must be assured not only for the encrypted data but also for the functions for which functional keys are provided. This paper presents a non-generic simple private key FE scheme for the inner product functionality, also known as inner product encryption (IPE). In contrast to the existing similar schemes, our construction achieves the strongest indistinguishability-based notion of function privacy in the private key setting without employing any computationally expensive 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.