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They don’t really have to, they can just mine Bitcoin by reversing SHA256 in polynomial time, inspect https messages to banks, or send Bitcoin to themselves by creating an ECDSA signature… or just set up a software as a service and have the biggest business in the world.



That's assuming that the solution to whether P=NP is P=NP and not P≠NP, isn't it?


>they can just mine Bitcoin by reversing SHA256 in polynomial time

This wouldn't be faster than ASICs. The coefficients would be too big for it to be practical.


n^10 is a polynomial too.

The equality of P and NP would not itself mean there are fast solutions.


Heck, even if P=NP meant there were fast solutions, merely proving that P=NP wouldn't necessarily give you those solutions, and they might turn out to be even harder problems!




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