Separating Local & Shuffled Differential Privacy via Histograms

Authors Victor Balcer, Albert Cheu



PDF
Thumbnail PDF

File

LIPIcs.ITC.2020.1.pdf
  • Filesize: 0.51 MB
  • 14 pages

Document Identifiers

Author Details

Victor Balcer
  • School of Engineering & Applied Sciences, Harvard University, Cambridge, MA, United States
Albert Cheu
  • Khoury College of Computer Sciences, Northeastern University, Boston, MA, United States

Acknowledgements

We are grateful to Daniel Alabi and Maxim Zhilyaev for discussions that shaped the early stages of this work. We are also indebted to Matthew Joseph and Jieming Mao for directing us to the pointer-chasing and multi-party pointer-jumping problems. Finally, we thank Salil Vadhan for editorial comments and providing a simpler construction for Claim 19.

Cite AsGet BibTex

Victor Balcer and Albert Cheu. Separating Local & Shuffled Differential Privacy via Histograms. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ITC.2020.1

Abstract

Recent work in differential privacy has highlighted the shuffled model as a promising avenue to compute accurate statistics while keeping raw data in users' hands. We present a protocol in this model that estimates histograms with error independent of the domain size. This implies an arbitrarily large gap in sample complexity between the shuffled and local models. On the other hand, we show that the models are equivalent when we impose the constraints of pure differential privacy and single-message randomizers.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy-preserving protocols
Keywords
  • Differential Privacy
  • Distributed Protocols
  • Histograms

Metrics

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

References

  1. Borja Balle, James Bell, Adria Gascon, and Kobbi Nissim. Differentially private summation with multi-message shuffling. arXiv preprint arXiv:1906.09116, 2019. Google Scholar
  2. Borja Balle, James Bell, Adrià Gascón, and Kobbi Nissim. The privacy blanket of the shuffle model. In Alexandra Boldyreva and Daniele Micciancio, editors, Advances in Cryptology - CRYPTO 2019 - 39th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 18-22, 2019, Proceedings, Part II, volume 11693 of Lecture Notes in Computer Science, pages 638-667. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-26951-7_22.
  3. Raef Bassily and Adam D. Smith. Local, private, efficient protocols for succinct histograms. In Rocco A. Servedio and Ronitt Rubinfeld, editors, Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, Portland, OR, USA, June 14-17, 2015, pages 127-135. ACM, 2015. URL: https://doi.org/10.1145/2746539.2746632.
  4. Amos Beimel, Shiva Prasad Kasiviswanathan, and Kobbi Nissim. Bounds on the sample complexity for private learning and private data release. In Daniele Micciancio, editor, Theory of Cryptography, 7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland, February 9-11, 2010. Proceedings, volume 5978 of Lecture Notes in Computer Science, pages 437-454. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-11799-2_26.
  5. Amos Beimel, Kobbi Nissim, and Eran Omri. Distributed private data analysis: Simultaneously solving how and what. In David A. Wagner, editor, Advances in Cryptology - CRYPTO 2008, 28th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2008. Proceedings, volume 5157 of Lecture Notes in Computer Science, pages 451-468. Springer, 2008. URL: https://doi.org/10.1007/978-3-540-85174-5_25.
  6. Andrea Bittau, Úlfar Erlingsson, Petros Maniatis, Ilya Mironov, Ananth Raghunathan, David Lie, Mitch Rudominer, Ushasree Kode, Julien Tinnés, and Bernhard Seefeld. Prochlo: Strong privacy for analytics in the crowd. In Proceedings of the 26th Symposium on Operating Systems Principles, Shanghai, China, October 28-31, 2017, pages 441-459. ACM, 2017. URL: https://doi.org/10.1145/3132747.3132769.
  7. Mark Bun, Kobbi Nissim, and Uri Stemmer. Simultaneous private learning of multiple concepts. In Madhu Sudan, editor, Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, Cambridge, MA, USA, January 14-16, 2016, pages 369-380. ACM, 2016. URL: https://doi.org/10.1145/2840728.2840747.
  8. Albert Cheu, Adam D. Smith, Jonathan Ullman, David Zeber, and Maxim Zhilyaev. Distributed differential privacy via shuffling. In Yuval Ishai and Vincent Rijmen, editors, Advances in Cryptology - EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Darmstadt, Germany, May 19-23, 2019, Proceedings, Part I, volume 11476 of Lecture Notes in Computer Science, pages 375-403. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-17653-2_13.
  9. Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam D. Smith. Calibrating noise to sensitivity in private data analysis. In Shai Halevi and Tal Rabin, editors, Theory of Cryptography, Third Theory of Cryptography Conference, TCC 2006, New York, NY, USA, March 4-7, 2006, Proceedings, volume 3876 of Lecture Notes in Computer Science, pages 265-284. Springer, 2006. URL: https://doi.org/10.1007/11681878_14.
  10. Úlfar Erlingsson, Vitaly Feldman, Ilya Mironov, Ananth Raghunathan, Kunal Talwar, and Abhradeep Thakurta. Amplification by shuffling: From local to central differential privacy via anonymity. In Timothy M. Chan, editor, Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pages 2468-2479. SIAM, 2019. URL: https://doi.org/10.1137/1.9781611975482.151.
  11. Alexandre Evfimievski, Johannes Gehrke, and Ramakrishnan Srikant. Limiting privacy breaches in privacy preserving data mining. In Frank Neven, Catriel Beeri, and Tova Milo, editors, PODS, pages 211-222. ACM, 2003. URL: https://doi.org/10.1145/773153.773174.
  12. Badih Ghazi, Noah Golowich, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh, and Ameya Velingker. Pure differentially private summation from anonymous messages. CoRR, abs/2002.01919, 2020. Google Scholar
  13. Badih Ghazi, Noah Golowich, Ravi Kumar, Rasmus Pagh, and Ameya Velingker. On the power of multiple anonymous messages. IACR Cryptology ePrint Archive, 2019:1382, 2019. Google Scholar
  14. Moritz Hardt and Kunal Talwar. On the geometry of differential privacy. In Leonard J. Schulman, editor, Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, Cambridge, Massachusetts, USA, 5-8 June 2010, pages 705-714. ACM, 2010. URL: https://doi.org/10.1145/1806689.1806786.
  15. Matthew Joseph, Jieming Mao, Seth Neel, and Aaron Roth. The role of interactivity in local differential privacy. In David Zuckerman, editor, 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019, Baltimore, Maryland, USA, November 9-12, 2019, pages 94-105. IEEE Computer Society, 2019. URL: https://doi.org/10.1109/FOCS.2019.00015.
  16. Matthew Joseph, Jieming Mao, and Aaron Roth. Exponential separations in local differential privacy. In Shuchi Chawla, editor, Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 515-527. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.31.
  17. Shiva Prasad Kasiviswanathan, Homin K. Lee, Kobbi Nissim, Sofya Raskhodnikova, and Adam D. Smith. What can we learn privately? In 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, October 25-28, 2008, Philadelphia, PA, USA, pages 531-540. IEEE Computer Society, 2008. URL: https://doi.org/10.1109/FOCS.2008.27.
  18. Tianhao Wang, Min Xu, Bolin Ding, Jingren Zhou, Ninghui Li, and Somesh Jha. Practical and robust privacy amplification with multi-party differential privacy. arXiv preprint arXiv:1908.11515, 2019. Google Scholar
  19. Stanley L Warner. Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309):63-69, 1965. Google Scholar
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