Tighter bounds on multi-party coin flipping via augmented weak martingales and differentially private sampling

Amos Beimel, Iftach Haitner, Nikolaos Makriyannis, Eran Omri

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

10 Scopus citations

Abstract

In his seminal work, Cleve [STOC '86] has proved that any r-round coin-flipping protocol can be efficiently biased by Θ(1/r). This lower bound was met for the two-party case by Moran, Naor, and Segev [Journal of Cryptology '16], and the three-party case (up to a polylog factor) by Haitner and Tsfadia [SICOMP '17], and was approached for n-party protocols when n < loglogr by Buchbinder, Haitner, Levi, and Tsfadia [SODA '17]. For n > loglogr, however, the best bias for n-party coin-flipping protocols remains O(n/√r) achieved by the majority protocol of Awerbuch, Blum, Chor, Goldwasser, and Micali [Manuscript '85]. Our main result is a tighter lower bound on the bias of coin-flipping protocols, showing that, for every constant ϵ > 0, an rϵ -party r-round coin-flipping protocol can be efficiently biased by Ω(1√r). As far as we know, this is the first improvement of Cleve's bound, and is only n = rϵ (multiplicative) far from the aforementioned upper bound of Awerbuch et al. We prove the above bound using two new results that we believe are of independent interest. The first result is that a sequence of ("augmented") weak martingales have large gap: with constant probability there exists two adjacent variables whose gap is at least the ratio between the gap between the first and last variables and the square root of the number of variables. This generalizes over the result of Cleve and Impagliazzo [Manuscript '93], who showed that the above holds for strong martingales, and allows in some setting to exploit this gap by efficient algorithms. We prove the above using a novel argument that does not follow the more complicated approach of Cleve and Impagliazzo. The second result is a new sampling algorithm that uses a differentially private mechanism to minimize the effect of data divergence.

Original languageEnglish
Title of host publicationProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
EditorsMikkel Thorup
PublisherIEEE Computer Society
Pages838-849
Number of pages12
ISBN (Electronic)9781538642306
DOIs
StatePublished - 30 Nov 2018
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: 7 Oct 20189 Oct 2018

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2018-October
ISSN (Print)0272-5428

Conference

Conference59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
Country/TerritoryFrance
CityParis
Period7/10/189/10/18

Keywords

  • Bias
  • Coin flipping
  • Cryptography
  • Differential privacy
  • Lower bounds
  • Martingales

Fingerprint

Dive into the research topics of 'Tighter bounds on multi-party coin flipping via augmented weak martingales and differentially private sampling'. Together they form a unique fingerprint.

Cite this