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Necessary Conditions in Multi-Server Differential Privacy

Authors Albert Cheu , Chao Yan

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LIPIcs.ITCS.2023.36.pdf
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Author Details

Albert Cheu
  • Department of Computer Science, Georgetown University, Washington D. C., USA
Chao Yan
  • Department of Computer Science, Georgetown University, Washington D. C., USA

Funding

The authors are members of the Data Co-Ops project (https://datacoopslab.org). This work was supported in part by a gift to Georgetown University.

Acknowledgements

We would like to thank Matthew Joseph for correspondence that refined our understanding of Bayesian re-sampling. We also thank Kobbi Nissim for suggestions for our sample complexity analysis.

Cite AsGet BibTex

Albert Cheu and Chao Yan. Necessary Conditions in Multi-Server Differential Privacy. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ITCS.2023.36

Abstract

We consider protocols where users communicate with multiple servers to perform a computation on the users' data. An adversary exerts semi-honest control over many of the parties but its view is differentially private with respect to honest users. Prior work described protocols that required multiple rounds of interaction or offered privacy against a computationally bounded adversary. Our work presents limitations of non-interactive protocols that offer privacy against unbounded adversaries. We prove that these protocols require exponentially more samples than centrally private counterparts to solve some learning, testing, and estimation tasks. This means sample-efficiency demands interactivity or computational differential privacy, or both.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Mathematics of computing → Probabilistic algorithms
  • Theory of computation → Distributed algorithms
  • Theory of computation → Online algorithms
  • Theory of computation → Sample complexity and generalization bounds
  • Security and privacy
  • Security and privacy → Privacy protections
Keywords
  • Differential Privacy
  • Parity Learning
  • Multi-server

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