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Local Pan-Privacy for Federated Analytics

Vitaly Feldman, Audra McMillan, Guy N. Rothblum, Kunal Talwar

TL;DR

The paper defines local pan-privacy to protect against on-device intrusions while estimating population statistics in federated analytics. It demonstrates that information-theoretic local pan-privacy for CountNonZero imposes a $\Omega(\sqrt{nT})$ additive error, making such a guarantee incompatible with scalable telemetry collection. To achieve practical privacy, the authors design computational local pan-private protocols for CountNonZero, histograms, and mean in both single- and two-server models, leveraging rerandomizable public-key cryptography and, in the two-server setting, non-interactive zero-knowledge proofs. These schemes preserve privacy under continual device intrusions with favorable privacy-utility trade-offs under standard cryptographic assumptions. The work also shows that rerandomizable public-key cryptography is necessary for achieving computational local pan-privacy and outlines avenues for future research on extending to other statistics and predicates.

Abstract

Pan-privacy was proposed by Dwork et al. as an approach to designing a private analytics system that retains its privacy properties in the face of intrusions that expose the system's internal state. Motivated by federated telemetry applications, we study local pan-privacy, where privacy should be retained under repeated unannounced intrusions on the local state. We consider the problem of monitoring the count of an event in a federated system, where event occurrences on a local device should be hidden even from an intruder on that device. We show that under reasonable constraints, the goal of providing information-theoretic differential privacy under intrusion is incompatible with collecting telemetry information. We then show that this problem can be solved in a scalable way using standard cryptographic primitives.

Local Pan-Privacy for Federated Analytics

TL;DR

The paper defines local pan-privacy to protect against on-device intrusions while estimating population statistics in federated analytics. It demonstrates that information-theoretic local pan-privacy for CountNonZero imposes a additive error, making such a guarantee incompatible with scalable telemetry collection. To achieve practical privacy, the authors design computational local pan-private protocols for CountNonZero, histograms, and mean in both single- and two-server models, leveraging rerandomizable public-key cryptography and, in the two-server setting, non-interactive zero-knowledge proofs. These schemes preserve privacy under continual device intrusions with favorable privacy-utility trade-offs under standard cryptographic assumptions. The work also shows that rerandomizable public-key cryptography is necessary for achieving computational local pan-privacy and outlines avenues for future research on extending to other statistics and predicates.

Abstract

Pan-privacy was proposed by Dwork et al. as an approach to designing a private analytics system that retains its privacy properties in the face of intrusions that expose the system's internal state. Motivated by federated telemetry applications, we study local pan-privacy, where privacy should be retained under repeated unannounced intrusions on the local state. We consider the problem of monitoring the count of an event in a federated system, where event occurrences on a local device should be hidden even from an intruder on that device. We show that under reasonable constraints, the goal of providing information-theoretic differential privacy under intrusion is incompatible with collecting telemetry information. We then show that this problem can be solved in a scalable way using standard cryptographic primitives.

Paper Structure

This paper contains 14 sections, 16 theorems, 19 equations, 5 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Definitions and Preliminaries
  4. Lower Bound
  5. The Single-Server Model
  6. Counting Devices that have at least one occurrence
  7. Computing Histograms of the Number of Occurrences
  8. Computing the Average Number of Occurrences per Device
  9. The Two Server Model
  10. Counting Devices that have at least one occurrence
  11. Computing Histograms of the Number of Occurrences
  12. On the need for rerandomizable Public-key cryptography
  13. Conclusions
  14. On the TV distance between Binomials

Key Result

Theorem 1

Any locally pan-private algorithm (for $\varepsilon=1$) for CountNonZero on $n$ devices, for large enough $T$, must incur additive error $\Omega(\sqrt{nT})$, even though a local DP algorithm can estimate CountNonZero with additive error $\Omega(\sqrt{n})$.

Figures (5)

  • Figure : $f_D$
  • Figure : $h$
  • Figure : CountNonZero, Client Algorithm
  • Figure : Counter, Client Algorithm
  • Figure : CountNonZero, Client Algorithm, Two-server model

Theorems & Definitions (34)

  • Theorem 1: Informal version of \ref{['thm:main_lb']}
  • Theorem 2: Informal version of \ref{['thm:ub_countnonzero']}
  • Theorem 3: Informal version of \ref{['thm:pkeneeded']}
  • Definition 2.1: $(\varepsilon,\delta)$-Indistinguishability
  • Definition 2.2: Differential Privacy
  • Definition 2.3: Local pan-privacy
  • Remark 4
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • ...and 24 more