Cryptology ePrint Archive: Report 2018/419

Homomorphic Secret Sharing: Optimizations and Applications

Elette Boyle and Geoffroy Couteau and Niv Gilboa and Yuval Ishai and Michele Orrù

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”) P 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.

Category / Keywords: cryptographic protocols / Homomorphic secret sharing, secure computation, applications

Original Publication (with major differences): CCS '17 Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security

Date: received 7 May 2018, last revised 11 May 2018

Contact author: geoffroy couteau at kit edu

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Version: 20180511:073505 (All versions of this report)

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