Coin Flipping of \emph{Any} Constant Bias Implies One-Way Functions

TL;DR

This paper proves that secure coin-flipping protocols with any constant bias imply the existence of one-way functions, extending previous results to weaker protocols and smaller biases.

Contribution

It establishes that even very slight biases in coin-flipping protocols imply one-way functions, broadening the scope of prior implications.

Findings

Any constant bias coin-flip implies one-way functions

Extends previous results to weak coin-flipping protocols

Improves bias threshold from 0.207 to any constant

Abstract

We show that the existence of a coin-flipping protocol safe against \emph{any} non-trivial constant bias (\eg $.499$) implies the existence of one-way functions. This improves upon a recent result of Haitner and Omri [FOCS '11], who proved this implication for protocols with bias $\frac{\sqrt2 -1}2 - o(1) \approx .207$. Unlike the result of Haitner and Omri, our result also holds for \emph{weak} coin-flipping protocols.