Design And Analysis Of Quantum Secret Sharing Protocols Based On Single Particles

Quantum secure communication is a research hotspot of the secure communication area,which has the unconditional security(in theory)and the capability of detecting eavesdropping.Quantum secret sharing(QSS)is one of the contents of quantum secure communication,which provides new ideas and methods for the multi-party key management of secure communication.In this thesis,we mainly study the design and security analysis of quantum secret sharing protocol based on single particles.Specific work contents are as follows.First,in the design aspect of quantum secret sharing protocol,a QSS protocol based on single dlevel particles is proposed,and its qubit capacity is analyzed.It is shown that the efficiency of the quantum resource utilization is higher than that of other QSS protocols based on single d-level particles in recent years.Then the security of the QSS protocol is also analyzed,which is secure against several common attacks.Besides the protocol is extended to many-to-many situation.Secondly,in the aspect of security analysis of quantum secret sharing protocols,on the basis of previous research,the relation between two-level unitary operation selection and the security of QSS protocols is studied more comprehensive and thoroughly.Based on 5 common unitary operations,the quantitative calculation and analysis of one-step unitary operation and two-step unitary operation are carried out.In the analysis of one-step unitary operation,we conclude a simplified minimum failure probability formula.Also we can obtain that with the increase of unitary operation number,the security of QSS protocols will not always be improved.In the analysis of two-step unitary operation,712 sets of the two-step unitary operation are calculated,then a diagram of probability distribution is given.Thus,we could choose the appropriate unitary operation set according to the security requirements when a QSS protocol is designed.Furthermore,the relation between three-level unitary operation selection and the security of QSS protocols is studied.According to the security analysis of two-level unitary operation,we choose 4 three-level unitary operation with better security,and also carry out the quantitative calculation and analysis of the sets of one-step and two-step unitary operation.In the analysis of one-step unitary operation,we calculate the security of 7 unitary operation sets.Besides,we obtain a more simplified formula of the minimum failure probability.In the analysis of two-step unitary operation,the security of 87 unitary operation sets is calculated,and a diagram the probability distribution is given.The conclusion is similar to that of two-level unitary operation,that is,with the increase of the number of three-level unitary operation,the security of QSS protocols will not always be improved.Known from the above calculation,the maximum security value of the one-step and two-step unitary operation is both 0.577,and that of two-level unitary operation is 0.707,which indicates that the safety of the threelevel unitary operation is no higher than the security of two-level unitary operation.In this thesis,the design of multidimensional high capacity QSS protocols is studied.We make a quantitative calculation and depth analysis on the relation between the selection of two-level and threelevel unitary operation and the security of QSS protocols.The conclusions play an important role in guiding when we choose the unitary operation to ensure the communication security.