What is the name of the crypto system used by ICANN’s DNS recovery system?


I once heard about a type of crypto system that behaves in the following way: I have x secret keys that work together to decrypt messages encrypted with a public key d. If I get at least n of the x secret keys together, I can decrypt messages encrypted with d in their entirety. If I have anything less than n, I get no information about those messages.

When this system was being described to me, I was told that an example of this system in the real world is ICANN’s system for recovering the DNS registry in the event of some catastrophic failure. In their case, x = 7.

I heard about this a little while ago, and I don’t remember exactly what the system is called. I have tried to research it with the ICANN website, but I can’t seem to find an actual name of the system that I can use to then do a deeper dive into this. Does anyone know the name of the system I just described? Also, since I am trying to dive rather deeply into this, I would also appreciate any resources (research papers, open-source implementations, additional real-world examples, etc.) that could be listed.

Thank you!