On the Complexity of Fair Coin Flipping

A two-party coin-flipping protocol is \(\varepsilon \)-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 \(\varepsilon \). Cleve [STOC ’86] showed that r-round o(1 / r)-fair coin-flipping protocols do not exist. Awerbuch et al. [Manuscript ’85] constructed a \(\varTheta (1/\sqrt{r})\)-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 \(\varTheta (1/r)\)-fair (thus matching the aforementioned lower bound of Cleve [STOC ’86]), assuming the existence of oblivious transfer.

[1]  Yehuda Lindell,et al.  On the Black-Box Complexity of Optimally-Fair Coin Tossing , 2011, TCC.

[2]  Eran Omri,et al.  Computational Two-Party Correlation , 2018, Electron. Colloquium Comput. Complex..

[3]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[4]  Russell Impagliazzo,et al.  One-way functions are essential for complexity based cryptography , 1989, 30th Annual Symposium on Foundations of Computer Science.

[5]  Amit Sahai,et al.  On the Computational Complexity of Coin Flipping , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[6]  Richard Cleve,et al.  Limits on the security of coin flips when half the processors are faulty , 1986, STOC '86.

[7]  Eran Omri,et al.  Tighter Bounds on Multi-Party Coin Flipping via Augmented Weak Martingales and Differentially Private Sampling , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

[8]  Manuel Blum,et al.  How to exchange (secret) keys , 1983, TOCS.

[9]  Bar Alon,et al.  Almost-Optimally Fair Multiparty Coin-Tossing with Nearly Three-Quarters Malicious , 2016, TCC.

[10]  Moni Naor,et al.  An Optimally Fair Coin Toss , 2015, Journal of Cryptology.

[11]  Itay Berman,et al.  Coin flipping of any constant bias implies one-way functions , 2014, STOC.

[12]  Tal Malkin,et al.  Can Optimally-Fair Coin Tossing Be Based on One-Way Functions? , 2014, TCC.

[13]  Eran Omri,et al.  Coin Flipping with Constant Bias Implies One-Way Functions , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[14]  Eran Omri,et al.  Protocols for Multiparty Coin Toss with a Dishonest Majority , 2015, Journal of Cryptology.

[15]  Niv Buchbinder,et al.  Fair Coin Flipping: Tighter Analysis and the Many-Party Case , 2017, SODA.

[16]  Iftach Haitner,et al.  An almost-optimally fair three-party coin-flipping protocol , 2014, STOC.