Proving the Security of Mediated Semi-Quantum Key Distribution Using Entropic Uncertainty Relation

In recent years, mediated semi-quantum key distribution (MSQKD) has become a hot topic in quantum cryptography. In this study, the original MSQKD protocol is revisited and a new scheme for proving security based on information theory is developed. At first, a new bound on the key rate of the protocol is derived using an entropic uncertainty relation, thus proving the unconditional security of the protocol. In addition, in the asymptotic scenario, a higher noise tolerance that improves the previous results is found. The legitimate communicating parties have to abort the protocol when they observe the error rate is larger than the noise tolerance. Furthermore, the security of a single-state MSQKD protocol and a single-state semi-quantum key distribution (SQKD) protocol is proven using a similar scheme.