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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

An improved scheme that the random matrix transformation used for BB84 protocol

Shumin Cui, Lihua Ma, Lei Shi, Zhiyan Xu, Hua Hong, Xiaoping Chen

Published Feb 19, 2015• 0 citations
Publisher

Abstract

The bit error rate is raised by the presence of the noise when the quantum key transmits in practice. So both sides of communication can not judge the presence of eavesdropping. For this issue, an improved scheme based on BB84 protocol is proposed by a paper of Luanxin that a matrix transformation is carried out for every quantum of both sides. The advantage of the transformation is that the eavesdropper can be found easily. But the disadvantage is that it leads to a low key generation rate. In this paper, an improvement that a matrix transformation is carried out randomly for the quantum of both sides based on the scheme of Luanxin is proposed. The result shows that not only the presence of eavesdropping can be judged easily, but also the key generation rate is increased significantly.

DOI
10.1117/12.2075882

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The bit error rate is raised by the presence of the noise when the quantum key transmits in practice. So both sides of communication can not judge the presence of eavesdropping. For this issue, an improved scheme based on BB84 protocol is proposed by a paper of Luanxin that a matrix transformation is carried out for every quantum of both sides. The advantage of the transformation is that the eavesdropper can be found easily. But the disadvantage is that it leads to a low key generation rate. In this paper, an improvement that a matrix transformation is carried out randomly for the quantum of both sides based on the scheme of Luanxin is proposed. The result shows that not only the presence of eavesdropping can be judged easily, but also the key generation rate is increased significantly.
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.
In order to solve the low key distribution efficiency problem of the BB84 protocol, an improved BB84 quantum key distribution scheme is presented in this paper. Firstly the same polarization basis is used by the sender and the receiver with the consistent agreement. This process could make quantum key distribution rate higher. Then signature combined with the error correction method based on the odd and even parity is used to ensure the safety of the transmission. The analyses results indicate that the advantage of the improved scheme lies in that the all photons sent to Bob by Alice are useful. It can not only reduce the time extracting the original key, but also solve the authentication problem in the process of communication. The key distribution efficiency is two times of the original BB84 protocol improved scheme.
Quantum key distribution (QKD) enables secure communication using the principles of quantum physics. The BB84 protocol is not only effective for secure key sharing but also for detecting eavesdropping. This study simulates a computational model of QKD and analyzes error rates under varying numbers of bits. Using Python-based simulations with n = 10, n = 100, and n = 1000 bits, and a fixed noise probability of 0.02, we evaluated scenarios both with and without eavesdropping over 1000 trials. The results show an average error rate of 2% without eavesdropping and over 26% with eavesdropping. Standard deviation increases with lower n, indicating higher variability. This study validates BB84’s robustness under noise and demonstrates its sensitivity to third-party interference.
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.
In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key distribution protocol, where Alice and Bob use two mutually unbiased bases with one of them encoding a '0' and the other one encoding a '1'. The security of the scheme is due to a minimum index transmission error rate (ITER) introduced by an eavesdropper that increases significantly for higher-dimensional photon states. This allows for more noise in the transmission line, thereby increasing the possible distance between Alice and Bob without the need for intermediate nodes.