We can secretly query inputs from a public DBs using what we call in the literature PIR. We can secretly query inputs from a privately held DB by means of Private Set Intersection (PSI). We can also secretly read/write from a private DB, using ORAM. We can even secretly query a private distributed state, by combining ORAM and MPC.
I wonder, however, what happens for the one use case not annotated above. Let us imagine the Query is public, but the DB is secretly held, how could this be achieved?
What if we take the problem a bit further, a secret distributed state, and a public query. Is there a way to do this? Does it even have a name?
