Foundations of homomorphic secret sharing

Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, Stefano Tessaro

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

21 Scopus citations

Abstract

Homomorphic secret sharing (HSS) is the secret sharing analogue of homomorphic encryption. An HSS scheme supports a local evaluation of functions on shares of one or more secret inputs, such that the resulting shares of the output are short. Some applications require the stronger notion of additive HSS, where the shares of the output add up to the output over some finite Abelian group. While some strong positive results for HSS are known under specific cryptographic assumptions, many natural questions remain open. We initiate a systematic study of HSS, making the following contributions. A definitional framework. We present a general framework for defining HSS schemes that unifies and extends several previous notions from the literature, and cast known results within this framework. Limitations. We establish limitations on information-theoretic multi-input HSS with short output shares via a relation with communication complexity. We also show that additive HSS for non-trivial functions, even the AND of two input bits, implies non-interactive key exchange, and is therefore unlikely to be implied by public-key encryption or even oblivious transfer. Applications. We present two types of applications of HSS. First, we construct 2-round protocols for secure multiparty computation from a simple constant-size instance of HSS. As a corollary, we obtain 2-round protocols with attractive asymptotic e ciency features under the Decision Di e Hellman (DDH) assumption. Second, we use HSS to obtain nearly.

Original languageEnglish
Title of host publication9th Innovations in Theoretical Computer Science, ITCS 2018
EditorsAnna R. Karlin
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770606
DOIs
StatePublished - 1 Jan 2018
Event9th Innovations in Theoretical Computer Science, ITCS 2018 - Cambridge, United States
Duration: 11 Jan 201814 Jan 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume94
ISSN (Print)1868-8969

Conference

Conference9th Innovations in Theoretical Computer Science, ITCS 2018
Country/TerritoryUnited States
CityCambridge
Period11/01/1814/01/18

Keywords

  • Communication complexity
  • Cryptography
  • Homomorphic secret sharing
  • Secure computation
  • Worst-case to average case reductions

ASJC Scopus subject areas

  • Software

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