Two-Level Private Information Retrieval

Ruida Zhou, Chao Tian, Hua Sun, James S. Plank

Abstract: In the conventional robust $T$ -colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any $T$ colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the ( $N, T_{1}: K_{1}, T_{2}: K_{2}$ ) two-level PIR system, where $K_{1}$ messages need to be retrieved privately against $T_{1}$ colluding servers, and all the messages need to be retrieved privately against $T_{2}$ colluding servers where $T_{2}\leq T_{1}$ . We obtain a lower bound to the capacity by proposing a novel coding scheme, namely the non-uniform successive cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bound is analyzed, and shown to vanish when $T_{1}=T_{2}$ .