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Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Abstract : At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. The main appeal of this scheme (compared to Gentry’s) is its conceptual simplicity. This simplicity comes at the expense of a public key size in O~(λ10) which is too large for any practical system. In this paper we reduce the public key size to O~(λ7) by encrypting with a quadratic form in the public key elements, instead of a linear form. We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al. We also describe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry’s scheme, we obtain roughly the same level of efficiency. This shows that fully homomorphic encryption can be implemented using simple arithmetic operations.
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Submitted on : Tuesday, January 27, 2015 - 4:44:09 PM
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Jean-Sébastien Coron, Avradip Mandal, David Naccache, Mehdi Tibouchi. Fully Homomorphic Encryption over the Integers with Shorter Public Keys. CRYPTO 2011 - 31st Annual Cryptology Conference, Aug 2011, Santa Barbara, CA, United States. pp.487-504, ⟨10.1007/978-3-642-22792-9_28⟩. ⟨hal-01110216⟩



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