Cheat-sensitive coin flipping and quantum gambling

Arindam Mitra

Carlos Mochon

Quantum protocols for coin flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with cheat sensitivity as well, and is used to derive two results: There are no quantum strong coin-flipping protocols with cheat sensitivity that is linear in the bias (or bit-commitment protocols with linear cheat detection) because these can be composed to produce strong coin flipping with arbitrarily small bias. On the other hand, it appears that quadratic cheat detection cannot be composed in series to obtain even weak coin flipping with arbitrarily small bias.

S. Abeyratne

Anna Pappa, Paul Jouguet, Thomas Lawson +5 more

Robert W. Spekkens, Terry Rudolph

We present a quantum protocol for the task of weak coin flipping. We find that, for one choice of parameters in the protocol, the maximum probability of a dishonest party winning the coin flip if the other party is honest is 1/sqrt[2]. We also show that if parties restrict themselves to strategies wherein they cannot be caught cheating, their maximum probability of winning can be even smaller. As such, the protocol offers additional security in the form of cheat sensitivity.

Satoshi Ishizaka

We show that a biased quantum coin flip (QCF) cannot provide the performance of a black-boxed biased coin flip, if it satisfies some fidelity conditions. Although such a QCF satisfies the security conditions of a biased coin flip, it does not realize the ideal functionality and, therefore, does not satisfy the demands for universally composable security. Moreover, through a comparison within a small restricted bias range, we show that an arbitrary QCF is distinguishable from a black-boxed coin flip unless it is unbiased on both sides of parties against insensitive cheating. We also point out the difficulty in developing cheat-sensitive quantum bit commitment in terms of the uncomposability of a QCF.