Lattice-based FHE as secure as PKE

Author(s)
Brakerski, Zvika; Vaikuntanathan, Vinod
Thumbnail
DownloadV_Lattice-based.pdf (406.8Kb)
OPEN_ACCESS_POLICY
Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of O(n[superscript 1.5+ε])-approximation for lattice problems (such as GapSVP) under quantum reductions for any ε ⟩ 0 (or O(n[superscript 2+ε])-approximation under classical reductions). This matches the best known hardness for "regular" (non-homomorphic) lattice based public-key encryption up to the ε factor. A number of previous methods had hit a roadblock at quasipolynomial approximation. (As usual, a circular security assumption can be used to achieve a non-leveled FHE scheme.)
Date issued
2014-01
URI
http://hdl.handle.net/1721.1/90959
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Proceedings of the 5th Conference on Innovations in Theoretical Computer Science - ITCS '14
Publisher
Association for Computing Machinery
Citation
Brakerski, Zvika, and Vinod Vaikuntanathan. “Lattice-Based FHE as Secure as PKE.” Proceedings of the 5th Conference on Innovations in Theoretical Computer Science - ITCS ’14 January 12–14, 2014, Princeton, New Jersey, USA. ACM, p.1-12.
Version: Author's final manuscript
ISBN
9781450326988
Collections