Two-Level Private Information Retrieval

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 ≤ T 1 . We obtain a lower bound to the capacity by proposing two novel coding schemes, namely the non-uniform successive cancellation scheme and the non-uniform block cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bounds is analyzed, and shown to vanish when T 1 = T 2 . Lastly, we show that the upper bound is in general not tight by providing a stronger bound for a special setting.

Single-Server Private Linear Transformation: The Joint Privacy Case

“…Different types of privacy can be considered for PLT. In this work, we focus on the PLT problem under a strong notion of privacy, called joint privacy, which was also considered previously for PIR and PLC (see, e.g., [4], [18], [35], [36]). We refer to this problem as PLT with Joint Privacy, or JPLT for short.…”