  Quantum key agreement enables remote participants to fairly establish a
secure shared key based on their private inputs. In the circular-type
multiparty quantum key agreement mode, two or more malicious participants can
collude together to steal private inputs of honest participants or to generate
the final key alone. In this work, we focus on a powerful collusive attack
strategy in which two or more malicious participants in particular positions,
can learn sensitive information or generate the final key alone without
revealing their malicious behaviour. Many of the current circular-type
multiparty quantum key agreement protocols are not secure against this
collusive attack strategy. As an example, we analyze the security of a recently
proposed multiparty key agreement protocol to show the vulnerability of
existing circular-type multiparty quantum key agreement protocols against this
collusive attack. Moreover, we design a general secure multiparty key agreement
model that would remove this vulnerability from such circular-type key
agreement protocols and describe the necessary steps to implement this model.
The proposed model is general and does not depend on the specific physical
implementation of the quantum key agreement.
