An Optimally Fair Coin Toss View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-02-21

AUTHORS

Tal Moran, Moni Naor, Gil Segev

ABSTRACT

We address one of the foundational problems in cryptography: the bias of coin-flipping protocols. Coin-flipping protocols allow mutually distrustful parties to generate a common unbiased random bit, guaranteeing that even if one of the parties is malicious, it cannot significantly bias the output of the honest party. A classical result by Cleve (Proceedings of the 18th annual ACM symposium on theory of computing, pp 364–369, 1986) showed that for any two-party r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}-round coin-flipping protocol there exists an efficient adversary that can bias the output of the honest party by Ω(1/r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega (1/r)$$\end{document}. However, the best previously known protocol only guarantees O(1/r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(1/\sqrt{r})$$\end{document} bias, and the question of whether Cleve’s bound is tight has remained open for more than 20 years. In this paper, we establish the optimal trade-off between the round complexity and the bias of two-party coin-flipping protocols. Under standard assumptions (the existence of oblivious transfer), we show that Cleve’s lower bound is tight: We construct an r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r$$\end{document}-round protocol with bias O(1/r)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(1/r)$$\end{document}. More... »

PAGES

491-513

References to SciGraph publications

  • 2003-06. Parallel Coin-Tossing and Constant-Round Secure Two-Party Computation in JOURNAL OF CRYPTOLOGY
  • 2000-01. Security and Composition of Multiparty Cryptographic Protocols in JOURNAL OF CRYPTOLOGY
  • 1991-01. Bit commitment using pseudorandomness in JOURNAL OF CRYPTOLOGY
  • <error retrieving object. in <ERROR RETRIEVING OBJECT
  • 2010-10-20. Efficient Secure Two-Party Protocols, Techniques and Constructions in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00145-015-9199-z

    DOI

    http://dx.doi.org/10.1007/s00145-015-9199-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1037719008


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