  The no-go theorem of unconditionally secure quantum bit commitment depends
crucially on the assumption that Alice knows in detail all the probability
distributions generated by Bob. We show that if a protocol is concealing, then
the cheating unitary transformation is independent of any parameters (including
probability distributions) secretly chosen by Bob, so that Alice can calculate
it without knowing Bob's secret choices. Otherwise the protocol cannot be
concealing. Our result shows that the original impossibility proof was based on
an incorrect assumption, despite the fact that its conclusion remains valid
within the adopted framework. Furthermore, our result eliminates a potential
loophole in the no-go theorem.
