I am not a mathematician, but this seems like something that might have crossed the minds of math savvy people. Yes, this seems extremely unlikely, but as a thought experiment, what would come next?<p>Given the impact and implications this would have:<p>- How would anyone even go about publishing anything like this without literally breaking the world?<p>- Would this actually break the world?<p>- What if they were malicious? Could something like this sneak under the radar and escape to the dark web to be exploited by criminals?<p>- What if they were not malicious, but had non-scientific (cough) monetary, goals in mind, would there even be a way to somehow milk this?<p>- What if they were a scientist, purest of heart, how would they go about this?<p>- Wouldn't this have to be done anonymously for personal security reasons?<p>Watching the humanity over the past few years has been.. illuminating. I am not sure we are even remotely close to being set up to handle something like this.<p>What do you think?
There is at least one [science fiction] short story where this happens. Greg Egan, maybe?<p>There is a fast quantum factorization method, Shor's Algorithm. As far as we know, it is not yet practical. However, there is ongoing work on post-quantum cryptography that would be safe against such attacks.<p>The most likely users for a fast factorization algorithm that could break RSA encryption are nation-states. They would obviously keep this capability secret.<p>Nation-states have compromised many systems anyway, without needing to break this kind of cryptography. We are not really set up to handle this either.