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arXiv:quant-ph/0206088

An introduction to quantum coin-tossing

C. Doescher, Michael Keyl

Published Jun 13, 2002• 3 citations
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Abstract

We review the quantum version of a well known problem of cryptography called coin tossing (``flipping a coin via telephone''). It can be regarded as a game where two remote players (who distrust each other) tries to generate a uniformly distributed random bit which is common to both parties. The only resource they can use to perform this task is a classical or quantum communication channel. In this paper we provide a general overview over such coin tossing protocols, concerning in particular their security.

DOI
10.48550/arxiv.quant-ph/0206088

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We review the quantum version of a well known problem of cryptography called coin tossing (``flipping a coin via telephone''). It can be regarded as a game where two remote players (who distrust each other) tries to generate a uniformly distributed random bit which is common to both parties. The only resource they can use to perform this task is a classical or quantum communication channel. In this paper we provide a general overview over such coin tossing protocols, concerning in particular their security.
We review the quantum version of a well known problem of cryptography called coin tossing ("flipping a coin via telephone"). It can be regarded as a game where two remote players (who distrust each other) try to generate a uniformly distributed random bit which is common to both parties. The only resource they can use to perform this task is a classical or quantum communication channel. In this paper we provide a general overview over such coin tossing protocols, concerning in particular their security.
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + \xi1/2+ξ where the bias ξ\xiξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2+ξ1/2 + ξ1/2+ξ where the bias ξξξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n∈O(lg⁡m)n \in O(\lg m)n∈O(lgm). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m1/m1/m. The result is discussed in the light of the impossibility result for exact coin tossing.
In this Letter we present the first implementation of a quantum coin-tossing protocol. This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits, resulting in a higher security than using qubits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bounds of a possible cheater and the ways of detecting him.
In this letter we present the first implementation of a quantum coin tossing protocol.This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other.As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits.In this way, we have also performed the first complete quantum communication protocol with qutrits.In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum.We also show the experimental bounds of a possible cheater and the ways of detecting him.