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Toward basing fully homomorphic encryption on worst-case hardness. (English) Zbl 1280.94059
Rabin, Tal (ed.), Advances in cryptology - CRYPTO 2010. 30th annual cryptology conference, Santa Barbara, CA, USA, August 15–19, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14622-0/pbk). Lecture Notes in Computer Science 6223, 116-137 (2010).
Summary: 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.
For the entire collection see [Zbl 1194.94022].

MSC:
94A60 Cryptography
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