  We investigate the security against the intercept/resend and translucent
attacks on the quantum key distribution protocol based on the pre- and
post-selection effect. In 2001, Bub proposed the quantum cryptography scheme,
which was an application of the so-called mean king's problem. We evaluate a
probability that legitimate users cannot detect eavesdropper's malicious acts
for Bub's protocol. We also estimate a probability that the eavesdropper
guesses right at the random secret key one of the legitimate users tries to
share with the other one. From rigorous mathematical and numerical analyses, we
conclude that Bub's protocol is weaker than the Bennett-Brassard protocol of
1984 (BB84) against both the intercept/resend and translucent attacks. Because
Bub's protocol uses a two-way quantum channel, the analyses of its security are
tough to accomplish. We refer to their technical points accurately in the
current paper. For example, we impose some constraints upon the eavesdropper's
strategies in order to let their degrees of freedom be small.
