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arXiv:quant-ph/0408121 · Physical Review Letters

Provably Secure Experimental Quantum Bit-String Generation

L.-P. Lamoureux, Edouard Brainis, David Amans, Jonathan Barrett, Serge Massar

Published Feb 7, 2005• 24 citations
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Abstract

Coin tossing is a cryptographic task in which two parties who do not trust each other aim to generate a common random bit. Using classical communication this is impossible, but nontrivial coin tossing is possible using quantum communication. Here we consider the case when the parties do not want to toss a single coin, but many. This is called bit-string generation. We report the experimental generation of strings of coins which are provably more random than achievable using classical communication. The experiment is based on the "plug and play" scheme developed for quantum cryptography, and therefore well suited for long distance quantum communication.

DOI
10.1103/physrevlett.94.050503

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Coin tossing is a cryptographic task in which two parties who do not trust each other aim to generate a common random bit. Using classical communication this is impossible, but nontrivial coin tossing is possible using quantum communication. Here we consider the case when the parties do not want to toss a single coin, but many. This is called bit-string generation. We report the experimental generation of strings of coins which are provably more random than achievable using classical communication. The experiment is based on the "plug and play" scheme developed for quantum cryptography, and therefore well suited for long distance quantum communication.
We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large nnn cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.
The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, who do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational resources, one of them can always cheat perfectly. If the parties use a quantum communication channel, there exist protocols such that neither party can cheat perfectly, although they may be able to significantly bias the coin. Here, we analyze in detail how the performance of a quantum coin tossing experiment should be compared to classical protocols, taking into account the inevitable experimental imperfections. We then report an all-optical fiber experiment in which a single coin is tossed whose randomness is higher than achievable by any classical protocol and present some easily realizable cheating strategies by Alice and Bob.
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.
Performing complex cryptographic tasks will be an essential element in future quantum communication networks. These tasks are based on a handful of fundamental primitives, such as coin flipping, where two distrustful parties wish to agree on a randomly generated bit. Although it is known that quantum versions of these primitives can offer information-theoretic security advantages with respect to classical protocols, a demonstration of such an advantage in a practical communication scenario has remained elusive. Here, we experimentally implement a quantum coin flipping protocol that performs strictly better than classically possible over a distance suitable for communication over metropolitan area optical networks. The implementation is based on a practical plug&play system, designed for quantum key distribution. We also show how to combine our protocol with coin flipping protocols that are almost perfectly secure against bounded adversaries, hence enhancing them with a level of information-theoretic security. Our results offer a powerful toolbox for future secure quantum communications.
We review recent advances in the field of quantum cryptography, focusing in particular on practical implementations of two central protocols for quantum network applications, namely key distribution and coin flipping. The former allows two parties to share secret messages with information-theoretic security, even in the presence of a malicious eavesdropper in the communication channel, which is impossible with classical resources alone. The latter enables two distrustful parties to agree on a random bit, again with information-theoretic security, and with a cheating probability lower than the one that can be reached in a classical scenario. Our implementations rely on continuous-variable technology for quantum key distribution and on a plug and play discrete-variable system for coin flipping, and necessitate a rigorous security analysis adapted to the experimental schemes and their imperfections. In both cases, we demonstrate the protocols with provable security over record long distances in optical fibers and assess the performance of our systems as well as their limitations. The reported advances offer a powerful toolbox for practical applications of secure communications within future quantum networks.