If it were in fact easier to factor the product of two primes than any other number, it would be much easier to break the RSA cryptosystem than it is known to be. However, there is no publicly known proof that this is the case, nor is there any known proof that factoring integers is hard.
(I say not *publicly* known because is is possible that the NSA or other similar organization has a proof or algorithm that they're not telling anyone about. They've certainly put a lot of resources into the area.)
That said, there /are/ asymptotically faster methods of factoring than trial division. The mains ones are the "quadratic sieve", "number field sieve", and "elliptic curve method". |
