Gentry proposed a fully homomorphic public key encryption scheme that uses ideal lattices. He based the security of his scheme on the hardness of two problems: an average-case decision problem over ideal lattices, and the sparse (or "low-weight") subset sum problem (SSSP). We provide a key generation algorithm for Gentry's scheme that generates ideal lattices according to a "nice" average-case distribution. Then, we prove a worst-case / average-case connection that bases Gentry's scheme (in part) on the quantum hardness of the shortest independent vector problem (SIVP) over ideal lattices in the worst-case. (We cannot remove the need to assume that the SSSP is hard.) Our worst-case / average-case connection is the first where the average-case lattice is an ideal lattice, which seems to be necessary to support the security of Gentry's scheme. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Gentry, C. (2010). Toward basing fully homomorphic encryption on worst-case hardness. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6223 LNCS, pp. 116–137). https://doi.org/10.1007/978-3-642-14623-7_7
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