Research On Data Reconciliation In Multiparty Quantum Key Distribution System

G. Vernam proposed the scheme of One Time Pad(OTP) for the first time in 1917. When Alice communicates with Bob, Alice only needs to encode the information with keys, the same length of information, and then sends the encoded information to Bob. And then Bob only needs to decode the information with the same keys as the keys Alice uses, When Bob receives the encoded information. OTP could guarantee the security of communication only with the keys which are completely random and are only used once. Quantum Key Distribution(QKD) is the combination of quantum theory and information theory. Based on the laws of quantum mechanics unconditional secure keys could be generated by QKD, then with the thought of OTP, unconditional secure communication could be realized. So far, most of the theoretical and experimental work are mainly based on the two-sides QKD. However, we must try to achieve multi-party QKD to realize the secure group communication. And this article mainly focuses on the research of data reconciliation in multi-party QKD.Firstly, we introduce the protocol of Multi-party Quantum Key Distribution(MQKD) based on GHZ state. Then three widely-used methods of data reconciliation, including the dichotomy, cascade method and Winnow algorithm based on hamming code, are introduced in detail. Comparing with these three algorithms, we find that Dichotomy is simple and easy to use, but can not correct an even number of errors. Cascade method can correct an even number of errors, and the error correction ability is strong, but it increase the number of the communication and burden of communication resources. Winnow algorithm based on hamming code can complete correction with few number of communication, but there is the risk of errors can be not decreased but increased.Secondly,we analyze the three methods of the generation of check matrix for LDPC codes, and choose the Mackay and the Progressive Edge Growth(PEG) methods to generate the check matrix, and Belief propagation(BP) decoding algorithm and the Log-Likelihood Ratio Belief Propagation(LLR BP) algorithm is given. After, we discuss the decoding performance of LDPC codes with Extrinsic information transfer(Exit) figure and determine the suitable degree of check matrix for data reconciliation. After that, simulations with different check matrixes, different code lengths and different numbers of iterations are performed to evaluate the impacts on the final key generation rate. The simulation results show that the efficiency is nearly 99% and performance of this method is much better than the three methods we introduced before.Then, we propose a new method of data reconciliation based on Low Density Parity Check code(LDPC).Thirdly, since the multi-party data reconciliations require Alice to copy the multiple copied information and to send them to each receiver, the method of multicast transmission to improve the efficiency and quality is proposed. The multicast transmission based on multicast routers requires Alice only to have one copy and send them once rather than multiple copies.Finally, we summarize the thesis, and prospect the further work.