Research On Quantum Secret Sharing And Its Application

With the successful launch of the first quantum scientific experimental satellite "Mo-Zi" in the world and the realization of intercontinental quantum communication,the practical technology of quantum communication has ushered in a new development climax.On the other side,the current research on quantum computers presents a global threat to the traditional cryptography system.This long-standing system was born with a severe security flaw,that is,incapability to detect eavesdropper.Both sides could benefit from the quantum communication protocol research,which not only provides a theoretical groundwork for the quantum communication technology application,but also provides a new method for secure information transmission.The quantum secret sharing(QSS)scheme is an important extension of the classical secret sharing scheme in the field of quantum cryptography.Because of its securer key protection and management mechanism,the QSS scheme has received extensive attention from scholars in recent years.There are various QSS schemes.Among them,the QSS scheme based on the local distinguishability of the orthogonal quantum state shows higher potential because of its following advantages:low cost of using quantum channel,improved security by detecting eavesdropping,and easier secret recovery without the need for the initial participants.Rooted on the QSS scheme,the objectives of this study were:1)perform a thorough investigation on the local distinguishability of the orthogonal Dicke state;2)design a(k,n)threshold QSS scheme that can resist the unambiguous attack;3)design a restricted(k,n)threshold QSS scheme with better universality;and 4)apply the above QSS schemes to a quantum auction protocol.The main research results and new findings are summarized as follows.(1)The local distinguishability of the orthogonal Dicke state is completed.Our results reveal a more accurate and intuitive evaluation parameter for the security of QSS scheme based on the local distinguishability of the orthogonal Dicke state.In distinction determination,we qualitatively provide the relationship between the number of participants and the local distinguishability;and quantitatively provide the probability calculation formula of the successful distinction.In distinction speculation,an intuitive guess probability formula is derived from the number of participants and the status of quantum states.Therefore,we achieve the goal of direct determination of the information leakage caused by the unambiguous attack and/or guessing attack when a specific pair of orthogonal Dicke States is given.(2)Based on the local distinguishability of high-dimensional orthogonal symmetric entangled states,we design a(k,n)threshold QSS scheme that can resist the unambiguous attack.To the best of our knowledge,it is the first time that the "judgement space" concept is proposed,which can be used to better describe the local distinguishability of quantum states.According to the local distinguishability analysis of the high dimensional orthogonal symmetric entangled states,it is found that the quantum state selected with the scheme to resist the unambiguous attack must satisfy the equal k level judgement space and two conditions of the k-1 level judgement space.To alleviate the constraints of the quantum state selection,a straightforward tri-quantum-states coding method is proposed and consequently proved to be sufficient.This new method utilizes the local distinguishability of three orthogonal quantum states,which eventually contributes to the resistant to the unambiguous attack.Our method shows a better adaptability compared to other similar methods.It lays out an important theoretical foundation for the design of LOCC-QSS scheme in the future.(3)A restricted(k,n)threshold QSS scheme with better universality is proposed based on the local distinguishability of GHZ-like state.In this scheme,all of the participants are divided into k groups.Any k participant from different k groups can obtain secret information by cooperating with each other.The advantage of this scheme is the inner monitoring ability among members within each group.Since each member has same right within each group,the concept of the derivative state is proposed.In addition,the characteristics of stabilizer of the GHZ-like state and its derivative state are further analyzed,which result in a measurements set that can be used to detect eavesdropper for this scheme.Compared with existing schemes,the k in our scheme can take any value not bigger than n,thus has better universality.(4)Several QSS schemes based on the local distinguishability of quantum state are successfully applied in a quantum auction protocol.Through comparison of multiple schemes,we find even the basic scheme(QSS scheme with potential unambiguous attach and guessing attack)can assure the overall security of the quantum auction protocol.In this section,we first analyze the existing quantum auction protocol.From this analysis,we propose a set of evaluation criteria for the effectiveness of conspiracy attack from malicious bidders.Subsequently,we obtain a secure auction protocol by eliminating the bidder altering the bidding price afterwards through utilization of public register and the unitary operation.Beyond that,in order to improve the feasibility of the quantum auction protocol,another modified method is proposed.This new protocol utilizes an economical single particle state instead of entangled state,and its security is also evaluated through information entropy.