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Journal of Jilin University

Security analysis and improvements of two QKD protrocols using complete Bell-state measurements

Yumin Wang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Security analysis for two quantum key distribution protocols was presented by using EPR pair and complete Bell-state measurements.It is also shown that those two protocols are totally equivalent from the point of view of the topological structures on how to measure the corresponding qubits at random.The paper proved that Bell-state measurement basis can detect some special eavesdropping behaviors,but not all of them.Thus,this enables all same errors occurring on the sampling qubits undetected,which impairs the security of quantum key distribution protocols.|0+,|0-,|1+,|1- measurement basis was used to replace complete Bell-state basis,which can avoid the incomplete error-detecting strategy.And unconditionally security was guaranteed bythe improved protocol.

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arXiv:1112.1110•Dec 5, 2011•1 citation
Security analysis for two quantum key distribution protocols was presented by using EPR pair and complete Bell-state measurements.It is also shown that those two protocols are totally equivalent from the point of view of the topological structures on how to measure the corresponding qubits at random.The paper proved that Bell-state measurement basis can detect some special eavesdropping behaviors,but not all of them.Thus,this enables all same errors occurring on the sampling qubits undetected,which impairs the security of quantum key distribution protocols.|0+,|0-,|1+,|1- measurement basis was used to replace complete Bell-state basis,which can avoid the incomplete error-detecting strategy.And unconditionally security was guaranteed bythe improved protocol.
In order to improve the security and efficiency of quantum key distribution protocol,a protocol was proposed based on entanglement swapping.The two parties of communication establish the key by performing the Bell state measurement.No other people can get the key without being found.Different from the proposed protocol,the Bell measurement of any two Bell states can be realized to achieve the purpose of quantum key distribution.It does not need multi-particle entangled state but only EPR pair to realize the protocol.Analysis results showed that this protocol not only ensures the security of the quantum key shared information,but also uses the entanglement states of two photons without unitary operation. And the protocol is simple and efficient.
This paper investigates the security vulnerabilities within quantum communication protocols focused on key agreement. Specifically, we analyze the Bell state measurement (BSM) protocol and its variations, examining the potential for eavesdropping attacks and compromised key generation. Our analysis utilizes concepts from quantum information theory, including quantum entropy, quantum mutual information, and the density operators describing the quantum states involved. We identify critical weaknesses related to the measurement process and propose modifications to enhance security. The primary focus is on quantifying the information leakage during the BSM process and demonstrating how a sophisticated adversary can exploit this leakage to gain knowledge about the shared key. The proposed improvements involve introducing redundancy in the measurement process and employing post-processing techniques to mitigate the impact of eavesdropping. The goal is to provide a foundational understanding of the security challenges inherent in quantum key distribution (QKD) protocols and to offer practical strategies for building more robust systems.
Quantum cryptography is anticipated to drive substantial advancements in cybersecurity. The impending arrival of quantum cryptography compromises current encryption methods, possibly compromising the effectiveness of traditional key management-based security protocols. One fundamental Quantum Key Distribution (QKD) protocol, BB84, encounters challenges when operating with fewer Quantum bits (Qubits) and bases that only support up to 8 Qubits. This limitation weakens the system’s security, making brute force, intercept, and resend attacks less challenging. Consequently, this study proposes a method to enhance the security of the BB84 protocol, to reduce susceptibility to attacks and eavesdropping. The improved BB84 protocol utilizes 9, 12, and 16 quantum bits along with two, and three bases to significantly bolster security. This allows authorized parties to eliminate the use of compromised keys. Additionally, the study implements the E91 QKD protocol utilizing the Entanglement Pair Generation (EPR) method to produce secure keys. While the existing E91 protocol ensures security through Bell’s theorem and Bell’s inequality, it overlooks the impact of noise, leading to inaccuracies in eavesdropper detection. To address this, the study introduces an additional security measure. Whenever an eavesdropper attempts to measure the quantum state, the proposed E91 protocol collapses its state from$\vert 10\rangle tototo\vert 11\rangle ,settingthefirstQubitto, setting the first Qubit to,settingthefirstQubitto\vert 1\rangle andtheotherQubittoand the other Qubit toandtheotherQubitto\vert 0\rangle $, thus providing the eavesdropper with incorrect information, accompanied by a phase angle of$15\pi $/8. This leads to a misconception, preventing eavesdroppers from obtaining useful details about transferred quantum states. Additionally, considering that the proposed E91 protocol relies on entangled particles and utilizes double Qubit gates, which are inherently noisier than single Qubit gates and more susceptible to quantum decoherence, this study employs error mitigation techniques during the final measurement to predict outcomes more efficiently.
Employing the fundamental laws of quantum physics, Quantum Key Distribution (QKD) promises the unconditionally secure distribution of cryptographic keys. However, in practical realisations, a QKD protocol is only secure, when the quantum bit error rate introduced by an eavesdropper unavoidably exceeds the system error rate. This condition guarantees that an eavesdropper cannot disguise his presence by simply replacing the original transmission line with a less faulty one. Unfortunately, this condition also limits the possible distance between the communicating parties, Alice and Bob, to a few hundred kilometers. To overcome this problem, we design a QKD protocol which allows Alice and Bob to distinguish system errors from eavesdropping errors. If they are able to identify the origin of their errors, they can detect eavesdropping even when the system error rate exceeds the eavesdropping error rate. To achieve this, the proposed protocol employs an alternative encoding of information in two-dimensional photon states. Errors manifest themselves as quantum bit and as index transmission errors with a distinct correlation between them in case of intercept-resend eavesdropping. As a result, Alice and Bob can tolerate lower eavesdropping and higher system error rates without compromising their privacy.