I'm often playing around with prime numbers, just for fun. Imagine, I found an algorithm by accident that factorizes numbers into their prime parts exactly as fast as multiplicating them in the first place. I know this is extremly unlikely. But imagine I did. Imagine also, that it's easy to proof having some new kind of "mathematical paradigm" I found that's valid.
Now, as far as I understand that, that would have many consequences in cryptography.
So, what to do then? Just release the information in a mathematical journal and risks many many businesses worldwide who are suddenly open to attack? Or contact the NSA?
Who would be responsible for any action? And if anyone at all, which actions will they do?