  Semi-quantum key distribution (SQKD) protocols attempt to establish a shared
secret key between users, secure against computationally unbounded adversaries.
Unlike standard quantum key distribution protocols, SQKD protocols contain at
least one user who is limited in their quantum abilities and is almost
"classical" in nature. In this paper, we revisit a mediated semi-quantum key
distribution protocol, introduced by Massa et al., in 2019, where users need
only the ability to detect a qubit, or reflect a qubit; they do not need to
perform any other basis measurement; nor do they need to prepare quantum
signals. Users require the services of a quantum server which may be controlled
by the adversary. In this paper, we show how this protocol may be extended to
improve its efficiency and also its noise tolerance. We discuss an extension
which allows more communication rounds to be directly usable; we analyze the
key-rate of this extension in the asymptotic scenario for a particular class of
attacks and compare with prior work. Finally, we evaluate the protocol's
performance in a variety of lossy and noisy channels.
