  We investigate how to attack Shor's quantum algorithm for factorization with
an entangling probe. We show that an attacker can steal an exact solution of
Shor's algorithm outside an institute where the quantum computer is installed
if he replaces its initialized quantum register with entangled qubits, namely
the entangling probe. He can apply arbitrary local operations to his own probe.
Moreover, we assume that there is an unauthorized person who helps the attacker
to commit a crime inside the institute. He tells garbage data obtained from
measurements of the quantum register to the attacker secretly behind a
legitimate user's back. If the attacker succeeds in cracking Shor's algorithm,
the legitimate user obtains a random answer and does not notice the attacker's
illegal acts. We discuss how to detect the attacker. Finally we estimate a
probability that the quantum algorithm inevitably makes an error, of which the
attacker can take advantage.
