Exponential Separations in Local Privacy

Author:

Joseph Matthew1ORCID,Mao Jieming1,Roth Aaron2

Affiliation:

1. Google Research New York, New York, NY

2. Computer and Information Sciences Department, University of Pennsylvania, Philadelphia, PA

Abstract

We prove a general connection between the communication complexity of two-player games and the sample complexity of their multi-player locally private analogues. We use this connection to prove sample complexity lower bounds for locally differentially private protocols as straightforward corollaries of results from communication complexity. In particular, we (1) use a communication lower bound for the hidden layers problem to prove an exponential sample complexity separation between sequentially and fully interactive locally private protocols, and (2) use a communication lower bound for the pointer chasing problem to prove an exponential sample complexity separation between k -round and ( k+1 )-round sequentially interactive locally private protocols, for every k .

Publisher

Association for Computing Machinery (ACM)

Subject

Mathematics (miscellaneous)

Reference27 articles.

1. John M. Abowd. 2016. The Challenge of Scientific Reproducibility and Privacy Protection for Statistical Agencies. Technical Report. Census Scientific Advisory Committee.

2. Jayadev Acharya, Clement Canonne, Cody Freitag, and Himanshu Tyagi. 2019. Test without trust: Optimal locally private distribution testing. In Proceedings of Machine Learning Research (Proceedings of Machine Learning Research), Kamalika Chaudhuri and Masashi Sugiyama (Eds.). Vol. 89. PMLR, 2067–2076. http://proceedings.mlr.press/v89/acharya19b.html.

3. Differential Privacy Team Apple. 2017. Learning with Privacy at Scale. Technical Report. Apple.

4. Local, Private, Efficient Protocols for Succinct Histograms

5. Distributed Private Data Analysis: Simultaneously Solving How and What

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