Document Open Access Logo

Differential Privacy and Sublinear Time Are Incompatible Sometimes

Authors Jeremiah Blocki , Hendrik Fichtenberger , Elena Grigorescu , Tamalika Mukherjee

PDF
Thumbnail PDF

File

LIPIcs.ITCS.2025.19.pdf
  • Filesize: 0.8 MB
  • 18 pages

Document Identifiers

Author Details

Jeremiah Blocki
  • Purdue University, West Lafayette, IN, USA
Hendrik Fichtenberger
  • Google Research, Zürich, Switzerland
Elena Grigorescu
  • University of Waterloo, ON, Canada
Tamalika Mukherjee
  • Columbia University, New York, NY, USA

Funding

  • Blocki, Jeremiah: Supported in part by NSF CAREER Award CNS-2047272, and NSF Award CCF-1910659.
  • Grigorescu, Elena: Funded in part by NSF CCF-1910659, NSF CCF-2205811, and NSF CCF-2228814.
  • Mukherjee, Tamalika: Funded in part by NSF CCF-1910659, NSF CCF-2205811, and NSF CCF-2228814. Supported in part by Amazon through the Columbia Center of Artificial Intelligence Technology, a Google Cyber NYC Award, and DARPA under contract number W911NF2110371. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Government or DARPA.

Cite As Get BibTex

Jeremiah Blocki, Hendrik Fichtenberger, Elena Grigorescu, and Tamalika Mukherjee. Differential Privacy and Sublinear Time Are Incompatible Sometimes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.19

Abstract

Differential privacy and sublinear algorithms are both rapidly emerging algorithmic themes in times of big data analysis. Although recent works have shown the existence of differentially private sublinear algorithms for many problems including graph parameter estimation and clustering, little is known regarding hardness results on these algorithms. In this paper, we initiate the study of lower bounds for problems that aim for both differentially-private and sublinear-time algorithms. Our main result is the incompatibility of both the desiderata in the general case. In particular, we prove that a simple problem based on one-way marginals yields both a differentially-private algorithm, as well as a sublinear-time algorithm, but does not admit a "strictly" sublinear-time algorithm that is also differentially private.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory of database privacy and security
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Security and privacy → Privacy-preserving protocols
Keywords
  • differential privacy
  • sublinear algorithms
  • sublinear-time algorithms
  • one-way marginals
  • lower bounds

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Borja Balle, Gilles Barthe, and Marco Gaboardi. Privacy amplification by subsampling: Tight analyses via couplings and divergences. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, pages 6280-6290, 2018. URL: https://proceedings.neurips.cc/paper/2018/hash/3b5020bb891119b9f5130f1fea9bd773-Abstract.html.
  2. Raef Bassily, Adam D. Smith, and Abhradeep Thakurta. Private empirical risk minimization: Efficient algorithms and tight error bounds. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, pages 464-473. IEEE Computer Society, 2014. URL: https://doi.org/10.1109/FOCS.2014.56.
  3. Jeremiah Blocki, Elena Grigorescu, and Tamalika Mukherjee. Differentially-private sublinear-time clustering. In 2021 IEEE International Symposium on Information Theory (ISIT), pages 332-337. IEEE, 2021. URL: https://doi.org/10.1109/ISIT45174.2021.9518014.
  4. Jeremiah Blocki, Elena Grigorescu, and Tamalika Mukherjee. Privately estimating graph parameters in sublinear time. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.26.
  5. Jeremiah Blocki, Elena Grigorescu, Tamalika Mukherjee, and Samson Zhou. How to make your approximation algorithm private: A black-box differentially-private transformation for tunable approximation algorithms of functions with low sensitivity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2023, volume 275 of LIPIcs, pages 59:1-59:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPICS.APPROX/RANDOM.2023.59.
  6. Jeremiah Blocki, Seunghoon Lee, Tamalika Mukherjee, and Samson Zhou. Differentially private L₂-heavy hitters in the sliding window model. In The Eleventh International Conference on Learning Representations, ICLR 2023. OpenReview.net, 2023. Google Scholar
  7. Mark Bun, Thomas Steinke, and Jonathan R. Ullman. Make up your mind: The price of online queries in differential privacy. J. Priv. Confidentiality, 9(1), 2019. URL: https://doi.org/10.29012/JPC.655.
  8. Mark Bun, Jonathan R. Ullman, and Salil P. Vadhan. Fingerprinting codes and the price of approximate differential privacy. SIAM J. Comput., 47(5):1888-1938, 2018. URL: https://doi.org/10.1137/15M1033587.
  9. T Tony Cai, Yichen Wang, and Linjun Zhang. The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy. The Annals of Statistics, 49(5):2825-2850, 2021. Google Scholar
  10. Itai Dinur, Uri Stemmer, David P. Woodruff, and Samson Zhou. On differential privacy and adaptive data analysis with bounded space. In Advances in Cryptology - EUROCRYPT 2023 - 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, volume 14006 of Lecture Notes in Computer Science, pages 35-65. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-30620-4_2.
  11. Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam D. Smith. Calibrating noise to sensitivity in private data analysis. In Theory of Cryptography, Third Theory of Cryptography Conference, TCC, Proceedings, pages 265-284, 2006. URL: https://doi.org/10.1007/11681878_14.
  12. Cynthia Dwork, Moni Naor, Omer Reingold, Guy N. Rothblum, and Salil P. Vadhan. On the complexity of differentially private data release: efficient algorithms and hardness results. In Michael Mitzenmacher, editor, Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, pages 381-390. ACM, 2009. URL: https://doi.org/10.1145/1536414.1536467.
  13. Cynthia Dwork and Aaron Roth. The algorithmic foundations of differential privacy. Foundations and Trendsregistered in Theoretical Computer Science, 9(3-4):211-407, 2014. URL: https://doi.org/10.1561/0400000042.
  14. Cynthia Dwork, Adam D. Smith, Thomas Steinke, Jonathan R. Ullman, and Salil P. Vadhan. Robust traceability from trace amounts. In Venkatesan Guruswami, editor, IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, pages 650-669. IEEE Computer Society, 2015. URL: https://doi.org/10.1109/FOCS.2015.46.
  15. Cynthia Dwork, Kunal Talwar, Abhradeep Thakurta, and Li Zhang. Analyze gauss: optimal bounds for privacy-preserving principal component analysis. In David B. Shmoys, editor, Symposium on Theory of Computing, STOC 2014, pages 11-20. ACM, 2014. URL: https://doi.org/10.1145/2591796.2591883.
  16. Oded Goldreich, Shari Goldwasser, and Dana Ron. Property testing and its connection to learning and approximation. Journal of the ACM (JACM), 45(4):653-750, 1998. URL: https://doi.org/10.1145/285055.285060.
  17. Moritz Hardt and Guy N. Rothblum. A multiplicative weights mechanism for privacy-preserving data analysis. In 51th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2010, pages 61-70. IEEE Computer Society, 2010. URL: https://doi.org/10.1109/FOCS.2010.85.
  18. Moritz Hardt and Kunal Talwar. On the geometry of differential privacy. In Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, pages 705-714. ACM, 2010. URL: https://doi.org/10.1145/1806689.1806786.
  19. Palak Jain, Sofya Raskhodnikova, Satchit Sivakumar, and Adam Smith. The price of differential privacy under continual observation. In International Conference on Machine Learning, pages 14654-14678. PMLR, 2023. URL: https://proceedings.mlr.press/v202/jain23b.html.
  20. Gautam Kamath, Jerry Li, Vikrant Singhal, and Jonathan R. Ullman. Privately learning high-dimensional distributions. In Conference on Learning Theory, COLT 2019, volume 99 of Proceedings of Machine Learning Research, pages 1853-1902. PMLR, 2019. URL: http://proceedings.mlr.press/v99/kamath19a.html.
  21. Gautam Kamath, Argyris Mouzakis, and Vikrant Singhal. New lower bounds for private estimation and a generalized fingerprinting lemma. In Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022, 2022. Google Scholar
  22. Naty Peter, Eliad Tsfadia, and Jonathan R. Ullman. Smooth lower bounds for differentially private algorithms via padding-and-permuting fingerprinting codes. In The Thirty Seventh Annual Conference on Learning Theory,, volume 247 of Proceedings of Machine Learning Research, pages 4207-4239. PMLR, 2024. URL: https://proceedings.mlr.press/v247/peter24a.html.
  23. Thomas Steinke and Jonathan R. Ullman. Between pure and approximate differential privacy. J. Priv. Confidentiality, 7(2), 2016. URL: https://doi.org/10.29012/JPC.V7I2.648.
  24. Thomas Steinke and Jonathan R. Ullman. Tight lower bounds for differentially private selection. In Chris Umans, editor, 58th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2017, pages 552-563. IEEE Computer Society, 2017. URL: https://doi.org/10.1109/FOCS.2017.57.
  25. Gábor Tardos. Optimal probabilistic fingerprint codes. J. ACM, 55(2):10:1-10:24, 2008. URL: https://doi.org/10.1145/1346330.1346335.
  26. Jonathan R. Ullman. Answering n^2+o(1) counting queries with differential privacy is hard. In Dan Boneh, Tim Roughgarden, and Joan Feigenbaum, editors, Symposium on Theory of Computing Conference, STOC'13, pages 361-370. ACM, 2013. URL: https://doi.org/10.1145/2488608.2488653.
  27. Jalaj Upadhyay. Sublinear space private algorithms under the sliding window model. In Proceedings of the 36th International Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pages 6363-6372. PMLR, 09-15 June 2019. URL: http://proceedings.mlr.press/v97/upadhyay19a.html.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact