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International Conference on Computational Intelligence and Software Engineering (CiSE)

Simulating B92 Protocol in Depolarizing Channel

Xiaofang Xu, Xiaoyu Chen

Published Sep 1, 2010• 3 citations
Publisher

Abstract

The B92 protocol is a two quantum states protocol in quantum cryptography. It is one of the basic models of quantum key distribution (QKD) in depolarizing channel. We simulate the rate of secure key distribution in depolarizing channel on a classical computer with the method of event-by-event simulation.After the event-by-event simulation of quantum transmission, data reconciliation and privacy amplification are done to obtain the secure key. We give the simulation results of private classical capacity with respect to the depolarizing coefficient.

DOI
10.1109/wicom.2010.5600108

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The B92 protocol is a two quantum states protocol in quantum cryptography. It is one of the basic models of quantum key distribution (QKD) in depolarizing channel. We simulate the rate of secure key distribution in depolarizing channel on a classical computer with the method of event-by-event simulation.After the event-by-event simulation of quantum transmission, data reconciliation and privacy amplification are done to obtain the secure key. We give the simulation results of private classical capacity with respect to the depolarizing coefficient.
It is well known that Quantum Key Distribution (QKD) can be used with the highest level of security for distribution of the secret key, which is further used for symmetrical encryption. B92 is one of the oldest QKD protocols. It uses only two non-orthogonal states, each one coding for one bit-value. It is much faster and simpler when compared to its predecessors, but with the idealized maximum efficiencies of 25% over the quantum channel. B92 consists of several phases in which initial key is significantly reduced: secret key exchange, extraction of the raw key (sifting), error rate estimation, key reconciliation and privacy amplification. QKD communication is performed over two channels: the quantum channel and the classical public channel. In order to prevent a man-in-the-middle attack and modification of messages on the public channel, authentication of exchanged values must be performed. We used Wegman-Carter authentication because it describes an upper bound for needed symmetric authentication key. We explained the reduction of the initial key in each of QKD phases.
Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 protocol in fully quantum cryptography into SQKD. In this protocol, the sender Alice just sends one quantum state to the classical Bob and Bob just prepares a fixed state in the preparation process. It is much simpler than the existing SQKD and potentially much easier to be implemented. It can be seen as a semi-quantum version of B92 protocol, compared to the protocol BKM07 as the semi-quantum version of BB84 in fully quantum cryptography. We verify that it is more efficient than the existing single-state SQKD protocols by introducing an efficiency parameter. Specifically, we prove it is secure against a restricted collective attack by computing a lower bound of the key rate in the asymptotic scenario. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be definitely established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case the reverse channel is a depolarizing one with parameter [Formula: see text]. Though the threshold value is a little smaller than those of some existing SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.
Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter ppp. Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.
Essential role of Internet-based communication is the security of information. Classical Cryptography is based on mathematical models and computational complexity to compute the secret key. It does not provide enough security because finding a fast method to calculate the secret key will compromise the security of the system. Quantum Key Distribution is one of the most promising methods which provide unconditional security. Quantum Key Distribution (QKD) uses a quantum property in exchanging information called photons, as carriers of information in security systems, and QKD cannot separate from protocols BB84, B92 and BBM92. In this paper, we are testing the probability error comparison of BB84 protocol, B92 protocol, and BBM92 using QuVis simulator software. The results show that the B92 protocol is more relevant in detecting eavesdropping in lower error rates than the other two protocols.
Background: The basic Protocols of Quantum Key Distribution (QKD) and their variations use a one way quantum channel for the transmission of quantum information and later use a classical channel for reconciliation phase. Objective: In this paper we are discussing a QKD protocol which is a variation over two basic protocols i.e. BB84 and B92 and uses two-way quantum channel instead of one way quantum channel and it also uses classical channel for reconciliation phase. Method: This protocol is synchronized in a manner that both parties who want to share key start communication at same point of time. Results: We have also given the design for proposed protocols and their comparison with basic protocols. Conclusion: Finally we analyzed the results and found the proposed protocols better with high capacity and low error estimation. Keywords: Variation of QKD protocols, enhanced methodology for QKD protocols, QKD protocols, BB84, B92, two way QKD.
This paper presents the development, comparison, and analysis of several implementations of the B92 Quantum Key Distribution (QKD) protocol. To achieve this goal three prototypes which consists of traditional simulators (non-quantum) were created, one for the B92 protocol, one for the B92 protocol with an eavesdropper, and one for the B92 protocol with the Quantum Bit Travel Time (QBTT) eavesdropper detection method. The principles of quantum mechanics were studied, as a foundation of quantum cryptography, for the implementation of the simulation programs that were written in C++, focusing mainly on the B92 protocol and QBTT eavesdropper detection method. We compared the Quantum Bit Error Rate (QBER) for the implementation of the B92 protocol without an eavesdropper, the B92 protocol with an eavesdropper and the B92 protocol with the QBTT eavesdropper detection method and found that the latest one significantly reduces the QBER from the final key.