Improved Multi-party Quantum Key Agreement with Four-qubit Cluster States

Quantum key agreement is a promising key establishing protocol that can play a significant role in securing 5G/6G communication networks. Recently, Liu et al. (Quantum Information Processing 18(8):1-10, 2019) proposed a multi-party quantum key agreement protocol based on four-qubit cluster states was proposed. The aim of their protocol is to agree on a shared secret key among multiple remote participants. Liu et al. employed four-qubit cluster states to be the quantum resources and the X operation to securely share a secret key. In addition, Liu et al.'s protocol guarantees that each participant makes an equal contribution to the final key. The authors also claimed that the proposed protocol is secure against participant attack and dishonest participants cannot generate the final shared key alone. However, we show here that Liu et al. protocol is insecure against a collusive attack, where dishonest participants can retrieve the private inputs of a trustworthy participant without being caught. Additionally, the corresponding modifications are presented to address these security flaws in Liu et al.'s protocol.