Homomorphic encryption as best I'm aware is more than a decade away from practical use. I believe the best libraries today have blowups of 100,000,000x in resource usage, meaning it's not even practical for basic crypto operations.
Multiparty computation makes some security sacrifices (breaks if M out of N people cheat, breaks undetectably iirc), but I think the blowup is less than 10x for some operations and less than 1000x for the others.
Still not pretty, but at least makes certain things possible. But not competitive search engines.
