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Journal of China Institute of Communications

Information investigation for BB84 protocol in quantum ceyptography

Zeng Gui

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

In this paper,we propose an information theory of quantum cryptography by intruducing the quantum measurement channel The mutual information is calculated,and a new criteria for checking Eve is estimated

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In this paper, we simulate the quantum channel with a binary symmetric channel and a binary erasure channel, a series channel and a Markovian chain channel in classical information theory, then calculate respectively the mutual information between the signal's deliverer, the legal receiver and the eavesdropper, the bit error rate during propagating the signals with the theory about the quantum measurement channel and the quantum information theory. For B92 protocol, a simple quantum cryptography distribution scheme, we study the bound and the property of mutual information obtained by the legal receiver and the eavesdropper, seek the relationship between the bit error rates and the eavesdropper's way, in two cases of the opaque eavesdropping and the translucent eavesdropping. A new criteria for checking the eavesdropper and ensuring the legal correspondent is estimated. Furthermore, the comparison in bit error rates caused respectively in two different measuring ways indicates that POVM is better than the standard measurement by the way of orthogonal projecting for reducing the bit error rate and increasing effective communication.
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 cryptography uses quantum mechanics to guarantee secure communication. BB84 is a widely used quantum key distribution that provides a way for two parties, a sender, Alice, and a receiver, Bob, to share an unconditionally secure key in the presence of an eavesdropper, Eve. Three different criteria can be assumed to study the BB84 protocol. They are the efficiency of the protocol, the probability that Eve remains undetected, and the amount of knowledge Eve has about Alice's bit sequence. In a previous approach, we only considered the probability that Eve remains undetected. We viewed this protocol as a three player static game in which Alice and Bob were two cooperative players and Eve was a competitive one. In our game model, Alice's and Bob's objective was to maximize the probability of detecting Eve, while Eve's objective was to minimize this probability. In this paper, our previous effort is extended and we also consider the other two criteria, i.e. the efficiency of the protocol and the amount of knowledge Eve has about Alice's bit sequence. Using these models, we show how game theory can be used to find the strategies for Alice, Bob and Eve.