Research On The Practical Security Analysis Of High-Dimensional Quantum Key Distribution

Quantum key distribution(QKD)technology can allow two distant legitimate parties to share secret key.Combined with “one-time pad” cryptographic algorithm,QKD can realize theoretical unconditionally secure secret communication.However,the secret key rates of existing QKD systems are so low that restricts the application and development of QKD technology.Compared with conventional QKD protocols,high-dimensional quantum key distribution(HD-QKD)protocol employs high-dimensional photonic degree of freedom to encode information.HD-QKD increases the photon information efficiency and has become one of the effective methods for improving the secure secret key rates of QKD systems.At present,HD-QKD protocol has complete theoretical security proof and has attracted extensive attention and deep research.However,the practical security analysis of HD-QKD is not yet complete.Whereas,the practical security of HD-QKD protocol is crucial to its practical application.In this paper,we focus our attention on the practical security of HD-QKD protocol and analyze the influence of imperfections in practical systems on the practical security of HD-QKD protocol.The main contexts of this paper are as follows:1.The practical security analysis of HD-QKD protocol under wavelength attack.The practical beam splitter may have strong correlations with wavelength where different incident wavelengths may have different coupling ratios.In this paper,we design a concrete wavelength attack scheme towards time-bin HD-QKD system.We calculate the quantum bit error rate introduced by this attacking strategy and analyze the practical security of HD-QKD under wavelength attack.Analysis results show that when the coupling ratio of beam splitter has a strong correlation with wavelength,the eavesdropper can obtain the secret key information without increasing the quantum bit error rate.We also demonstrate that wavelength attack is a universal attacking strategy towards arbitrary d-dimensional QKD systems,and higher-dimensional QKD system is more vulnerable to this attacking strategy.Finally,we analyze the resistance of HD-QKD systems with different basis choice schemes against wavelength attack.We prove that systems with biased basis choice are more vulnerable to wavelength attack.2.The analysis on the influence of non-randomness problem on the practical security of HDQKD protocol.The security of QKD is guaranteed by true random numbers.If the assumption of true random numbers is broken due to practical imperfections,the eavesdropper may have the ability to steal the secret key and threaten the security of QKD systems.Based on the nonrandomness model,we calculate the secret key rates of HD-QKD protocol under the circumstances of single photon source without signal loss,single photon source with signal loss and practical weak coherent source,respectively.Results of numerical simulation show that non-randomness arise from leakage of random numbers will decrease the secret key rate for arbitrary d-dimensional QKD protocol.When signal loss is taken into consideration,the non-randomness is amplified and secret key rate decreases sharply.For practical decoy-state HD-QKD scheme with weak coherent source,the secret key rate will decrease rapidly with increasing the transmission distance even if the nonrandom probability is small.3.The analysis on the influence of the finite intensity modulator extinction on the practical security of HD-QKD protocol.The extinction ratio of realistic intensity modulator is finite,so the incident light cannot be attenuated to zero intensity.Therefore,this imperfect device will always introduce some extra noises and result in higher quantum bit error rate.This will have impact on the practical security of HD-QKD protocol.In this paper,we characterize the mathematical model of extinction ratio in HD-QKD system.Based on this model,we derive the expressions of quantum bit error rate and secure secret key rate of HD-QKD protocol and conduct numerical simulation on the secret key rate.Numerical simulation results show that the secret key rate is improved when taking the finite extinction ratio of practical intensity modulator into account.Moreover,this improvement is more obvious for higher dimensional QKD systems and the superiority of HDQKD protocol is revealed.In addition,the combined effect of finite extinction of intensity modulator and intensity fluctuation of laser source is investigated as well.The secret key rate is improved when considering the finite extinction of intensity modulator.And this improvement is more obvious for larger intensity fluctuation.