Multi-Party Quantum Key Agreement with Four-Qubit Cluster States Immune to Collusive Attack

Collusion attack is a complex cryptanalysis method that can effectively attack quantum key agreement protocol, where some dishonest participants can conspire to steal the final key or the private key of other participants during the implementation of the protocol. Based on the analysis of the four-particle cluster quantum entangled state, a novel multiparty quantum key agreement protocol is proposed to address the above issues, which can effectively resist collusion attacks. By utilizing a novel particle transfer structure, namely the bidirectional travel structure, the protocol achieves secure key negotiation with the help of a semi-honest third party by using additional particles. In the key negotiation process, all participants' contributions to the key are equal. During the protocol execution process, each participant only needs to perform simple unitary operations, single particle measurements, and Bell state measurements, making the protocol more practical. Analysis shows that this protocol has the characteristics of simple operation and security.