Improving the security of quantum key agreement protocols with single photon in both polarization and spatial-mode degrees of freedom

Abstract

Quantum key agreement enables remote users to fairly establish a secure shared key based on their private inputs. In the circular-type multiparty quantum key agreement protocol, two or more malicious participants can collude together to steal the private inputs of honest participants or to generate the final key alone. In this paper, we focus on a powerful collusive attack strategy in which two malicious participants in particular positions, can learn sensitive information or generate the final key alone without revealing their malicious behavior. Most of the proposed circular-type multiparty quantum key agreement protocols are not secure against this particular 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. We then 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. Our model is general and does not depend on the specific physical implementation of quantum key agreement.