One-way (trapdoor) functions are at the heart of some encryption schemes such as RSA and PGP. So far there is no known method or algorithm of factoring product of two large primes in polynomial time. Absent breakthroughs in quantum computing, a 4096bit RSA PGP key would take much longer than the known age of the universe to brute force, even with general number field sieve (GNFS) algorithm... <br /><br />As far as I know, no one has published anything either way that proves there cannot possibly be a way to factor in polynomial time (using conventional non-quantum computing techniques) nor has there been a proof that states there is or should/could be a way to factor in polynomial time. Basically it is a big unknown...<br /><br />Is there any literally or explanation that shed light on why and how it is so fundamentally different to factor the product of two very large and approximately equal length primes? Is there a law of mathematics or some sort of platonic barrier to strictly forbids there being a shortcut?
