How to ethically publish the result in case we prove that P = NP? Suppose a researcher discovers that $P=NP$, and has an efficient algorithm for some common NP-Complete problem.  Given the implications for cryptography, what would be the most ethical way for them to reveal this knowledge to the world, without causing the downfall and destruction of technological civilization?
I'll try to answer what I view to be a much easier question to answer, while still (in my view) capturing the &quot;essence&quot; of the problem.

How can one &quot;prove&quot; that they have an efficient algorithm for an NP-complete problem without publishing the algorithm?

There are many things one can do, but the simplest is to solve challenges.
There are a large number of computational challenges which have been posted over the years, for example:

RSA factoring challenges

Lattice Crypto challenges


If one solved a variety of these challenges in extremely high dimension and posted the solutions publicly, it would very quickly erode confidence in the hardness of the underlying problems.
After waiting a suitable amount of time, you could then publicly post your algorithm.
Of course, it is difficult to talk about what a &quot;suitable amount of time&quot; is for public disclosure that would break all of cryptography, which is why I avoided your initial question.