Characterization of Secure Multiparty Computation Without Broadcast

Ran Cohen*, Iftach Haitner, Eran Omri, Lior Rotem

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 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 point-to-point 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 ≤ tOpenSPiltSPi n/ 2 corruptions (i.e., honest majority), if and only if it is (n- 2 t) -dominated; a functionality is k-dominated, if anyk-size subset of its input variables can be set to determine its output to some predetermined value.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
Pages (from-to)587-609
Number of pages23
JournalJournal of Cryptology
Volume31
Issue number2
DOIs
StatePublished - 1 Apr 2018

Funding

FundersFunder number
Check Point Institute for Information Security544/13
National Cyber Bureau of Israel
Horizon 2020 Framework Programme638121
European Research Council
Ministry of Science, Technology and Space
United States-Israel Binational Science Foundation2010196
Israel Science Foundation189/11, 1076/11
Israeli Centers for Research Excellence

    Keywords

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

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