PIR Over Wireless Channels: Achieving Privacy with Public Responses

In this paper, we address the problem of Private Information Retrieval (PIR) over a public Additive White Gaussian Noise (AWGN) channel. In this setting, a curious server—a passive adversary following the protocol but attempting to infer private information from intercepted transmissions—can eavesdrop on other servers' responses, compromising the user's privacy. Prior work on PIR over shared media typically assumed that servers could not overhear each other's transmissions. In contrast, we remove this assumption and consider a fully public channel. We propose a novel joint PIR–channel coding scheme based on nested lattice codes to meet the resulting privacy and reliability challenges. The scheme simultaneously addresses channel noise, ensures user privacy, and protects against curious servers. We demonstrate that a positive PIR rate is achievable even in cases where the channel to the curious server is stronger than the channel to the user.