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 multi-key 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 homomorphically 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.