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.

If p == np, then interger factorization can be reduced to k-sat, which is solvable in p time

https://cs.stackexchange.com/questions/6650/how-can-p-np-enh...

> then integer factorization can be reduced to k-sat,

It can be reduced already, but then 3-sat can be solved in P time

Neat, thanks!

If there's an efficient algorithm for solving NP-complete problems then 99% of current cryptography would be broken. Only one-time-pads would still be secure.

But don't worry, if that happens the world would be so different there might no longer be a need for cryptography.

There exist crypto systems independent on P vs NP, both symmetric and asymnetric. The general approach exploits polynomial time complexity differences. However key-sizes increase accordingly: last I saw a key-pair was a few 100's of megabytes. (an enourmous reduction from originally GB's)

But there aren't a lot of proven bounds on polynomial time complexity either. For all we know it may be possible to solve 3-SAT in linear time.