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Up: 3.4 Factoring and Discrete
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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.