Function-Hiding Inner Product Encryption.

We extend the reach of functional encryption schemes that are provably secure under simple assumptions against unbounded collusion to include function-hiding inner product schemes. Our scheme is a private key functional encryption scheme, where ciphertexts correspond to vectors $$\\vec {x}$$, secret keys correspond to vectors $$\\vec {y}$$, and a decryptor learns $$\\langle \\vec {x}, \\vec {y} \\rangle $$. Our scheme employs asymmetric bilinear maps and relies only on the SXDH assumption to satisfy a natural indistinguishability-based security notion where arbitrarily many key and ciphertext vectors can be simultaneously changed as long as the key-ciphertext dot product relationships are all preserved.