Black-box use of One-way Functions is Useless for Optimal Fair Coin-Tossing.

A two-party fair coin-tossing protocol guarantees output delivery to the honest party even when the other party aborts during the protocol execution. Cleve (STOC–1986) demonstrated that a computationally bounded fail-stop adversary could alter the output distribution of the honest party by (roughly) 1/r (in the statistical distance) in an r-message coin-tossing protocol. An optimal fair coin-tossing protocol ensures that no adversary can alter the output distribution beyond 1/r.