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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Fully Homomophic Encryption over the Integers Revisited
verfasst von : Jung Hee Cheon, Damien Stehlé
Erschienen in: Advances in Cryptology -- EUROCRYPT 2015
Verlag: Springer Berlin Heidelberg
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Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev’s Learning With Errors problem (
$$\mathrm {LWE}$$
) and Howgrave-Graham’s Approximate Greatest Common Divisor problem (
$$\mathrm {AGCD}$$
). Our first contribution is a reduction from
$$\mathrm {LWE}$$
to
$$\mathrm {AGCD}$$
. As a second contribution, we describe a new
$$\mathrm {AGCD}$$
-based fully homomorphic encryption scheme, which outperforms all prior
$$\mathrm {AGCD}$$
-based proposals: its security does not rely on the presumed hardness of the so-called Sparse Subset Sum problem, and the bit-length of a ciphertext is only
$$\widetilde{O}(\lambda )$$
, where
$$\lambda $$
refers to the security parameter.