### What are
the Prospects for a Theoretical Factoring Breakthrough?

Factoring is widely believed to be a
difficult mathematical problem, but 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 remote by the researchers
most actively engaged in factoring research.

Another possibility is that someone
will prove that factoring is difficult. Such a development,
while unexpected at the current state of theoretical
factoring research, would guarantee the security of RSA
beyond a certain key size.

Even if no breakthroughs are discovered
in factoring algorithms, both factoring and discrete
logarithm problems can be solved efficiently on a quantum
computer (see
Question 109) if one is ever
developed.