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Eavesdropper's Optimal Information in Variations of Bennett-Brassard 1984 Quantum Key Distribution in the Coherent Attacks

Hwang, W Y, Ahn, D, Hwang, S W

Published Jan 1, 2001• 13 citations
OpenAlex

Abstract

First, we calculate eavesdropper's optimal information on raw bits in Bennett-Brassard 1984 quantum key distribution (BB84 QKD) scheme and six-states one in coherent attacks, using the method by Lo and Chau [Science {\\bf 283}, 2050 (1999)]. Next, we show that eavesdropper's optimal information in multiple-basis scheme is the same as that of six-states one. Then, we consider QKD without public announcement of bases [Phys. Lett. A {\\bf244}(1998), 489]: we find that eavesdropper's optimal information in it is the same as that of a corresponding QKD with public announcement of bases. This fact suggests that QKD without public announcement of bases is as secure as BB84 scheme even in coherent attacks.

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First, we calculate eavesdropper's optimal information on raw bits in Bennett-Brassard 1984 quantum key distribution (BB84 QKD) scheme and six-states one in coherent attacks, using the method by Lo and Chau [Science {\bf 283}, 2050 (1999)]. Next, we show that eavesdropper's optimal information in multiple-basis scheme is the same as that of six-states one. Then, we consider QKD without public announcement of bases [Phys. Lett. A {\bf244}(1998), 489]: we find that eavesdropper's optimal information in it is the same as that of a corresponding QKD with public announcement of bases. This fact suggests that QKD without public announcement of bases is as secure as BB84 scheme even in coherent attacks.
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}.
We consider the security of the BB84 (Bennett and Brassard 1984 Proc. IEEE Int. Conf. on Computers, Systems, and Signal Processing pp 175–9), six-state (Bruß 1998 Phys. Rev. Lett. 81 3018 ) and SARG04 (Scarani et al 2004 Phys. Rev. Lett. 92 057901 ) quantum key distribution protocols when the eavesdropper does not have access to a quantum memory. In this case, Eve’s most general strategy is to measure her ancilla with an appropriate positive operator-valued measure designed to take advantage of the post-measurement information that will be released during the sifting phase of the protocol. After an optimization on all the parameters accessible to Eve, our method provides us with new bounds for the security of six-state and SARG04 against a memoryless adversary. In particular, for the six-state protocol we show that the maximum quantum bit error ratio for which a secure key can be extracted is increased from 12.6% (for collective attacks) to 20.4% with the memoryless assumption.
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.
We present and analyze a quantum key distribution protocol based on sending entangled NNN-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper's information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound 1∕(2N)1∕(2N)1∕(2N) for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case N=2N=2N=2. In general, the protocol is at least as secure as BB84.