Characterization of secure multiparty computation without broadcast

Ran Cohen, Iftach Haitner, Eran Omri, Lior Rotem

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

11 Scopus citations

Abstract

A major challenge in the study of cryptography is characterizing the necessary and sufficient assumptions required to carry out a given cryptographic task. The focus of this work is the necessity of a broadcast channel for securely computing symmetric functionalities (where all the parties receive the same output) when one third of the parties, or more, might be corrupted. Assuming all parties are connected via a peer-to-peer network, but no broadcast channel (nor a secure setup phase) is available, we prove the following characterization: A symmetric n-party functionality can be securely computed facing n/3≤t<n/2 corruptions (i.e., honest majority), if and only if it is (n−2t) -dominated; a functionality is k-dominated, if any k-size subset of its input variables can be set to determine its output. Assuming the existence of one-way functions, a symmetric n-party functionality can be securely computed facing t≥n/2 corruptions (i.e., no honest majority), if and only if it is 1-dominated and can be securely computed with broadcast. It follows that, in case a third of the parties might be corrupted, broadcast is necessary for securely computing non-dominated functionalities (in which “small” subsets of the inputs cannot determine the output), including, as interesting special cases, the Boolean XOR and coin-flipping functionalities.

Original languageEnglish
Title of host publicationTheory of Cryptography - 13th International Conference, TCC 2016-A, Proceedings
EditorsEyal Kushilevitz, Tal Malkin
PublisherSpringer Verlag
Pages596-616
Number of pages21
ISBN (Print)9783662490952
DOIs
StatePublished - 2016
Event13th International Conference on Theory of Cryptography, TCC 2016 - Tel Aviv, Israel
Duration: 10 Jan 201613 Jan 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9562
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Theory of Cryptography, TCC 2016
Country/TerritoryIsrael
CityTel Aviv
Period10/01/1613/01/16

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2016.

Keywords

  • Broadcast
  • Coin flipping
  • Fairness
  • Impossibility result
  • Multiparty computation
  • Point-to-point communication

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