Research And Design On Quantum(k,n)-Threshold Secret Sharing

The first quantum security communication protocol was proposed by Bennett and Brassard in 1984.Compared with classical transport protocol,the security of quantum transport protocol is higher.In 1999,the first quantum secret sharing protocol,HBB protocol,expended the field of quantum protocol to the secret sharing for the first time.Also at the same year,the quantum threshold secret sharing protocol which was based on HBB and was proposed by Kalsson et.broadened the use range of quantum security communication protocol further.In recent years,some researchers have devoted to the research of quantum threshold secret sharing.In this page,we give a modify of classical Shamir secret sharing scheme based on the method of quantum compute.In the classical scheme,the honesty of participants has been thought positively.But in the real world,the data given by the participants may not be right because of many reasons.In this scheme,we first device the secret based the math method of classical scheme,and design the checking function which is also based on the same method.Then,to protect the security of sub-secret during the transmission phase,we conceive of a transport strategy which based on the entanglement swapping of Bell state and Pauli operator for the scheme.On the last recovery phase,the honesty checking must be done before the real recovery operator,which means the recovery can be done only when the honesty checking has passed.Both the honesty checking and recovery operator are based on the Lagrange interpolation formula.After calculation and analysis,the transmission of modified scheme has feasibility and during the transmission phase,data can not be monitor or copy.At the same time,if any participant wants to cheat during the execution of agreement,it can be detected during the recovery phase with a relatively high probability,that is,the more number of checking bits is,the closer the probability to 1.Compared with classical scheme,this scheme has a higher transmission security,and can be used in the situation which not all the participants are trusted.Compared with other quantum verifiable threshold secret sharing scheme,this scheme is much easier to execute and understand.