Paper 2009/214

An Optimally Fair Coin Toss

Tal Moran, Moni Naor, and Gil Segev


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 [STOC '86] showed that for any two-party $r$-round coin-flipping protocol there exists an efficient adversary that can bias the output of the honest party by $\Omega(1/r)$. However, the best previously known protocol only guarantees $O(1/\sqrt{r})$ bias, and the question of whether Cleve's bound is tight has remained open for more than twenty 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 $r$-round protocol with bias $O(1/r)$.

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Publication info
A major revision of an IACR publication in TCC 2009
Fair computationcoin-flipping protocols
Contact author(s)
segev @ cs huji ac il
2015-01-04: last of 2 revisions
2009-05-26: received
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      author = {Tal Moran and Moni Naor and Gil Segev},
      title = {An Optimally Fair Coin Toss},
      howpublished = {Cryptology ePrint Archive, Paper 2009/214},
      year = {2009},
      note = {\url{}},
      url = {}
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