How to Construct Quantum FHE, Generically

We construct a (compact) quantum fully homomorphic encryption (QFHE) scheme starting from any (classical) fully homomorphic encryption scheme (with decryption in NC^1) together with a dual-mode trapdoor claw-free function family. Compared to previous constructions (Mahadev, FOCS 2018; Brakerski, CRYPTO 2018) which made non-black-box use of similar underlying primitives, our construction provides a pathway to instantiations from different assumptions. Our construction uses the techniques of Dulek, Schaffner and Speelman (CRYPTO 2016) and shows how to make the client in their QFHE scheme classical using dual-mode trapdoor claw-free functions. As an additional contribution, we show a new instantiation of dual-mode trapdoor claw-free functions from group actions. This is based on joint work with Vinod Vaikuntanathan.