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arXiv:1106.1099 · Physical Review A

Practical quantum coin flipping

Anna Pappa, André Chailloux, Eleni Diamanti, Iordanis Kerenidis

Published Nov 7, 2011• 22 citations
arXivHTMLPDF

Abstract

We show that in the unconditional security model, a single quantum strong coin flip with security guarantees that are strictly better than in any classical protocol is possible to implement with current technology. Our protocol takes into account all aspects of an experimental implementation, including losses, multiphoton pulses emitted by practical photon sources, channel noise, detector dark counts, and finite quantum efficiency. We calculate the abort probability when both players are honest, as well as the probability of one player forcing his desired outcome. For a channel length up to 21 km and commonly used parameter values, we can achieve honest abort and cheating probabilities that are better than in any classical protocol. Our protocol is, in principle, implementable using attenuated laser pulses, with no need for entangled photons or any other specific resources.

DOI
10.1103/physreva.84.052305

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We show that in the unconditional security model, a single quantum strong coin flip with security guarantees that are strictly better than in any classical protocol is possible to implement with current technology. Our protocol takes into account all aspects of an experimental implementation, including losses, multiphoton pulses emitted by practical photon sources, channel noise, detector dark counts, and finite quantum efficiency. We calculate the abort probability when both players are honest, as well as the probability of one player forcing his desired outcome. For a channel length up to 21 km and commonly used parameter values, we can achieve honest abort and cheating probabilities that are better than in any classical protocol. Our protocol is, in principle, implementable using attenuated laser pulses, with no need for entangled photons or any other specific resources.
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the participants or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player can completely bias the outcome to his choosing. If we allow for quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they cannot tolerate realistic losses on the quantum channel between the participants or in their quantum storage and measurement apparatus. In this paper, we introduce a novel quantum protocol and we prove its unconditional security even when such losses are taken into account.
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to agree on a random bit. Classical and quantum coin flipping protocols have been studied extensively for more than twenty‐five years. However, until recently, quantum coin flipping protocols were designed without taking into consideration the losses of quantum information that would be unavoidable in any realistic implementation. We introduced in 2008 a novel protocol and proved its security even when losses are taken into account: no cheating player could obtain a desired outcome with a probability greater than (6+2)/8≈93%. Here, we refine our earlier protocol by making it fair in the sense that the optimal cheating strategies allow either player to bias the outcome by the same amount. Specifically, either player can cheat to obtain a desired outcome with probability exactly 90%, but no more. An implementation is underway.
Weak coin flipping is among the fundamental cryptographic primitives which ensure the security of modern communication networks. It allows two mistrustful parties to remotely agree on a random bit when they favor opposite outcomes. Unlike other two-party computations, one can achieve information-theoretic security using quantum mechanics only: both parties are prevented from biasing the flip with probability higher than $1/2+\ensuremath{\epsilon}$, where $\ensuremath{\epsilon}$ is arbitrarily low. Classically, the dishonest party can always cheat with probability 1 unless computational assumptions are used. Despite its importance, no physical implementation has been proposed for quantum weak coin flipping. Here, we present a practical protocol that requires a single photon and linear optics only. We show that it is fair and balanced even when threshold single-photon detectors are used, and reaches a bias as low as $\ensuremath{\epsilon}=1/\sqrt{2}\ensuremath{-}1/2\ensuremath{\approx}0.207$. We further show that the protocol may display a quantum advantage over a few-hundred meters with state-of-the-art technology.
Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which allows a cheater to force a bias that is complete or arbitrarily close to complete in all previous protocols and implementations. Here we report on the first experimental demonstration of a quantum coin-flipping protocol for which loss cannot be exploited to cheat better. By eliminating the problem of loss, which is unavoidable in any realistic setting, quantum coin flipping takes a significant step towards real-world applications of quantum communication. When two spatially separated parties flip a coin, it is impossible to choose between two alternatives in an unbiased manner. This study presents a quantum coin-flipping protocol that overcomes this problem and ensures a dishonest party cannot bias the outcome completely.
Coin flipping is a cryptographic primitive in which two spatially separated players, who do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires either assumptions on the computational power of the players or it requires them to send messages to each other with sufficient simultaneity to force their complete independence. Without such assumptions, all classical protocols are so that one dishonest player has complete control over the outcome. If we use quantum communication, on the other hand, protocols have been introduced that limit the maximal bias that dishonest players can produce. However, those protocols would be very difficult to implement in practice because they are susceptible to realistic losses on the quantum channel between the players or in their quantum memory and measurement apparatus. In this paper, we introduce a quantum protocol and we prove that it is completely impervious to loss. The protocol is fair in the sense that either player has the same probability of success in cheating attempts at biasing the outcome of the coin flip. We also give explicit and optimal cheating strategies for both players.
In quantum cryptography, fundamental laws of quantum physics are exploited to enhance the security of cryptographic tasks. Quantum key distribution (QKD) is by far the most studied protocol to date, enabling the establishment of a secret key between trusted parties. Many practical use-cases in communication networks, however, involve parties who do not know or trust each other. The most fundamental quantum cryptographic building block in such a distrustful setting is quantum coin flipping, which has been studied only in few experimental studies to date using probabilistic quantum light sources facing fundamental limitations. Here, we experimentally implement a quantum strong coin flipping protocol using single-photon states and demonstrate an advantage compared to both classical realizations and implementations using faint laser pulses. We achieve this by employing a state-of-the-art deterministic single-photon source based on the Purcell-enhanced emission of a semiconductor quantum dot in combination with fast polarization-state encoding with sufficiently low quantum bit error ratio. The reduced multi-photon emission of the single-photon source yields a smaller bias of the coin flipping protocol compared to an attenuated laser implementation, both in simulations and in the experiment. By demonstrating a single-photon quantum advantage in a cryptographic primitive beyond QKD, our work represents a major advance towards the implementation of complex cryptographic tasks in a future quantum internet.