Couple of corrections: 1) Public key cryptography relies on difficulty of factoring products of large primes. 2) Non-quantum computers can factor these number

Couple of corrections: 1) Public key cryptography relies on difficulty of factoring products of large primes. 2) Non-quantum computers can factor these numbers, it is just that the nature of the problem seems to require an expensive (non-polynomial to size of input) algorithm on classical computers. With quantum computers a polynomial time algorithm exists (Shor's algorithm).