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In this paper we provide a proof of unconditional security for a semi-quantumkey distribution protocol introduced in a previous work. This particularprotocol demonstrated the possibility of using $X$ basis states to contributeto the raw key of the two users (as opposed to using only direct measurementresults) even though a semi-quantum participant cannot directly manipulate suchstates. In this work we provide a complete proof of security by deriving alower bound of the protocol's key rate in the asymptotic scenario. Using thisbound we are able to find an error threshold value such that for all errorrates less than this threshold, it is guaranteed that $A$ and $B$ may distill asecure secret key; for error rates larger than this threshold, $A$ and $B$should abort. We demonstrate that this error threshold compares favorably toseveral fully quantum protocols. We also comment on some interestingobservations about the behavior of this protocol under certain noise scenarios.

Security of a Semi-Quantum Protocol Where Reflections Contribute to the Secret Key