I dont remember exactly, but it's possible to create a completely anon search engine. User encrypts the query using their key and sends it to search engine, search engine now doesn't know the query, but then it encrypts its entire database using public key of user and see if hashes meet for keywords?... something like that

I think you might be referring to homomorphic encryption. If I recall, the issues with it are the operations are expensive and it has a large overhead.