Design And Analysis Of Rational Quantum Secret Sharing Scheme

Quantum cryptography is a cross research field arising from the combination of cryptography and quantum mechanics.Quantum cryptography has the property of unconditional security in theory because its security does not depend on difficult problems.At the same time,the development of quantum computers has posed new challenges to classical cryptography,and quantum cryptography has become an important option to deal with the challenges.In the process of long-term development,quantum cryptography has also produced some important branches,such as quantum key distribution,quantum secure summation,quantum key agreement and quantum secret sharing.Quantum secret sharing protocol is a kind of protocol that uses the knowledge of quantum cryptography to solve the secret sharing problem.In traditional quantum secret sharing,agents are divided into “honest” and “dishonest” ones.However,agents tend to be selfish which is called “rationality” in game theory.Rational agents who obtain secrets also hope that other agents cannot obtain secrets or obtain false secrets.However,rational secret sharing protocols prevent rational agents from doing this with a specific mechanism.In this paper,a rational quantum secret sharing(RQSS)protocol is analyzed and modified,and another two new RQSS protocols are designed.Specific research works include:(1)There is a problem in Maitra’s rational quantum secret sharing scheme,that is,the probability of participants guessing the correct secret is greater than the pre-set value.To solve this problem,this paper proposes an improved scheme.By using the new secret distribution method,the probability of participants guessing the correct secret can be less than or equal to the pre-set value.The theoretical analysis of the improved scheme shows that the improved scheme will satisfy the fairness,correctness and Nash equilibrium in rational secret sharing.(2)A rational quantum secret sharing scheme based on GHZ state is proposed.It realizes the secret sharing among n agents by encoding the secret with the link between the measurement base and the measured result.Comprehensive security analysis shows that our presented scheme can defend eavesdropping attack,entanglement attack and collusion attack.Moreover,it is also proved that the new protocol can achieve correctness,fairness,strict Nash equilibrium and K-resilient equilibrium required by rational secret sharing protocol.Compared with the existing rational quantum secret sharing schemes,our scheme is simple and can achieve stronger equilibrium.Besides,it is feasible in practical application since a relevant protocol has been recently implemented on the IBM quantum computer.(3)A rational quantum secret sharing threshold protocol based on multi-qudit entangled states is proposed.The protocol is based on and extends the local operation and classical communication quantum secret sharing(LOCC-QSS)protocol.Through security analysis,the new protocol can resist eavesdropping attack,entanglement attack and collusion attack.Similarly,it also meets a series of requirements of rational protocol:correctness,fairness,strict Nash equilibrium and K-Resilient equilibrium.Finally,the secret recovery process of the protocol only requires local quantum measurement and classical communication to the agent,without any quantum joint measurement.