Theoretical Research On Quantum Cryptographic Protocols

Quantum cryptography is the interdiscipline of quantum mechanics and cryptogra-phy.While the security of modern cryptography is mostly based on hard mathematical problems,the security of quantum cryptography is guaranteed by the quantum mechanic principles,such as quantum no-cloning theorem and uncertainty principle.The core of quantum cryptography is quantum key distribution(QKD),which can distribute secret key between two legitimate parties in an unconditionally secure man-ner.If QKD is combined with the one-time pad encryption algorithm,it can make the information transmission be unconditionally secure.The first QKD protocol is BB84,which was proposed by Bennett and Brassard in 1984.The theoretical security of BB84 protocol has been rigorously proved,and the experiments are developing rapidly.More-over,the practical BB84 system has begun to go to the market gradually.However,there are always deviations between the actual system and the theoretical model,which may lead to potential security loopholes.Therefore,it is important to study the practical security of BB84 protocol.In addition to the QKD protocols,quantum mechanics also has other important applications in cryptography,such as quantum bit commitment protocol,quantum coin tossing(QCT),quantum oblivious transfer protocol and so on.Although these quantum cryptographic protocols do not always have unconditional security like the QKD,in the quantum age,the solutions to these cryptographic tasks within the modern cryptography based on hard mathematical problems will become completely insecure.Therefore,it is of great theoretical significance to study how much degree of security these crypto-graphic tasks can obtain based only on the principles of quantum mechanics.It will provide forward looking for the information security in the quantum age.Among them,practical methods to solve the coin tossing and private queries problems have been pro-posed.However,the quantum processes of these protocols are similar to QKD.There-fore,there may exist practical security loopholes in their practical systems.According to the above analysis,we first study the BB84 QKD protocols,which is focus on its practical security under the finite-key length and the imperfections of quantum devices.Furthermore,we analyze the practical security of the measurement device of QCT and quantum private queries(QPQ)protocols.The results of my research work are summarized as below:1.The finite-size effect of the biased BB84 protocol against the collective attack has been analyzed by using the law of large numbers.Specifically,we have considered the statistical fluctuations when estimating the channel parameters for single-photon source and weak coherent state source,respectively.The confidence interval and confi-dence probability of each channel parameter have been given,following the correspond-ing secret key rate.In the numerical simulations,for single photon source,we simulate the relationship between the secret key rate and the number of received pulses under different channel noises.For weak coherent state source,we simulate that when the number of transmitted pulses is fixed,the relationship between the secret key rate and the transmission distance.In the simulations,we also give the corresponding optimal basis choice probability,which is useful for the experimental realization.2.The main threats for the well known practical BB84 systems are that its encod-ing is inaccurate and measurement device may be vulnerable to particular attacks.Thus,a general physical model or security proof to tackle these loopholes simultaneously and quantitatively is highly desired.Here we give a framework on the security of BB84 when imperfect qubit encoding and vulnerability of measurement device are both con-sidered.In our analysis,the potential attacks to measurement device are generalized by the recently proposed weak randomness model which assumes the input random num-bers are partially biased depending on a hidden variable planted by an eavesdropper.And the inevitable encoding inaccuracy is also introduced here.From a fundamental view,our work reveals the potential information leakage due to encoding inaccuracy and weak randomness input.For applications,our result can be viewed as a useful tool to quantitatively evaluate the security of a practical QKD system.3.QCT is an important primitive of quantum cryptography and has received con-tinuous interest.However,in practical QCT,Bob's detectors can be subjected to detector-side channel attacks launched by dishonest Alice,which will possibly make the proto-col completely insecure.Here,we report a simple strategy of a detector-blinding attack based on a recent experiment.To remove all the detector side-channels,we present a solution of measurement-device-independent QCT(MDI-QCT).This method is similar to the idea of MDI-QKD.MDI-QCT is loss-tolerant with single-photon sources and has the same bias as the original loss-tolerant QCT under a coherent attack.Moreover,it provides the potential advantage of doubling the secure distance for some special case.Finally,MDI-QCT can also be modified to fit the weak coherent state sources.Thus,based on the rapid development of practical MDI-QKD,our proposal can be imple-mented easily.4.QPQ is an important cryptography protocol aiming to protect both the user's and database's privacy when the database is queried privately.Recently,a variety of practi-cal QPQ protocols based on QKD have been proposed.However,for QKD-based QPQ the user' s imperfect detectors can be subjected to some detector-side-channel attacks launched by the dishonest owner of the database.Here,we present a simple example that shows how the detector-blinding attack can damage the security of QKD-based QPQ completely.To remove all the known and unknown detector side channels,we propose a solution of measurement-device-independent QPQ(MDI-QPQ)with single-photon sources.The security of the proposed protocol has been analyzed under some typical attacks.Moreover,we prove that its security is completely loss independent.The results show that practical QPQ will remain the same degree of privacy as before even with seriously uncharacterized detectors.