Multi-party quantum key agreement protocol secure against collusion attacks

The fairness of a secure multi-party quantum key agreement (MQKA) protocol requires that all involved parties are entirely peer entities and can equally influence the outcome of the protocol to establish a shared key wherein no one can decide the shared key alone. However, it is found that parts of the existing MQKA protocols are sensitive to collusion attacks, i.e., some of the dishonest participants can collaborate to predetermine the final key without being detected. In this paper, a multi-party QKA protocol resisting collusion attacks is proposed. Different from previous QKA protocol resisting $$N-1$$N-1 coconspirators or resisting 1 coconspirators, we investigate the general circle-type MQKA protocol which can be secure against t dishonest participants’ cooperation. Here, $$t < N$$t<N. We hope the results of the presented paper will be helpful for further research on fair MQKA protocols.