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A fully homomorphic encryption scheme
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CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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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.) 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.