<http://www.math.okstate.edu/~wrightd/crypt/crypt-intro/node23.html> >> ... It is suspected but not yet known that factoring is NP-complete.
Of course, if factoring were to be shown NP-complete and quantum computers could be built to run Shor's factoring algorithm in polynomial time, then quantum computers could solve all NP-complete problems in polynomial time. Big advance for quantum computation.