  The mediated semi-quantum key distribution (MSQKD) protocol is an important
research issue that lets two classical participants share secret keys securely
between each other with the help of a third party (TP). However, in the
existing MSQKD protocols, there are two improvable issues, namely (1) the
classical participants must be equipped with expensive detectors to avoid
Trojan horse attacks and (2) the trustworthiness level of TP must be honest. To
the best of our knowledge, none of the existing MSQKD protocols can resolve
both these issues. Therefore, this study takes Bell states as the quantum
resource to propose a MSQKD protocol, in which the classical participants do
not need a Trojan horse detector and the TP is dishonest. Furthermore, the
proposed protocol is shown to be secure against well-known attacks and the
classical participants only need two quantum capabilities. Therefore, in
comparison to the existing MSQKD protocols, the proposed protocol is better
practical.
