Conference on Innovations in Theoretical Computer Science

Lattice-based FHE as secure as PKE

Zvika Brakerski, Vinod Vaikuntanathan

Published Jan 12, 2014• 272 citations

Abstract

We show that (leveled) fully homomorphic encryption (FHE) can be based on the hardness of O(n1.5+ε)-approximation for lattice problems (such as GapSVP) under quantum reductions for any ε 〉 0 (or O(n2+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.)

DOI: 10.1145/2554797.2554799

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