PSI protocols have been studied for over a decade already. A recent work in our group is to see how much private-contact discovery, a special-case of private-set intersection (PSI), can be sped up such that it can scale to global use-cases. The result is that we have identified two protocols based on MPC, and proposed efficient instantiations and implementations of them for mobile environments that are up to 1000x faster than the previously best approaches. This leads already to acceptable runtimes even if server-sets contain hundreds of millions of contacts, one-time setup data transfers are still prohibitive for popular use though.
The goal of the project is to push this direction further, study more potential approaches and their efficient implementations such that broader use-cases can be realized and remaining obstacles are addressed.
Taiga RIG Inventory project here