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Weakly-Private Information Retrieval From MDS-Coded Distributed Storage

Asbjørn O. Orvedal, Hsuan-Yin Lin, Eirik Rosnes

TL;DR

This paper tackles WPIR for data stored with an $[ ext{N}, ext{K}]$ MDS code across $N$ servers by using the maximal leakage privacy metric to quantify information disclosure about the target file. It adapts two existing MDS-PIR schemes (ZYQT and ZTSL) to permit leakage, and establishes a convex optimization framework to characterize the optimal download-rate versus leakage trade-off; the optimal trade-off curves are obtained via solving a convex program. To address practicality, it introduces a new OLR WPIR scheme with a substantially smaller query space while achieving comparable or improved rate-leakage performance, demonstrated via a motivating example with $(M,N,K)=(2,3,2)$ and numerical results across different server counts and file counts. Overall, the work demonstrates that controlled information leakage can significantly improve download efficiency in MDS-coded WPIR and provides a convex optimization-based method to derive optimal rate-leakage curves, with concrete schemes and numerical validation for deployment considerations.

Abstract

We consider the problem of weakly-private information retrieval (WPIR) when data is encoded by a maximum distance separable code and stored across multiple servers. In WPIR, a user wishes to retrieve a piece of data from a set of servers without leaking too much information about which piece of data she is interested in. We study and provide the first WPIR protocols for this scenario and present results on their optimal trade-off between download rate and information leakage using the maximal leakage privacy metric.

Weakly-Private Information Retrieval From MDS-Coded Distributed Storage

TL;DR

This paper tackles WPIR for data stored with an MDS code across servers by using the maximal leakage privacy metric to quantify information disclosure about the target file. It adapts two existing MDS-PIR schemes (ZYQT and ZTSL) to permit leakage, and establishes a convex optimization framework to characterize the optimal download-rate versus leakage trade-off; the optimal trade-off curves are obtained via solving a convex program. To address practicality, it introduces a new OLR WPIR scheme with a substantially smaller query space while achieving comparable or improved rate-leakage performance, demonstrated via a motivating example with and numerical results across different server counts and file counts. Overall, the work demonstrates that controlled information leakage can significantly improve download efficiency in MDS-coded WPIR and provides a convex optimization-based method to derive optimal rate-leakage curves, with concrete schemes and numerical validation for deployment considerations.

Abstract

We consider the problem of weakly-private information retrieval (WPIR) when data is encoded by a maximum distance separable code and stored across multiple servers. In WPIR, a user wishes to retrieve a piece of data from a set of servers without leaking too much information about which piece of data she is interested in. We study and provide the first WPIR protocols for this scenario and present results on their optimal trade-off between download rate and information leakage using the maximal leakage privacy metric.
Paper Structure (19 sections, 1 theorem, 24 equations, 2 figures)

This paper contains 19 sections, 1 theorem, 24 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and System Model
  3. Notation
  4. System Model
  5. Maximal Leakage Metric
  6. WPIR Download Cost and Rate
  7. General MDS-WPIR Schemes
  8. The ZYQT Scheme and the ZTSL Scheme
  9. Storage Data Structure
  10. Query Generation
  11. Answer Construction
  12. Time-Sharing MDS-WPIR Scheme
  13. Minimization of MaxL for MDS-WPIR Schemes
  14. New Proposed MDS-WPIR Scheme
  15. Motivating Example: $(\textnormal{ M},\textnormal{ N},\textnormal{ K})=(2,3,2)$
  16. ...and 4 more sections

Key Result

Theorem 1

The optimization problem eq:optimization_MaxL-download is convex.

Figures (2)

  • Figure 1: Rate-leakage trade-off curve for the proposed MDS-WPIR protocols from $(3,2)$ MDS-coded storage with $\textnormal{ M}=2$ (circle markers), $\textnormal{ M}=3$ (square markers), $\textnormal{ M}=4$ (diamond markers), and $\textnormal{ M}=5$ (pentagon markers).
  • Figure 2: Rate-leakage trade-off curve for the proposed MDS-WPIR protocols from $(5,3)$ MDS-coded storage with $\textnormal{ M}=2$ (circle markers) and $\textnormal{ M}=3$ (square markers).

Theorems & Definitions (5)

  • Definition 1: MDS-WPIR Scheme
  • Definition 2: Time-Sharing MDS-WPIR Scheme
  • Remark 1
  • Theorem 1
  • Example 1