Function-Hiding Inner Product Encryption

We extend the reach of functional encryption schemes that are provably secure under simpleassumptions against unbounded collusion to include function-hiding inner product schemes.Our scheme is a private key functional encryption scheme, where ciphertexts correspond tovectors ~x, secret keys correspond to vectors ~y, and a decryptor learns 〈~x, ~y〉. Our schemeemploys asymmetric bilinear maps and relies only on the SXDH assumption to satisfy a naturalindistinguishability-based security notion where arbitrarily many key and ciphertext vectorscan be simultaneously changed as long as the key-ciphertext dot product relationships are allpreserved.