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Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

Abstract : We describe a compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan’s (DGHV) fully homomorphic scheme over the integers from O~(λ^7) to O~(λ^5). Our variant remains semantically secure, but in the random oracle model. We obtain an implementation of the full scheme with a 10.1 MB public key instead of 802 MB using similar parameters as in [7]. Additionally we show how to extend the quadratic encryption technique of [7] to higher degrees, to obtain a shorter public-key for the basic scheme. This paper also describes a new modulus switching technique for the DGHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with the DGHV scheme. Finally we describe an improved attack against the Approximate GCD Problem on which the DGHV scheme is based, with complexity O~(2^ρ) instead of O~(2^3ρ/2).
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https://hal.inria.fr/hal-01111541
Contributor : Brigitte Briot <>
Submitted on : Friday, January 30, 2015 - 3:14:37 PM
Last modification on : Thursday, July 1, 2021 - 5:58:06 PM

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Jean-Sébastien Coron, David Naccache, Mehdi Tibouchi. Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers. EUROCRYPT 2012 - 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Apr 2012, Cambridge, UK, United Kingdom. pp.446-464, ⟨10.1007/978-3-642-29011-4_27⟩. ⟨hal-01111541⟩

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