How to Construct Quantum FHE, Generically

Aparna Gupte; Vinod Vaikuntanathan

Paper 2024/893

How to Construct Quantum FHE, Generically

Aparna Gupte, Massachusetts Institute of Technology

Vinod Vaikuntanathan, Massachusetts Institute of Technology

Abstract

We construct a (compact) quantum fully homomorphic encryption (QFHE) scheme starting from any (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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: A major revision of an IACR publication in CRYPTO 2024
Keywords: quantum fully homomorphic encryption learning with errors group actions
Contact author(s): agupte @ mit edu
vinodv @ mit edu
History: 2024-06-05: approved; 2024-06-04: received; See all versions
Short URL: https://ia.cr/2024/893
License: CC BY

BibTeX

@misc{cryptoeprint:2024/893,
      author = {Aparna Gupte and Vinod Vaikuntanathan},
      title = {How to Construct Quantum {FHE}, Generically},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/893},
      year = {2024},
      url = {https://eprint.iacr.org/2024/893}
}