Chosen-Ciphertext Secure Fully Homomorphic Encryption

We give three fully homomoprhic encryption (FHE) schemes that are secure against non-adaptive chosen ciphertext attacks (CCA1). For the first two, we extend the generic transformation of Boneh, Canetti, Halevi and Katz to turn any multi-key identity-based FHE scheme into a CCA1-secure FHE scheme. We then show two instantiations of multikey identity-based FHE: One from LWE in the random oracle model, and one from sub-exponentially secure indistinguishability obfuscation. Both constructions are compact with respect to the function evaluated homo-morphically but not compact with respect to the number of ciphertext involved in the homomorphic evaluation. The third scheme uses succinct non-interactive arguments of knowledge (SNARKs) and is fully compact.