Research Of Designing Novel Quantum Secret Sharing Protocols

With the development of information technology,the importance of private data has been considered.As a vital branch of cryptography,quantum cryptography is only based on the fundamental principles of quantum mechanics,so it offers the possibility of designing unconditional secure cryptography protocols a nd ensure the security of data.And therefore it is widely developed and researched thoroughly.Quantum secret sharing is a kind of quantum cryptography protocol which could be utilized to resolve secret sharing problem.It is also a hot topic of research in quantum cryptography.Up to now,many quantum secret sharing protocols have been proposed.The focuses of quantum secret sharing protocols are to improve the efficiency and practicality on the premise of guaranteeing the security and correctness.On one hand,the security of existing(k,n)-threshold quantum secret sharing protocols based on local operations and classical communication(LOCC-QSS)needs to be enhanced.Moreover,in existing quantum secret sharing protocols,there are fewer researches on universality and fairness for participants which have much influence on the practicality of protocol.In this thesis,security,universality and fairness of protocols are studied in depth,respectively.The optimal LOCC-QSS protocol,universal quantum secret sharing protocol and rational quantum state sharing protocol which certificates the fairness are designed.On the other hand,since secret sharing is widely utilized in secure multi-party computation,the rational quantum secure multi-party computation protocol are also proposed based on rational secret sharing protocol in this thesis.(1)The research of optimal LOCC-QSS protocol based on local distinguishability.In this thesis,the(k,n)-threshold quantum secret sharing protocol is an important field in quantum information processing and quantum cryptography.The(k,n)-threshold LOCC-QSS protocol is investigated.Firstly,in order to effectively study the LOCC-QSS protocol,the digital and graphical representations of judgement space are introduced creatively.These representations are simple and convenient.Secondly,an algorithm is designed to search optional states for any given k and n.The unambiguous probability of distinguishing optional states obtained by this algorithm equals 0 when x participants cooperate(x<k).Thirdly,a method is proposed to decrease the guessing probability.Based on the method,some protocols obtained are more secure than existing ones.Last but not least,the conditions of optimal LOCC-QSS protocols are given for the first time.(2)The research of universal quantum secret sharing protocol.Universality which affects the practicality of protocol must be considered in large-scale applications.In this thesis,a kind of universal quantum secret sharing protocol is studied.Firstly,a quantum secret sharing protocol is investigated via Borras-Plastino-Batle(BPB)state.Participants in this protocol only need to perform projection measurement operators instead of any unitary operator,which makes our protocol easy to implement.Secondly,the universality of quantum cryptography protocol is researched for the first time.Concretely,the module division of quantum cryptography protocol,and the coupling of different modules are discussed.The proposed universal protocol is analyzed as an example.On one hand,plenty of quantum states(the BPB-class states and the BPB-like-class states which are proposed in this thesis)could be employed as the quantum carriers in this protocol.On the other hand,this protocol could be modified as a quantum private comparison protocol by changing a few operations.These situations are rare in quantum cryptography protocols,which make our protocol more robust.Thirdly,the entanglement of BPB-class states is calculated using pseudo entanglement and geometric measure.The results show that BPB-class states are highly entangled,and have value in research and application.(3)The research of rational quantum state sharing protocol.The aim of rational participants is maximizing their utilities.They may choose any strategy to achieve their aims.The protocol with rational participants will be more in line with actual situation than that with honest,semi-honest or dishonest participants.The rational non-hierarchical quantum state sharing protocol is investigated.Firstly,learning from Li et al.'s protocol,a novel rational protocol is designed to share arbitrary two qubits among multiple participants.Assumptions in our protocol are more practical than existing rational quantum state sharing protocol.Secondly,general steps of some existing non-hierarchical quantum state sharing protocols are summarized.A new rational protocol is proposed by modifying these steps.It means that numerous common protocols could be modified as rational protocols.Therefore,the proposed protocol is widely applicable in this view.Thirdly,the utilities,security,correctness,fairness,Nash equilibrium and Pareto optimality of protocol are discussed in detail.Here,since the participant who recovers the state plays a more important role in a quantum state sharing protocol,the utilities,correctness and fairness of protocol are formally defined.Analyses prove that our protocol is rational and secure.The protocol is also all-win for participants.(4)The research of quantum secure multi-party computation.Rational protocol is more practical and important,but less researched in quantum multi-party computation.In this thesis,a multi-functional rational quantum secure multi-party computation is investigated.Firstly,a rational quantum summation protocol is proposed.Secondly,the protocol is generalized to a rational quantum multi-party computation protocol.The problem which is homomorphic could be resolved using our protocol.Thirdly,from the view of utilities,correctness,Nash equilibrium and fairness,analyses show that our protocol satisfies the conditions of rational protocols.Moreover,analyses also prove that our protocol is secure,efficient and practical.Our research will contribute to the progress of quantum secure multi-party computation protocol.