TCC 2011: Theory of Cryptography pp 450-467

On the Black-Box Complexity of Optimally-Fair Coin Tossing

• Dana Dachman-Soled
• Yehuda Lindell
• Tal Malkin
Conference paper

DOI: 10.1007/978-3-642-19571-6_27

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6597)
Cite this paper as:
Dachman-Soled D., Lindell Y., Mahmoody M., Malkin T. (2011) On the Black-Box Complexity of Optimally-Fair Coin Tossing. In: Ishai Y. (eds) Theory of Cryptography. TCC 2011. Lecture Notes in Computer Science, vol 6597. Springer, Berlin, Heidelberg

Abstract

A fair two-party coin tossing protocol is one in which both parties output the same bit that is almost uniformly distributed (i.e., it equals 0 and 1 with probability that is at most negligibly far from one half). It is well known that it is impossible to achieve fair coin tossing even in the presence of fail-stop adversaries (Cleve, FOCS 1986). In fact, Cleve showed that for every coin tossing protocol running for r rounds, an efficient fail-stop adversary can bias the output by Ω(1/r). Since this is the best possible, a protocol that limits the bias of any adversary to O(1/r) is called optimally-fair. The only optimally-fair protocol that is known to exist relies on the existence of oblivious transfer, because it uses general secure computation (Moran, Naor and Segev, TCC 2009). However, it is possible to achieve a bias of $$O(1/\sqrt{r})$$ in r rounds relying only on the assumption that there exist one-way functions. In this paper we show that it is impossible to achieve optimally-fair coin tossing via a black-box construction from one-way functions for r that is less than O(n/logn), where n is the input/output length of the one-way function used. An important corollary of this is that it is impossible to construct an optimally-fair coin tossing protocol via a black-box construction from one-way functions whose round complexity is independent of the security parameter n determining the security of the one-way function being used. Informally speaking, the main ingredient of our proof is to eliminate the random-oracle from “secure” protocols with “low round-complexity” and simulate the protocol securely against semi-honest adversaries in the plain model. We believe our simulation lemma to be of broader interest.

Keywords

black-box separations coin tossing optimally-fair coin tossing round-complexity lower-bound

© International Association for Cryptologic Research 2011

Authors and Affiliations

• Dana Dachman-Soled
• 1
• Yehuda Lindell
• 2
• 3
• Tal Malkin
• 1
1. 1.Columbia UniversityUSA
2. 2.Bar-Ilan UniversityIsrael
3. 3.Cornell UniversityUSA