Comment by devy
7 hours ago
> if AI frontier labs do find that P=NP via an efficient algorithm, it could have implications on all modern public key based cryptography.
The fact that other math problems are bulk solved yet nothing from cryptography was released/published as solved could be a strong indicator that "all modern public key based cryptography" could have been at risk.
> The fact that other math problems are bulk solved yet nothing from cryptography was released/published as solved could be a strong indicator that "all modern public key based cryptography" could have been at risk.
“Could be”, but I think the correct way to describe it is “the general public doesn’t know”. It could be any of
- they tried very hard without finding weak spots
- they tried for a while, and gave up because the LLMs didn’t even produce leads
- they tried, found something and kept it for themselves
I think the first is not unlikely. Before LLMs, the likes of the NSA must have looked really hard into these problems, and IMO it’s not likely they found something substantial (if they did, their counterpoints in other large countries likely would find it, too, and some of them would have used that knowledge)
Or it could indicate that more resources have been put into cryptography than most other math fields, so AI hasn't yet caught up to our progress.
It seems rather unlikely that solving the Navier-Stokes problem is harder than e.g. a better attack on a reduced-round AES. Perhaps they think an epsilon improvement in the exponent isn't worth publishing, but it seems more likely that they're intentionally withholding any results they have.
It's a reasonable assumption that the cases where the NSA, etc, had a role in designing cryptographic systems, and reportedly made specific suggestions that could be forms of a backdoor, would all be revealed by AI being tasked to find it. Maybe even indirectly as part of the broader defensive security research by models unreleased to the public. If algorithmic complexity or a really obscure backdoor has existed in cryptographic systems and put there by the Gov't, it seems that current frontier models would have the best chance of revealing it.
Either that or they've not put the model(s) on those problems. Remember that even the Navier-Stokes solution did use a large amount of compute. I'm not sure they'd even want to waste it on problems that they can't get PR from.