A lower bound for adaptively-secure collective coin-flipping protocols

Yael Tauman Kalai; Ilan Komargodski; Ran Raz

doi:10.4230/LIPIcs.DISC.2018.34

A lower bound for adaptively-secure collective coin-flipping protocols

Yael Tauman Kalai, Ilan Komargodski, Ran Raz

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

In 1985, Ben-Or and Linial (Advances in Computing Research’89) introduced the collective coin-flipping problem, where n parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party in the course of the protocol as a function of the messages seen so far. They showed that the majority protocol, in which each player sends a random bit and the output is the majority value, tolerates O(n) adaptive corruptions. They conjectured that this is optimal for such adversaries. We prove that the majority protocol is optimal (up to a poly-logarithmic factor) among all protocols in which each party sends a single, possibly long, message. Previously, such a lower bound was known for protocols in which parties are allowed to send only a single bit (Lichtenstein, Linial, and Saks, Combinatorica’89), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP’15).

Original language	English
Title of host publication	32nd International Symposium on Distributed Computing, DISC 2018
Editors	Ulrich Schmid, Josef Widder
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959770927
DOIs	https://doi.org/10.4230/LIPIcs.DISC.2018.34
State	Published - 1 Oct 2018
Externally published	Yes
Event	32nd International Symposium on Distributed Computing, DISC 2018 - New Orleans, United States Duration: 15 Oct 2018 → 19 Oct 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	121
ISSN (Print)	1868-8969

Conference

Conference	32nd International Symposium on Distributed Computing, DISC 2018
Country/Territory	United States
City	New Orleans
Period	15/10/18 → 19/10/18

Bibliographical note

Publisher Copyright:
© Yael T. Kalai, Ilan Komargodski, and Ran Raz.

Keywords

Adaptive corruptions
Byzantine faults
Coin flipping
Lower bound

Access to Document

10.4230/LIPIcs.DISC.2018.34

Cite this

Kalai, Y. T., Komargodski, I., & Raz, R. (2018). A lower bound for adaptively-secure collective coin-flipping protocols. In U. Schmid, & J. Widder (Eds.), 32nd International Symposium on Distributed Computing, DISC 2018 Article 34 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 121). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.DISC.2018.34

Kalai, Yael Tauman ; Komargodski, Ilan ; Raz, Ran. / A lower bound for adaptively-secure collective coin-flipping protocols. 32nd International Symposium on Distributed Computing, DISC 2018. editor / Ulrich Schmid ; Josef Widder. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).

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abstract = "In 1985, Ben-Or and Linial (Advances in Computing Research{\textquoteright}89) introduced the collective coin-flipping problem, where n parties communicate via a single broadcast channel and wish to generate a common random bit in the presence of adaptive Byzantine corruptions. In this model, the adversary can decide to corrupt a party in the course of the protocol as a function of the messages seen so far. They showed that the majority protocol, in which each player sends a random bit and the output is the majority value, tolerates O(n) adaptive corruptions. They conjectured that this is optimal for such adversaries. We prove that the majority protocol is optimal (up to a poly-logarithmic factor) among all protocols in which each party sends a single, possibly long, message. Previously, such a lower bound was known for protocols in which parties are allowed to send only a single bit (Lichtenstein, Linial, and Saks, Combinatorica{\textquoteright}89), or for symmetric protocols (Goldwasser, Kalai, and Park, ICALP{\textquoteright}15).",

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Kalai, YT, Komargodski, I & Raz, R 2018, A lower bound for adaptively-secure collective coin-flipping protocols. in U Schmid & J Widder (eds), 32nd International Symposium on Distributed Computing, DISC 2018., 34, Leibniz International Proceedings in Informatics, LIPIcs, vol. 121, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 32nd International Symposium on Distributed Computing, DISC 2018, New Orleans, United States, 15/10/18. https://doi.org/10.4230/LIPIcs.DISC.2018.34

A lower bound for adaptively-secure collective coin-flipping protocols. / Kalai, Yael Tauman; Komargodski, Ilan; Raz, Ran.
32nd International Symposium on Distributed Computing, DISC 2018. ed. / Ulrich Schmid; Josef Widder. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 34 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 121).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kalai YT, Komargodski I, Raz R. A lower bound for adaptively-secure collective coin-flipping protocols. In Schmid U, Widder J, editors, 32nd International Symposium on Distributed Computing, DISC 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 34. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.DISC.2018.34

A lower bound for adaptively-secure collective coin-flipping protocols

Abstract

Publication series

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Bibliographical note

Keywords

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