On the complexity of fair coin flipping

Iftach Haitner*, Nikolaos Makriyannis, Eran Omri

*Corresponding author for this work

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

11 Scopus citations

Abstract

A two-party coin-flipping protocol is ε -fair if no efficient adversary can bias the output of the honest party (who always outputs a bit, even if the other party aborts) by more than ε. Cleve [STOC ’86] showed that r-round o(1 / r)-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript ’85] constructed a Θ(1/r) -fair coin-flipping protocol, assuming the existence of one-way functions. Moran et al. [Journal of Cryptology ’16] constructed an r-round coin-flipping protocol that is Θ(1 / r) -fair (thus matching the aforementioned lower bound of Cleve [STOC ’86]), assuming the existence of oblivious transfer. The above gives rise to the intriguing question of whether oblivious transfer, or more generally “public-key primitives”, is required for an o(1/r) -fair coin flipping. This question was partially answered by Dachman-Soled et al. [TCC ’11] and Dachman-Soled et al. [TCC ’14], who showed that restricted types of fully black-box reductions cannot establish o(1/r) -fair coin-flipping protocols from one-way functions. In particular, for constant-round coin-flipping protocols, [10] yields that black-box techniques from one-way functions can only guarantee fairness of order 1/r. We make progress towards answering the above question by showing that, for any constant, the existence of an 1/(c·r) -fair, r-round coin-flipping protocol implies the existence of an infinitely-often key-agreement protocol, where c denotes some universal constant (independent of r). Our reduction is non black-box and makes a novel use of the recent dichotomy for two-party protocols of Haitner et al. [FOCS ’18] to facilitate a two-party variant of the attack of Beimel et al. [FOCS ’18] on multi-party coin-flipping protocols.

Original languageEnglish
Title of host publicationTheory of Cryptography - 16th International Conference, TCC 2018, Proceedings
EditorsAmos Beimel, Stefan Dziembowski
PublisherSpringer Verlag
Pages539-562
Number of pages24
ISBN (Print)9783030038069
DOIs
StatePublished - 2018
Event16th Theory of Cryptography Conference, TCC 2018 - Panaji, India
Duration: 11 Nov 201814 Nov 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11239 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th Theory of Cryptography Conference, TCC 2018
Country/TerritoryIndia
CityPanaji
Period11/11/1814/11/18

Funding

FundersFunder number
European Research Council638121
Israel Science Foundation152/17

    Keywords

    • Coin-flipping
    • Fairness
    • Key-agreement

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