  Shor's factoring algorithm uses two quantum registers. By introducing more
registers we show that the measured numbers in these registers which are of the
same pre-measurement state, should be equal if the original Shor's complexity
argument is sound. This contradicts the argument that the second register has
$r$ possible measured values. There is an anonymous comment which argues that
the states in these registers are entangled. If so, the entanglement involving
many quantum registers can not be interpreted by the mechanism of EPR pairs and
the like. In view of this peculiar entanglement has not yet been mentioned and
investigated, we think the claim that the Shor's algorithm runs in polynomial
time needs more physical verifications. We also discuss the problem to certify
quantum computers.
