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Journal of Computer Science

A Modified Secure Scheme of Quantum Key Distribution Without Public Announcement Bases

Es-Said Chanigui, Abdelmalek Azizi

Published Jan 1, 2015• 1 citation
Publisher

Abstract

This study provides a simple variation of the protocol of quantum key expansion proposed by Hwang. Some weaknesses relating to the step of public discussions for error detection are analyzed and an attack strategy, allowing the eavesdropper to get partial information about the used bases, is put forward. Using the One-Time Pad cipher, we propose a possible scheme which is secure against the presented attack.

DOI
10.3844/jcssp.2015.75.81

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This study provides a simple variation of the protocol of quantum key expansion proposed by Hwang. Some weaknesses relating to the step of public discussions for error detection are analyzed and an attack strategy, allowing the eavesdropper to get partial information about the used bases, is put forward. Using the One-Time Pad cipher, we propose a possible scheme which is secure against the presented attack.
We give a Shor-Preskill-type security proof to quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, which is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.
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}.
A novel quantum key distribution protocol is presented, based on entanglement and dense coding and allowing asymptotically secure key distribution. Considering the storage time limit of quantum bits, a grouping quantum key distribution protocol is proposed, which overcomes the vulnerability of first protocol and improves the maneuverability. Moreover, a security analysis is given and a simple type of eavesdropper's attack would introduce at least an error rate of 46.875%. Compared with the "Ping-pong" protocol involving two steps, the proposed protocol does not need to store the qubit and only involves one step.
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.