FHE Circuit Privacy Almost for Free

Florian Bourse 1, 2, 3, 4 Rafaël del Pino 1, 2, 3, 4 Michele Minelli 1, 2, 3, 4 Hoeteck Wee 1, 2, 3, 4
Abstract : Circuit privacy is an important property for many applications of fully homomorphic encryption. Prior approaches for achieving circuit privacy rely on superpolynomial noise flooding or on bootstrapping. In this work, we present a conceptually different approach to circuit privacy based on a novel characterization of the noise growth amidst homomorphic evaluation. In particular, we show that a variant of the GSW FHE for branching programs already achieves circuit privacy; this immediately yields a circuit-private FHE for NC1 circuits under the standard LWE assumption with polynomial modulus-to-noise ratio. Our analysis relies on a variant of the discrete Gaussian leftover hash lemma which states that e G −1 (v) + small noise does not depend on v. We believe that this result is of independent interest.
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https://hal.inria.fr/hal-01360110
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Submitted on : Monday, September 5, 2016 - 1:56:59 PM
Last modification on : Saturday, December 7, 2019 - 1:35:29 AM
Long-term archiving on: Tuesday, December 6, 2016 - 1:16:21 PM

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Florian Bourse, Rafaël del Pino, Michele Minelli, Hoeteck Wee. FHE Circuit Privacy Almost for Free. Crypto 2016 - 36th Annual International Cryptology Conference, Aug 2016, Santa Barbara, United States. ⟨10.1007/978-3-662-53008-5_3⟩. ⟨hal-01360110⟩

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