A Bitcoin wallet wants to ask a server: "Do I own any UTXOs under scripthash X?" A naive request writes X in the clear. The server — or anyone who can see the traffic — learns every address you care about.

The only other option is to download the whole UTXO set yourself and check locally. That's > 10 GB and growing, and it ships every ratchet of other people's addresses to your device just so you can check your own. Private Information Retrieval (PIR) sits between these two extremes: the server answers the question without ever learning which question you asked.

nothing about which row → nothing about Alice

What PIR guarantees: the server processes your query without learning which entry in the database you read. What it costs: the server must touch every row — privacy comes from making every query look identical. BitcoinPIR is about making that cost acceptable for real wallets on real devices.