The Capacity of Symmetric Private Information Retrieval

Abstract

Private information retrieval (PIR) is the problem of retrieving as efficiently as possible, one out of $K$ messages from $N$ non-communicating replicated databases (each holds all $K$ messages) while keeping the identity of the desired message index a secret from each individual database. Symmetric PIR (SPIR) is a generalization of PIR to include the requirement that beyond the desired message, the user learns nothing about the other $K-1$ messages. The information theoretic capacity of SPIR (equivalently, the reciprocal of minimum download cost) is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. We show that the capacity of SPIR is $1-1/N$ regardless of the number of messages $K$, if the databases have access to common randomness (not available to the user) that is independent of the messages, in the amount that is at least $1/(N-1)$ bits per desired message bit, and zero otherwise. Extensions to the capacity region of SPIR and the capacity of finite length SPIR are provided.

Cited by in corpus (7)

• Private Information Retrieval from MDS Coded Databases with Colluding Servers under Several Variant Models
• Private Information Retrieval from Storage Constrained Databases -- Coded Caching meets PIR
• The Capacity of Private Information Retrieval with Partially Known Private Side Information
• Multi-Message Private Information Retrieval: Capacity Results and Near-Optimal Schemes
• Fundamental Limits of Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching
• The Capacity of Private Information Retrieval with Private Side Information Under Storage Constraints
• Cache-Aided Private Information Retrieval with Partially Known Uncoded Prefetching: Fundamental Limits