3.4.7 What are the prospects for theoretical factoring breakthroughs?

  Although factoring is strongly believed to be a difficult mathematical problem, it has not been proved so. Therefore there remains a possibility that an easy factoring algorithm will be discovered. This development, which could seriously weaken RSA, would be highly surprising and the possibility is considered extremely remote by the researchers most actively engaged in factoring research.

Another possibility is that someone will prove that factoring is difficult. This negative breakthrough is probably more likely than the positive breakthrough discussed above, but would also be unexpected at the current state of theoretical factoring research. This development would guarantee the security of RSA beyond a certain key size.