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This paper presents a heuristic attack on the fully homomorphic encryption over the integers by using lattice reduction algorithm. The authors' result shows that the FHE in [DGHV10] is not secure for some parameter settings. They also present an improvement scheme to avoid the lattice attack in this paper. Rivest, Adleman and Dertouzos introduced a notion of privacy homomorphism. But until 2009, Gentry constructed the first fully homomorphic encryptions based on ideal lattice, all previous schemes are insecure.
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