Lattice-based FHE as secure as PKE
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V_Lattice-based.pdf
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Author(s)
Brakerski, Zvika
Vaikuntanathan, Vinod
Date Issued
January 2014
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
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.)
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/2554797.2554799
