If P=NP, then you can invert in polynomial time (assuming this is practical) arbitrary boolean functions and thus solve any equations (that can be specified as a boolean circuit), find keys to any cryptosystem etc.

For example, you can assume part of the plaintext (like a header in transmission) and solve an equation (which can be restated as a SAT instance) that yields you a key assuming certain cryptographic algorithm was used. So pretty much all cryptography relies on P!=NP.