Improving the security of protocols of quantum key agreement solely using Bell states and Bell measurement

Abstract

In a recent study, Shukla et al. (Quantum Inf Process 13:2391---2405, 2014) proposed two quantum key agreement protocols based on Bell state and Bell measurement, and they claimed that their two protocols were secure. However, in this study, we will show that the three-party protocol they proposed is not secure. Any participant in the protocol can directly obtain other two participants' secret keys. More seriously, two dishonest participants in the protocol can conclude to determine the shared key alone. Furthermore, we will show that there is another minor flaw in their two protocols; that is, eavesdroppers can flip any bit of the final key without introducing any error. In the end, some possible improvements are proposed to avoid these flaws.