International Association
for Cryptologic Research

We construct a (compact) quantum fully homomorphic encryption (QFHE) scheme starting from {\em any} (classical) fully homomorphic encryption scheme (with decryption in $\mathsf{NC}^{1}$) 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 claw-free trapdoor functions. As an additional contribution, we show a new instantiation of dual-mode trapdoor claw-free functions from group actions.