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AIP conference proceedings

Composability of biased quantum coin flipping

Satoshi Ishizaka, Alexander I. Lvovsky

Published Jan 1, 2009• 0 citations
Publisher

Abstract

A biased quantum coin flip (QCF) does not realize the functionality of a classical black‐boxed coin flip, if it satisfies some fidelity condition. We consider a quantum black‐boxed coin flip and show that the fidelity condition is well‐explained as the functionality of the quantum black‐boxed coin flip. Moreover, we show the results of the security analysis for a QCF like protocol.

DOI
10.1063/1.3131354

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A biased quantum coin flip (QCF) does not realize the functionality of a classical black‐boxed coin flip, if it satisfies some fidelity condition. We consider a quantum black‐boxed coin flip and show that the fidelity condition is well‐explained as the functionality of the quantum black‐boxed coin flip. Moreover, we show the results of the security analysis for a QCF like protocol.
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.
Weak coin flipping is a cryptographic primitive in which two mutually distrustful parties generate a shared random bit to agree on a winner via remote communication. While a stand-alone secure weak coin flipping protocol can be constructed from noiseless quantum communication channels, its composability remains unexplored. In this work, we demonstrate that no weak coin flipping protocol can be abstracted as a simple black-box resource with composable security. Despite this, we also establish the overall stand-alone security of quantum weak coin flipping protocols under composition in sequential order.
So far, most existing single-shot quantum coin flipping (QCF) protocols have failed in a noisy quantum channel. Here, we present a nested-structure framework that makes it possible to achieve partially noise-tolerant QCF, due to a trade-off between the security and the justice correctness. It is showed that noise-tolerant single-shot QCF protocols can be produced by filling the presented framework up with existing or even future protocols. We also proved a lower bound of 0.25, with which a cheating Alice or Bob could bias the outcome.
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.