SPIR ⇒ IT-PIR

Fully-black-box reduction · standard model · folklore · security loss: None: construction and reduction are the identity.

Statement

Multi-server SPIR strengthens multi-server PIR by data privacy — the client learns nothing about the database beyond the retrieved entry — and keeps its correctness and per-server query-privacy requirements, so every SPIR protocol is an IT-PIR protocol, with the servers’ shared randomness that information-theoretic SPIR uses folded into the answer algorithm — folklore.

Sketch

Drop the data-privacy requirement from the SPIR definition; what remains is the multi-server PIR definition, met by the same queries and answers.