A Complete Characterization of Game-Theoretically Fair, Multi-Party Coin Toss

Ke Wu, Gilad Asharov, Elaine Shi

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

2 Scopus citations

Abstract

Cleve’s celebrated lower bound (STOC’86) showed that a de facto strong fairness notion is impossible in 2-party coin toss, i.e., the corrupt party always has a strategy of biasing the honest party’s outcome by a noticeable amount. Nonetheless, Blum’s famous coin-tossing protocol (CRYPTO’81) achieves a strictly weaker “game-theoretic” notion of fairness—specifically, it is a 2-party coin toss protocol in which neither party can bias the outcome towards its own preference; and thus the honest protocol forms a Nash equilibrium in which neither party would want to deviate. Surprisingly, an n-party analog of Blum’s famous coin toss protocol was not studied till recently. The work by Chung et al. (TCC’18) was the first to explore the feasibility of game-theoretically fair n-party coin toss in the presence of corrupt majority. We may assume that each party has a publicly stated preference for either the bit 0 or 1, and if the outcome agrees with the party’s preference, it obtains utility 1; else it obtains nothing. A natural game-theoretic formulation is to require that the honest protocol form a coalition-resistant Nash equilibrium, i.e., no coalition should have incentive to deviate from the honest behavior. Chung et al. phrased this game-theoretic notion as “cooperative-strategy-proofness” or “CSP-fairness” for short. Unfortunately, Chung et al. showed that under (n- 1 ) -sized coalitions, it is impossible to design such a CSP-fair coin toss protocol, unless all parties except one prefer the same bit. In this paper, we show that the impossibility of Chung et al. is in fact not as broad as it may seem. When coalitions are majority but not n- 1 in size, we can indeed get feasibility results in some meaningful parameter regimes. We give a complete characterization of the regime in which CSP-fair coin toss is possible, by providing a matching upper- and lower-bound. Our complete characterization theorem also shows that the mathematical structure of game-theoretic fairness is starkly different from the de facto strong fairness notion in the multi-party computation literature.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings
EditorsOrr Dunkelman, Stefan Dziembowski
PublisherSpringer Science and Business Media Deutschland GmbH
Pages120-149
Number of pages30
ISBN (Print)9783031069437
DOIs
StatePublished - 2022
Event41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022 - Trondheim, Norway
Duration: 30 May 20223 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13275 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022
Country/TerritoryNorway
CityTrondheim
Period30/05/223/06/22

Bibliographical note

Publisher Copyright:
© 2022, International Association for Cryptologic Research.

Funding

Acknowledgments. This work is in part supported by NSF under the award numbers CNS-1601879 and CNS-1561209, a Packard Fellowship, an ONR YIP award, a DARPA SIEVE grant, by the Israel Science Foundation (grant No. 2439/20), by JPM Faculty Research Award, and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 891234.

FundersFunder number
BIU Center for Research in Applied Cryptography
Marie Sk lodowska-Curie
National Science FoundationCNS-1561209, CNS-1601879
Office of Naval Research
Defense Advanced Research Projects Agency
JPMorgan Chase and Company
Horizon 2020 Framework Programme891234
Israel Science Foundation2439/20

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