Not sure if it's AI slop yet, but I also found the core part (the "oblivious transfers") to be explained too handwavy to really understand the properties of this system. I don't want to know all the mathematical details, but I do want to understand who is exchanging what data with whom. "oblivious transfer" doesn't tell me anything here.
The other (maybe more interesting) question is how this tech would be deployed. So ok, we have a system, where something can only be signed/decrypted/encrypted/etc if several parties are in agreement. Who should the parties be? How is the threshold itself actually managed?
OP also seems to drift between different usage scenarios here:
- some sort of collectively owned good (like the DAO or resources in a cooperative?) - seems straightforward on a technical level (every owner has a partial key) but also a niche usecase and quite inflexible: What happens if an owner drops out or you want to introduce a new one? What happens if you want to change the quorum?
- traditional authentication of individual users against a server, in a federated setup like the fediverse: Seems like the most practical usecase: One party is the user, the other is the server, the verifying party would be other servers of the network. But then you have to pick your poison by how you set the quorum: Either the quorum is "any party can decrypt the data", at which point you're not better than normal password auth; or "both parties are needed", which would protect against the user or the server accidentally leaking the key - but then you're back to "single point of failure" if any party accidentally loses the key.
- the last scenario would be server-side keys that could cause massive problems if they leaked. But I don't understand at all who should be the other parties here. Also how would this be better than HSMs?