Obfuscating Many-to-one Functional Re-encryption, and its Connection to Fully-Homomorphic Encryption

Following up on its first construction by Gentry (STOC 2009), fully-homomorphic encryption (FHE) has generated a multitude of different works, seeking both for new theoretical approaches as well as for more efficient instantiations. All existing FHE schemes, however, are tightly connected to specific assumptions, and no generic constructions are known. In this paper, we investigate generic constructions of FHE. Specifically, we introduce a new primitive, called Many-to-One Functional Re-encryption, which allows, given multiple messages encrypted under a public key for one encryption scheme, to produce an encryption of a function of these messages under another key— possibly for a different encryption scheme. We introduce a new notion of obfuscation for many-to-one functional re-encryption, and show that such obfuscation yields a generic transformation from a semantically-secure encryption scheme to leveled FHE. We further demonstrate that existing FHE schemes (both those that employ bootstrapping and relinearization) can be viewed as instantiations of this paradigm.