Simulation algorithm on the quantum BB84 protocol based on Monte Carlo method in classical computer environment
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Simulation algorithm on the quantum BB84 protocol based on Monte Carlo method in classical computer environment Jian Li1 · Leilei Li1
· Hengji Li1 · Na Wang1 · Xiubo Chen2 · Yuguang Yang3
Received: 26 September 2019 / Accepted: 19 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A simulation algorithm based on the law of large number and Monte Carlo method in the classical computer environment is presented. During the simulation of the original quantum BB84 protocol in ideal environment, the sender Alice tries to send classical bit 0 or 1 to the receiver Bob, and the eavesdropper Eve tries to get the transmission information by intercepting and resending the quantum particles. The bit error rate in the quantum BB84 protocol is also given, and the value of the bit error rate can be analyzed if Eve eavesdrops the communication. In addition, the mean square error is introduced to describe the similarity between the simulation data and the theoretical data. (The smaller the mean square error is, the more reasonable the simulation will be.) In this simulation, the value of MSE is 6.705 × 10−5 after 5000 times simulation when Eve eavesdrops the communication with the probability of 100%. The time complexity of the simulation algorithm is O(n) in our experiment. The reason why there is always an error between the simulation data and theoretical data is analyzed, and the correctness and rationality of the simulation algorithm are also analyzed. Keywords Quantum BB84 protocol · Monte Carlo method · The law of large number · Bit error rate · Mean square error
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Leilei Li [email protected]
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School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
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School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing 100876, China
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College of Computer Science and Technology, Beijing University of Technology, Beijing 100124, China 0123456789().: V,-vol
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J. Li et al.
1 Introduction The security of classical cryptography is usually based on computational complexity, and only the security of the one-time pad protocol has been proved in theory by Shannon [1–6]. The other protocols (such as RAS) are based on the computational complexity of large prime number decomposition [7–9]. If Alice and Bob change the key in time before the key is decrypted, the security of these protocols can be guaranteed. However, these protocols’ security has not been proved in theory. In 1994, Shor presented a quantum algorithm called the Las Vegas algorithm [10], indicating that some Non-deterministic Polynomial hard (NP-hard) problems can be solved in limited time with the parallelization of quantum computing. Different from the fact that classical communication protocols ensure their safety by the complexity of the computation, quantum secure communication protocols use the quantum bits (qubits) to transmit the secret message or the keys instead of the classical bits. The security of the quantum secure
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