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Paper 2013/541

Lattice-Based FHE as Secure as PKE

Zvika Brakerski and Vinod Vaikuntanathan

Abstract

We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of $\otild(n^{1.5+\epsilon})$-approximation for lattice problems (such as GapSVP) under quantum reductions for any $\epsilon>0$ (or $\otild(n^{2+\epsilon})$-approximation under classical reductions). This matches the best known hardness for ``regular'' (non-homomorphic) lattice based public-key encryption up to the $\epsilon$ 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.) Our approach consists of three main ideas: Noise-bounded sequential evaluation of high fan-in operations; Circuit sequentialization using Barrington's Theorem; and finally, successive dimension-modulus reduction.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
public key encryptionfully homomorphic encryptionlattice based cryptographyLWE
Contact author(s)
zvika brakerski @ weizmann ac il
History
2013-08-30: received
Short URL
https://ia.cr/2013/541
License
Creative Commons Attribution
CC BY
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