Group-based secure computation: Optimizing rounds, communication, and computation

Elette Boyle, Niv Gilboa, Yuval Ishai

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

38 Scopus citations

Abstract

A recent work of Boyle et al. (Crypto 2016) suggests that “group-based” cryptographic protocols, namely ones that only rely on a cryptographically hard (Abelian) group, can be surprisingly powerful. In particular, they present succinct two-party protocols for securely computing branching programs and NC1 circuits under the DDH assumption, providing the first alternative to fully homomorphic encryption. In this work we further explore the power of group-based secure computation protocols, improving both their asymptotic and concrete efficiency. We obtain the following results. – Black-box use of group. We modify the succinct protocols of Boyle et al. so that they only make a black-box use of the underlying group, eliminating an expensive non-black-box setup phase. – Round complexity. For any constant number of parties, we obtain 2-round MPC protocols based on a PKI setup under the DDH assumption. Prior to our work, such protocols were only known using fully homomorphic encryption or indistinguishability obfuscation. – Communication complexity. Under DDH, we present a secure 2- party protocol for any NC1 or log-space computation with n input bits and m output bits using n + (1 + o(1))m + poly(λ) bits of communication, where λ is a security parameter. In particular, our protocol can generate n instances of bit-oblivious-transfer using (4 + o(1)) · n bits of communication. This gives the first constant-rate OT protocol under DDH. – Computation complexity. We present several techniques for improving the computational cost of the share conversion procedure of Boyle et al., improving the concrete efficiency of group-based protocols by several orders of magnitude.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsJean-Sebastien Coron, Jesper Buus Nielsen
PublisherSpringer Verlag
Pages163-193
Number of pages31
ISBN (Print)9783319566139
DOIs
StatePublished - 1 Jan 2017
Event36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2017 - Paris, France
Duration: 30 Apr 20174 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10211 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2017
Country/TerritoryFrance
City Paris
Period30/04/174/05/17

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