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 [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 Ω(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).
Keywords
- Security Parameter
- Message Authentication Code
- Oblivious Transfer
- Honest Party
- Corrupted Party
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The original version of the book was revised: The copyright line was incorrect. The Erratum to the book is available at DOI: 10.1007/978-3-642-00457-5_36
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Moran, T., Naor, M., Segev, G. (2009). An Optimally Fair Coin Toss. In: Reingold, O. (eds) Theory of Cryptography. TCC 2009. Lecture Notes in Computer Science, vol 5444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00457-5_1
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