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Acta Physica Sinica

Quantum key distribution secure threshold based on BB84 protocol

Nan Zhao, Changxing Pei, Dan Liu, Dongxiao Quan, Sun Xiao-Nan

Published Jan 1, 2011• 4 citations
Publisher

Abstract

Quantum state in the channel is affected by several factors, which will bring detection error and make secure threshold of quantum distribution protocol unable to judge whether eavesdropping exists. We analyze the factors in real quantum channel, which affects the quantum state, develop a channel model, and derive a judging eavesdrop secure threshold formula of BB84 protocol based on an imperfect channel. Through calculating and simulating, the formula is proved to be more accurate to estimate the secure threshold of the BB84 protocol and more effective to judge eavesdropping. Meanwhile, this method can improve the security and the efficiency of key distribution.

DOI
10.7498/aps.60.090307

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Quantum state in the channel is affected by several factors, which will bring detection error and make secure threshold of quantum distribution protocol unable to judge whether eavesdropping exists. We analyze the factors in real quantum channel, which affects the quantum state, develop a channel model, and derive a judging eavesdrop secure threshold formula of BB84 protocol based on an imperfect channel. Through calculating and simulating, the formula is proved to be more accurate to estimate the secure threshold of the BB84 protocol and more effective to judge eavesdropping. Meanwhile, this method can improve the security and the efficiency of key distribution.
This paper establishes a channel model by analyzing various factors which affect the quantum state in the process of practical quantum communication, and derives, through calculation and simulation, a new formula for a safety threshold of eavesdropping discrimination by the BB84 Protocol. This formula can be used to estimate the safety communication threshold of the BB84 Protocol in non-ideal channels. The method for estimating the practical safety thresholds can decide more accurately whether or not eavesdropping exists in the process of quantum cipher key distribution, thus raising the safety and efficiency of communication process.
Most of quantum cryptography protocols are designed under the ideal conditions without considering the impact of noise in actual communication; thus they may result in that the confidential information cannot be transmitted to the receiver accurately or eavesdroppers can steal the confidential information by mixing in noise. Therefore, analyzing the security of quantum cryptography protocols under noise conditions is of great significance. For the purpose of analyzing the security of quantum BB84 protocol in collective-rotation noise, firstly this paper introduces the quantum BB84 protocol, and considers the influence of environmental noise on it. An explanation should be stated that in a noise environment, the effects of noise and eavesdropping cannot be distinguished between each other. So the mechanism for which the error bit is simply used as the criterion to judge whether there exists eavesdropping in the BB84 protocol, cannot be used in the noise environment. The mechanism to judge whether there exists eavesdropping in quantum noise channel needs to be modified and improved for protecting the information. An initial qubit error rate can be set according to the noisy quantum channel. If the qubit error rate of the quantum communication channel is larger than that, it can be determined that the quantum channel is not secure and exists eavesdropping, no matter what the reason is. And on this basis, the collective-rotation noise model will be established in quantum channel by using the particle deflection model and distinguish the noise from the eavesdropping in quantum channel quantitatively, and the relationship of the amount of information that eavesdroppers can steal, the quantum bits error rate and the noise level will be analyzed by using the von Neumann entropy. Finally, the noise critical point will be calculated by using the collective noise model and the relationship between the amount of information that eavesdroppers can steal, at the quantum bits error rate, and the noise level. Through the analysis, we can know that in the existing noise level, the most of the eavesdropping can steal 25% of the key from the communication. However, the Eve's eavesdropping behavior will be detected, so that Alice and Bob will give up the current consultation key, and restart the key negotiation. This result shows that the quantum BB84 protocol is safe and secure in the collective-rotation noise channel. The research results of this paper will enrich the theory of quantum cryptography, and the innovation of security detection methods in quantum cryptographic protocols will help promote the process of practical quantum cryptography.
Quantum Key Distribution (QKD) provides an innovative approach for secure communication by utilizing the principles of quantum mechanics. Among various QKD protocols, the BB84 protocol remains the most widely studied and implemented due to its simplicity and theoretical security guarantees. However, practical implementations of BB84 are vulnerable to several eavesdropping attacks and channel imperfections. This paper presents a comprehensive study on the detection and analysis of eavesdropping attacks in the BB84 protocol. The work focuses on common attacks such as intercept-resend attack, photon-number splitting attack, Trojan horse attack, and phase-covariant cloning attack. The effect of these attacks on Quantum Bit Error Rate (QBER) is analyzed in detail. Simulation-based observations are discussed to demonstrate how QBER increases under malicious interference. The study further explores statistical methods for detecting eavesdropping and examines practical countermeasures including decoy states, privacy amplification, and error correction techniques. The paper concludes that BB84 remains robust against eavesdropping when proper detection and mitigation mechanisms are employed.
In practical quantum key distribution system, the state preparation and measurement have state-dependent imperfections comparing with the ideal BB84 protocol. If the state-dependent imperfection can not be regarded as an unitary transformation, it should not be considered as part of quantum channel noise introduced by the eavesdropper, the commonly used secret key rate formula GLLP can not be applied correspondingly. In this paper, the unconditional security of quantum key distribution with state-dependent imperfections will be analyzed by estimating upper bound of the phase error rate in the quantum channel and the imperfect measurement. Interestingly, since Eve can not control all phase error in the quantum key distribution system, the final secret key rate under constant quantum bit error rate can be improved comparing with the perfect quantum key distribution protocol.
The nature of quantum mechanics provides us with an opportunity to statistically detect eavesdropping in quantum key distribution (QKD) protocols, which is unimaginable in classical digital communications. By utilizing Hoeffding’s inequality, this study analyzes the upper bounds of the false-positive ratio (FPR) and false-negative ratio (FNR) of eavesdropping detection in the Bennett–Brassard-84 (BB84) QKD protocol, where eavesdropping is detected if the measured quantum bit error rate (QBER) is equal to or higher than a threshold. The analysis clarifies the trade-off between the accuracy of eavesdropping detection and the economy of quantum resources in the BB84 protocol. Owing to the central limit theorem, the QBER measured by 300 quantum bits (qubits) is sufficient to guarantee lower than 0.009% of the FPR and FNR of eavesdropping detection. To deal with rapidly varying quantum channel conditions, this study further introduces grouped BB84 protocol and combinatory eavesdropping detection algorithms. A polarization basis is changeable for a group of qubits, and eavesdropping is judged by a combination of criteria between QBER and group-QBER in the proposed protocol and algorithms. In our extensive simulation study, the grouped BB84 protocol with 300 qubits comparison guarantees at least 99.92% accuracy in eavesdropping detection under rapidly varying quantum channel conditions.