Welcome to the resource topic for 2011/441
Title:
Fully Homomorphic Encryption over the Integers with Shorter Public Keys
Authors: Jean-Sebastien Coron, Avradip Mandal, David Naccache, Mehdi Tibouchi
Abstract:At Eurocrypt 2010 van Dijk {\sl 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 {\cal \tilde O}(\lambda^{10}) which is too large for any practical system. In this paper we reduce the public key size to {\cal \tilde O}(\lambda^{7}) 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 {\sl 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.
ePrint: https://eprint.iacr.org/2011/441
Talk: https://www.youtube.com/watch?v=yaEf3C6Pvm4
Slides: http://www.iacr.org/cryptodb/archive/2011/CRYPTO/presentation/09-1-Tibouchi.pdf
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