Maliciously Circuit-Private FHE

We present a framework for transforming FHE (fully homomorphic encryption) schemes with no circuit privacy requirements into maliciously circuit-private FHE. That is, even if both maliciously formed public key and ciphertext are used, encrypted outputs only reveal the evaluation of the circuit on some well-formed input

x

*

. Previous literature on FHE only considered semi-honest circuit privacy. Circuit-private FHE schemes have direct applications to computing on encrypted data. In that setting, one party (a receiver) holding an input

x

wishes to learn the evaluation of a circuit

C

held by another party (a sender). The goal is to make receiver’s work sublinear (and ideally independent) of

$\left\lvert C \right\rvert $

, using a 2-message protocol. The transformation technique may be of independent interest, and have various additional applications. The framework uses techniques akin to Gentry’s bootstrapping and conditional disclosure of secrets (CDS [AIR01]) combining a non circuit private FHE scheme, with a homomorphic encryption (HE) scheme for a smaller class of circuits which is maliciously circuit-private. We devise the first known circuit private FHE, by instantiating our framework by various (standard) FHE schemes from the literature.