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arXiv:quant-ph/9802025 · Journal of the ACM

Unconditional security in quantum cryptography

Dominic Mayers

Published May 1, 2001• 1,036 citations
arXivHTMLPDF

Abstract

Basic techniques to prove the unconditional security of quantum crypto graphy are described. They are applied to a quantum key distribution protocol proposed by Bennett and Brassard [1984]. The proof considers a practical variation on the protocol in which the channel is noisy and photos may be lost during the transmission. Each individual signal sent into the channel must contain a single photon or any two-dimensional system in the exact state described in the protocol. No restriction is imposed on the detector used at the receiving side of the channel, except that whether or not the received system is detected must be independent of the basis used to measure this system.

DOI
10.1145/382780.382781

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•Jan 1, 2011•4 citations
Basic techniques to prove the unconditional security of quantum crypto graphy are described. They are applied to a quantum key distribution protocol proposed by Bennett and Brassard [1984]. The proof considers a practical variation on the protocol in which the channel is noisy and photos may be lost during the transmission. Each individual signal sent into the channel must contain a single photon or any two-dimensional system in the exact state described in the protocol. No restriction is imposed on the detector used at the receiving side of the channel, except that whether or not the received system is detected must be independent of the basis used to measure this system.
In this paper I present a protocol for quantum cryptography which is secure against attacks on individual signals. It is based on the Bennett-Brassard protocol of 1984. The security proof is complete as far as the use of single photons as signal states is concerned. Emphasis is placed on the practicability of the resulting protocol. For each run of the quantum key distribution the security statement gives the probability of a successful key generation and the probability for an eavesdropper's knowledge, measured as change in Shannon entropy, to be below a specified maximal value.
We prove the unconditional security of the original Bennett 1992 protocol with strong reference pulse. We show that we may place a projection onto suitably defined qubit spaces before the receiver, which makes the analysis as simple as qubit-based protocols. Unlike the single-photon-based qubits, the qubits identified in this scheme are almost surely detected by the receiver even after a lossy channel. This leads to the key generation rate that is proportional to the channel transmission rate for proper choices of experimental parameters.
It is generally accepted that quantum key distribution (QKD) could supply legitimate users with unconditional security during their communication. Quite a lot of satisfactory efforts have been achieved on experimentations with quantum cryptography. However, when the eavesdropper has extra-powerful computational ability, has access to a quantum computer, for example, and can carry into execution any eavesdropping measurement that is allowed by the laws of physics, the security against such attacks has not been widely studied and rigorously proved for most QKD protocols. Quite recently, Shor and Preskill proved concisely the unconditional security of the Bennett-Brassard 1984 (BB84) protocol. Their method is highly valued for its clarity of concept and concision of form. In order to take advantage of the Shor-Preskill technique in their proof of the unconditional security of the BB84 QKD protocol, we introduced in this paper a transformation that can translate the Bennett 1992 (B92) protocol into the BB84 protocol. By proving that the transformation leaks no more information to the eavesdropper, we proved the unconditional security of the B92 protocol. We also settled the problem proposed by Lo about how to prove the unconditional security of the B92 protocol with the Shor-Preskill method.
The peculiar properties of quantum mechanics enable possibilities not allowed by classical physics. In particular, two parties can generate a random, secret key at a distance, even though an eavesdropper can do anything permitted by the laws of physics. Measuring the quantum properties of the signals generating the key, would ultimately change them, and thus reveal the eavesdropper’s presence. This exchange of a random, secret key is known as quantum cryptography.\n\nQuantum cryptography can be, and has been proven unconditionally secure using perfect devices. However, when quantum cryptography is implemented, one must use components available with current technology. These are usually imperfect. Although the security of quantum cryptography has been proven for components with certain imperfections, the question remains: can quantum cryptography be implemented in a provable, unconditionally secure way, using components available with current technology? This thesis contains both a theoretical, and an experimental contribution to the answer of this question. On the experimental side, components used in, and complete quantum cryptography systems have been carefully examined for security loopholes. In particular, it turned out that two commercial quantum cryptography systems contained loopholes, which would allow an eavesdropper to capture the full secret key, without exposing her presence. Furthermore, this detector control attack could be implemented with current technology. The attack is applicable against a variety of quantum cryptography implementations and protocols.\n\nThe theoretical contribution consists of security proofs for quantum cryptography in a very general setting. Precisely, the security is proven with arbitrary individual imperfections in the source and detectors. These proofs should make it possible to use a wide array of imperfect devices in implementations of quantum cryptography.\n\nFinally, a secure detection scheme is proposed, immune to the detector control attack and compatible with those security proofs. Therefore, if this scheme is implemented correctly, it offers provable security.