Research Of Rational Quantum State Sharing Protocols

In the information age with the rapid development of science and technology,communication between people is becoming more and more smooth.However,the frequent occurrence of information security events has seriously threatened people’s normal life.Therefore,how to ensure the security of communication is an important problem to be solved urgently.Based on the basic principles of quantum mechanics,quantum cryptography enables the unconditional security of communication.As an important branch of quantum cryptography,quantum secret sharing protocol has become the main research field.In the quantum secret sharing protocol,the dealer and multiple participants share secret information,and the secret information can be classical information or quantum information.If the secret information is quantum information,the corresponding protocol is also called quantum state sharing protocol.The rational quantum state sharing protocol combines the quantum state sharing protocol with game theory to enable participants can participate in the protocol with rational thought,which is of great significance for the development and application of the quantum state sharing protocol.However,there are two problems in the current rational quantum state sharing protocol:the first is the frequent information exchanging between the dealer and the participants because the dealer is online;the second is the rational quantum state sharing protocol with stronger generality has not been studied,which is not conducive to the further development of the rational quantum state sharing protocol.So,in view of the above problems,this paper proposes a rational quantum state sharing protocol with the semi-off-line dealer and a rational hierarchical quantum state sharing protocol.The specific research contents are as follows:(1)A rational quantum state sharing protocol with the semi-off-line dealer.In order to solve the problem that the information exchanging between the dealer and the participants due to the fact that the dealer is online,a rational quantum state sharing protocol with the semi-off-line dealer is proposed.Firstly,the dealer shares an arbitrary two-particle entangled state with n+1 participants through EPR pairs and GHZ states.The EPR pairs are prepared by the participant who can reconstruct the shared quantum state,reducing the workload of the dealer.Secondly,all participants have the same probability of reconstructing the shared quantum state,which guarantees the fairness of the protocol.In addition,the dealer is semi-off-line in this protocol,which considerably reduces frequency of information exchanging between the dealer and the participants,and reduces the risk of the dealer directly providing the secret to the participants.Finally,the security,fairness,correctness and strict Nash equilibrium of this protocol are analyzed.The results show that the rational quantum state sharing protocol with the semi-off-line dealer has certain research and application value.(2)A rational hierarchical quantum state sharing protocol.In order to solve the problem that the generality of the rational non-hierarchical quantum state sharing protocol is not good enough,a rational hierarchical quantum state sharing protocol is proposed by using the Rubenstein bargaining model.Firstly,the dealer Alice shares an arbitrary two-particle entangled state with m high-power participants and n low-power participants through m+n+1-particle cluster states.The high-power participants and low-power participants have different authorities to reconstruct the shared quantum state.Therefore,in order to ensure the fairness of the protocol,the participant David who can reconstruct the shared quantum state is jointly elected by all participants,so that the participants with different powers have the same possibility to be David.Secondly,in the process of reconstructing the shared quantum state,when David is a high-power participant,David does not need the help of all the low-power participants.Under this circumstance,based on the Rubenstein bargaining model,the process between David and the low-power participants is analyzed,and the bargaining equilibrium of the bargaining game is solved.Finally,the security,fairness,correctness and strict Nash equilibrium of this protocol are analyzed,and the comparative analysis shows that this protocol is more general.Therefore,this research is beneficial to promote the development of the rational quantum state sharing protocol.