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

Amos Beimel, Iftach Haitner, Nikolaos Makriyannis, Eran Omri

פרסום מחקרי: פרק בספר / בדוח / בכנספרסום בספר כנסביקורת עמיתים

16 ציטוטים ‏(Scopus)

תקציר

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.

שפה מקוריתאנגלית
כותר פרסום המארחProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
עורכיםMikkel Thorup
מוציא לאורIEEE Computer Society
עמודים838-849
מספר עמודים12
מסת"ב (אלקטרוני)9781538642306
מזהי עצם דיגיטלי (DOIs)
סטטוס פרסוםפורסם - 30 נוב׳ 2018
אירוע59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, צרפת
משך הזמן: 7 אוק׳ 20189 אוק׳ 2018

סדרות פרסומים

שםProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
כרך2018-October
ISSN (מודפס)0272-5428

כנס

כנס59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
מדינה/אזורצרפת
עירParis
תקופה7/10/189/10/18

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