Abstract: Fully Homomorphic Encryption schemes (FHEs) and Functional Encryption schemes (FunctEs) have a tremendous impact in Cryptography both for the natural questions that they address and for the wide range of applications in which they have been (sometimes critically) used. In this work we put forth the notion of a Controllable Homomorphic Encryption Scheme (CHES), a new primitive that includes features of both FHEs and FunctEs. In a CHES it is possible (similarly to a FHE) to homomorphically evaluate a ciphertext Ct = Enc(m) and a circuit C therefore obtaining Enc(C(m)) but only if (similarly to a FunctE) a token for C has been received from the owner of the secret key. We discuss difficulties in constructing a CHES and then show a construction based on any FunctE.
Status: Submitted to PKC 14. Currently under revision.