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PIR Over Wireless Channels: Achieving Privacy With Public Responses

Or Elimelech, Asaf Cohen

TL;DR

This paper proposes a novel joint PIR–channel coding scheme based on nested lattice codes to meet the resulting privacy and reliability challenges and demonstrates 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.

Abstract

In this paper, we address the problem of Private Information Retrieval (PIR) over a public Additive White Gaussian Noise (AWGN) channel. In such a setup, the server's responses are visible to other servers. Thus, a curious server can listen to the other responses, compromising the user's privacy. Indeed, previous works on PIR over a shared medium assumed the servers cannot instantaneously listen to other responses. To address this gap, we present a novel randomized lattice -- PIR coding scheme that jointly codes for privacy, channel noise, and curious servers which may listen to other responses. 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.

PIR Over Wireless Channels: Achieving Privacy With Public Responses

TL;DR

This paper proposes a novel joint PIR–channel coding scheme based on nested lattice codes to meet the resulting privacy and reliability challenges and demonstrates 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.

Abstract

In this paper, we address the problem of Private Information Retrieval (PIR) over a public Additive White Gaussian Noise (AWGN) channel. In such a setup, the server's responses are visible to other servers. Thus, a curious server can listen to the other responses, compromising the user's privacy. Indeed, previous works on PIR over a shared medium assumed the servers cannot instantaneously listen to other responses. To address this gap, we present a novel randomized lattice -- PIR coding scheme that jointly codes for privacy, channel noise, and curious servers which may listen to other responses. 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.
Paper Structure (14 sections, 5 theorems, 70 equations, 2 figures)

This paper contains 14 sections, 5 theorems, 70 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model Preliminaries
  3. Notational Conventions
  4. System Model and Problem Statement
  5. Performance Metric
  6. Lattice Code and Lattice Gaussian Distribution
  7. Main results
  8. A Joint PIR Scheme Over Public AWGN MISO channel
  9. A Joint Scheme for Secure PIR Over Non-Fading AWGN MAC With $N=2$ Servers
  10. Coding Scheme
  11. A Joint Scheme for Secure PIR Over Non-Fading AWGN MAC With $N>2$ Servers
  12. A Joint Scheme for PIR Over Public Block-Fading AWGN MAC with $N>2$ Servers
  13. Coding Scheme
  14. Conclusion

Key Result

Theorem 1

For the $N=2$ databases public AWGN channel, the following PIR rate is achievable, where $SNR_y=\frac{P}{\sigma^2_y}$, and $SNR_w=\frac{P}{\sigma^2_w}$.

Figures (2)

  • Figure 1: System model with two servers connected to a user via an AWGN MAC channel. Server $1$ acts as a malicious entity, monitoring the communication and having access to $w_1$.
  • Figure 2: The average PIR rate as a function of the number of servers $N$. The transmit power is set to $P=1$ and the different colors represent varying values of $\sigma_w$ with $\sigma_y$ fixed at $1$.

Theorems & Definitions (15)

  • Definition 1
  • Definition 2
  • Definition 3: Quantizer
  • Definition 4: Voronoi Region
  • Definition 5: Modulus
  • Definition 6: $\Lambda$-Periodic Function
  • Definition 7: Discrete Gaussian
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • ...and 5 more