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)

1 PSL - Université Paris Sciences et Lettres
2 ENS-PSL - École normale supérieure - Paris
3 CNRS - Centre National de la Recherche Scientifique
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities

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.

Mots clés: Homomorphic Encryption; Circuit Privacy; Branching Program; Noise Flooding; Learning With Errors; Rerandomization

Domaines: Cryptographie et sécurité [cs.CR]

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⟩