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arXiv:quant-ph/0011056

Efficient Quantum Key Distribution Scheme And Proof of Its Unconditional Security

Hoi‐Kwong Lo, H. F. Chau, M. Ardehali

Published Nov 14, 2000• 18 citations
arXivHTMLPDF

Abstract

We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We divide the accepted data into various subsets according to the basis employed and estimate an error rate for each subset *separately*. We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing Shor and Preskill's proof of security of BB84 to our new scheme. Up till now, most proposed proofs of security of single-particle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly and independently. Our proof removes this symmetry requirement.

DOI
10.48550/arxiv.quant-ph/0011056

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We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We divide the accepted data into various subsets according to the basis employed and estimate an error rate for each subset separately. We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing Shor and Preskill's proof of security of BB84 to our new scheme. Up till now, most proposed proofs of security of single-particle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly and independently. Our proof removes this symmetry requirement.
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different polarization bases during both transmission and reception to reduce the fraction of discarded data. The actual probabilities used in the scheme are announced in public. As the number of transmitted signals increases, the efficiency of our scheme can be made to approach 100%. An eavesdropper may try to break such a scheme by eavesdropping mainly along the predominant basis. To defeat such an attack, we perform a refined analysis of accepted data: Instead of lumping all the accepted data together to estimate a single error rate, we separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset individually.
We devise a simple modification that essentially doubles the efficiency of a well-known quantum key distribution scheme proposed by Bennett and Brassard (BB84). Our scheme assigns significantly different probabilities for the different polarization bases during both transmission and reception to reduce the fraction of discarded data. The actual probabilities used in the scheme are announced in public. As the number of transmitted signals increases, the efficiency of our scheme can be made to approach 100%. An eavesdropper may try to break such a scheme by eavesdropping mainly along the predominant basis. To defeat such an attack, we perform a refined analysis of accepted data: Instead of lumping all the accepted data together to estimate a single error rate, we separate the accepted data into various subsets according to the basis employed and estimate an error rate for each subset {\it individually}.
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.
We propose an efficient quantum-key-distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. The sender and receiver choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that refined data analysis like that proposed by Lo et al. (H. K. Lo, H. F. Chau, and M. Adrehali, e-print quant-ph/0011056) guarantees the security of our scheme against a biased eavesdropping strategy. Remarkably, our scheme is more efficient than distillation of singlets out of the nonmaximally entangled states and biased detection afterward.
We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.
The theoretical Quantum Key-Distribution scheme of Bennett and Brassard (BB84) has been proven secure against very strong attacks including the collective attacks and the joint attacks. Though the latter are the most general attacks, collective attacks are much easier to analyze, yet, they are conjectured to be as informative to the eavesdropper. Thus, collective attacks are likely to be useful in the analysis of many theoretical and practical schemes that are still lacking a proof of security, including practical BB84 schemes. We show how powerful tools developed in previous works for proving security against the joint attack, are simplified when applied to the security of BB84 against collective attacks whilst providing the same bounds on leaked information and the same error threshold.