How to Construct Quantum FHE, Generically

TL;DR

This paper presents a new method for constructing quantum fully homomorphic encryption schemes using classical FHE and dual-mode trapdoor functions, enabling more flexible instantiations from various assumptions.

Contribution

It introduces a generic construction of quantum FHE from classical FHE and dual-mode trapdoor functions, including a novel instantiation from group actions.

Findings

Provides a pathway for instantiations from different assumptions.

Shows how to make the client in a QFHE scheme classical.

Introduces a new instantiation of dual-mode trapdoor functions from group actions.

Abstract

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