  The proof of the No-Go Theorem of unconditionally secure quantum bit
commitment depends on the assumption that Alice knows every detail of the
protocol, including the probability distributions associated with all the
random variables generated by Bob. We argue that this condition may not be
universally satisfied. In fact it can be shown that when Bob is allowed to use
a secret probability distribution, the joint quantum state is inevitably mixed.
It is then natural to ask if Alice can still cheat. A positive answer has been
given by us [13] for the perfect concealing case. In this paper, we present a
simplified proof of our previous result, and extend it to cover the imperfect
concealing case as well.
