Homomorphic Secret Sharing: Optimizations and Applications

3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We continue the study of Homomorphic Secret Sharing (HSS), recently introduced by Boyle et al. (Crypto 2016, Eurocrypt 2017). A (2-party) HSS scheme splits an input x into shares (x0,x1) such that (1) each share computationally hides x, and (2) there exists an efficient homomorphic evaluation algorithm $\Eval$ such that for any function (or "program") from a given class it holds that Eval(x0,P)+Eval(x1,P)=P(x). Boyle et al. show how to construct an HSS scheme for branching programs, with an inverse polynomial error, using discrete-log type assumptions such as DDH. We make two types of contributions. Optimizations. We introduce new optimizations that speed up the previous optimized implementation of Boyle et al. by more than a factor of 30, significantly reduce the share size, and reduce the rate of leakage induced by selective failure. Applications. Our optimizations are motivated by the observation that there are natural application scenarios in which HSS is useful even when applied to simple computations on short inputs. We demonstrate the practical feasibility of our HSS implementation in the context of such applications.
Document type :
Conference papers

https://hal.inria.fr/hal-01614451
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Submitted on : Tuesday, October 10, 2017 - 10:07:46 PM
Last modification on : Thursday, July 1, 2021 - 5:58:08 PM

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• HAL Id : hal-01614451, version 1

Citation

Elette Boyle, Geoffroy Couteau, Niv Gilboa, Yuval Ishai, Michele Orrù. Homomorphic Secret Sharing: Optimizations and Applications. CCS '17 - ACM SIGSAC Conference on Computer and Communications Security , Oct 2017, Dallas, United States. ⟨hal-01614451⟩

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