Research On Information Reconciliation For Continuous-Variable Quantum Key Distribution

Information security is related to national security,and cryptography is the foundation and core of information security.With the coming of "the second quantum revolution",the threat for the classical encryption algorithm based on mathematical complexity not only comes from quantum computing but also from potential advances in number theory,where an efficient factorization al-gorithm might be found for classical Turing machines.Quantum key distribu-tion is based on the basic principles of quantum physics,which can generate a secure key for both sides of the legitimate communication.When there is an eavesdropper in the communication link,it will be found by both sides of the communication.Combined with the "one-time pad" encryption,it can achieve unconditional secure communication in theory.In recent years,quantum key distribution(QKD)has been widely studied as an ideal alternative to classical encryption algorithms.QKD is mainly divided into discrete variable(DV)protocol and contin-uous variable(CV)protocol.CV-QKD protocol started relatively late,among which Gaussian modulated coherent state CV-QKD protocol has the advantages of easy implementation and low cost.In recent years,it has developed rapidly in the improvement of related protocols,security proof and experimental system.Complex post-processing algorithm,especially information reconciliation algorithm,has always been an important factor limiting the performance of CV-QKD system,because information reconciliation algorithm has an impact on the transmission distance and security rate of the system.Especially when the system transmission environment is unstable,the information reconciliation al-gorithm with signal-to-noise ratio(SNR)compatibility is the guarantee of the stable key generation.Aiming at the above problems,this thesis studies the in-formation reconciliation algorithm of CV-QKD.The main work is as follows:1.Analyze and optimize low code rate high performance Raptor codes and Raptor-like LDPC codes.The encoding and decoding methods of Raptor codes are studied,and the optimization method and error correction performance un-der the condition of low SNR are analyzed.This thesis studies the design and construction methods of Raptor-like LDPC codes.We use the degree distribu-tion of multi-type LDPC codes to design Raptor-like LDPC codes with code rate of 0.02,and analyze the error correction performance at low SNR.When the frame error rate is reduced to 10-2,the gap from Shannon limit is only 0.3 dB.Taking code rate 0.02 as an example,this thesis introduces the construction method of lower-triangular form Raptor-like LDPC code,which can greatly re-duce the encoding complexity and facilitate the implementation on hardware platform.2.Research on rateless reconciliation algorithm based on Raptor code.This algorithm can solve the problem that the traditional fixed rate decoding method(such as LDPC code)can only get better error correction performance in some fixed SNR,and the optimization for low SNR is complex.The algo-rithm not only maintains the rateless property but also achieves high efficiency(more than 95%)in different SNRs(-20-0 dB)using just one degree distri-bution.It significantly decreases the complexity of optimization and increases the robustness of the system.Using this protocol,the CV-QKD system can operate with the optimal modulation variance,which can further inmprove the secret key rate.The proposed protocol can maintain highly efficient key ex-traction under the wide range of SNRs and paves the way toward the practical application of CV QKD systems in flexible scenarios.3.Research on the application of the rateless reconciliation algorithm based on Raptor code.The first is applied in the free space channel CV-QKD system.We analyze the influence of transmittance fluctuation on SNR and pro-pose a information reconciliation algorithm for free space CV-QKD system.This algorithm can obtain a stable reconciliation efficiency when the SNR of the channel fluctuates.The second is that it can support the system to extract the key at very low SNR.In the experiment of CV-QKD over long distance and ultra-low loss optical fiber,the secure key can be extracted at ultra-low SNR(less than-26 dB)by using the rateless reconciliation algorithm.The secret key rate is 6.214 bps at 202.81 km.4.Research on the rate compatible information reconciliation algorithm based on Raptor-like LDPC codes.For the first time,we introduce Raptor-like LDPC codes into CV-QKD system.According to the puncture and extension method of parity-check matrix,we optimize the structure of submatrix.We de-sign the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034.Simulation results show that we can achieve more than 98%reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than-16.45 dB.Through the test of the algorithm on GPU platform,we compare and analyze the influence of different code rate,matrix size and itera-tion times on the decoding speed.This algorithm allows the system to maintain a high key extraction rate under various SNRs,paving the way for practical applications of CV-QKD systems with different transmission distances.