[betterunix]

For what it's worth, practical secure cryptosystems only exist under a number of assumptions that, thus far, have no proof. Commonly used public-key systems are in an even more precarious position: even if P!=NP, the RSA and discrete logarithm problems may still be computationally feasible (and thus RSA, Diffie-Hellman, and ElGamal would be insecure). Cryptography based on NP-hard problems is possible (e.g. Atjai's lattice system), but these remain research topics and have seen little real-world use.

The point is this: there is a lot we do not know about cryptography.