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arXiv:quant-ph/0702152 · Physical Review Letters

Device-Independent Security of Quantum Cryptography against Collective Attacks

Antonio Acín, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, Valerio Scarani

Published Jun 4, 2007• 1,711 citations
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Abstract

We present the optimal collective attack on a quantum key distribution protocol in the "device-independent" security scenario, where no assumptions are made about the way the quantum key distribution devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.

DOI
10.1103/physrevlett.98.230501

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We present the optimal collective attack on a quantum key distribution protocol in the "device-independent" security scenario, where no assumptions are made about the way the quantum key distribution devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.
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We present a quantum key distribution protocol in a model in which the legitimate users gather statistics as in the measurement-device-independent entanglement witness to certify the sources and the measurement devices. We show that the task of measurement-device-independent quantum communication can be accomplished based on monogamy of entanglement, and it is fairly loss tolerate including source and detector flaws. We derive a tight bound for collective attacks on the Holevo information between the authorized parties and the eavesdropper. Then with this bound, the final secret key rate with the source flaws can be obtained. The results show that long-distance quantum cryptography over 144 km can be made secure using only standard threshold detectors.
A symmetric device-independent quantum key distribution (DIQKD) protocol is proposed in this paper, with Holevo limit and subadditivity of von Neumann entropy, one can bound Eve's ability with collective attack. Together with symmetry of this protocol, the state Eve prepared for Alice and Bob, and at the same time, her eavesdropping on Alice's and Bob's measurements can be definitely inferred at the assumption that Eve aims at maximizing her information gain. The optimal state under this circumstance can be solely bounded with Alice and Bob's statistical results on the quantity of Clauser-Horne-Shimony-Holt (CHSH) polynomial SSS, that is, our symmetric DIQKD has the same secure basis as that of Ekert91 protocol.
In device-independent quantum key distribution (DIQKD) the security is not based on any assumptions about the intrinsic properties of the devices and the quantum signals but on the violation of a Bell inequality. We introduce a DIQKD scenario in which an optimal Bell inequality is constructed from the performed measurement data rather than fixing beforehand a specific Bell inequality. Our method can be employed in a general way, for any number of measurement settings and any number of outcomes. We provide an implementable DIQKD protocol and perform finite-size security key analysis for collective attacks. We compare our approach with related procedures in the literature and analyze the robustness of our protocol. We also study the performance of our method in several Bell scenarios as well as for random measurement settings.
Similar to device-independent quantum key distribution (DI-QKD), semi-device-independent quantum key distribution (SDI-QKD) provides secure key distribution without any assumptions about the internal workings of the QKD devices. The only assumption is that the dimension of the Hilbert space is bounded. But SDI-QKD can be implemented in a one-way prepare-and-measure configuration without entanglement compared with DI-QKD. We propose a practical SDI-QKD protocol with four preparation states and three measurement bases by considering the maximal violation of dimension witnesses and specific processes of a QKD protocol. Moreover, we prove the security of the SDI-QKD protocol against collective attacks based on the min-entropy and dimension witnesses. We also show a comparison of the secret key rate between the SDI-QKD protocol and the standard QKD.
Evaluating the theoretical limit of the amount of information Eve can steal from a quantum key distribution protocol under given conditions is one of the most important things that need to be done in security proof. In addition to source loopholes and detection loopholes, channel attacks are considered to be the main ways of information leakage, while collective attacks are considered to be the most powerful active channel attacks. Here we deduce in detail the capability limit of Eve's collective attack in non-entangled quantum key distribution, like BB84 and measurement-device-independent protocols, and entangled quantum key distribution, like device-independent protocol, in which collective attack is composed of quantum weak measurement and quantum unambiguous state discrimination detection. The theoretical results show that collective attacks are equivalent in entangled and non-entangled quantum key distribution protocols. We also find that compared with the security proof based on entanglement purification, the security proof based on collective attack not only improves the system's tolerable bit error rate, but also improves the key rate.