Basic Differentially Private Mechanisms

  • Jerome Le NyEmail author
Part of the SpringerBriefs in Electrical and Computer Engineering book series (BRIEFSELECTRIC)


This chapter presents simple mechanisms for signal filtering under differential privacy constraints, which add white noise directly on the sensitive input signals or at the output of a desired filter. We introduce concrete examples of adjacency relations for individual and collective privacy-sensitive input signals. We then describe the Laplace and Gaussian mechanisms to enforce \(\varepsilon \)- or \((\varepsilon , \delta )\)-differential privacy with respect to these adjacency relations, by adding Laplace and Gaussian noise respectively. For these mechanisms, adding noise at the output of the desired filter requires computing the sensitivity of this filter with respect to the signal variations allowed by the chosen adjacency relation.


  1. Bolot et al J (2013) Private decayed predicate sums on streams. In: Proceedings of the 16th international conference on database theory, Genoa, Italy, pp 284–295Google Scholar
  2. Chan T-HH, Shi E, Song D (2011) Private and continual release of statistics. ACM Trans Inf Syst Secur 14(3):26:1–26:24Google Scholar
  3. Dwork C, Roth A (2014) The algorithmic foundations of differential privacy. Found Trends Theor Comput Sci 9(3–4):211–407MathSciNetzbMATHGoogle Scholar
  4. Dwork C et al (2006a) Calibrating noise to sensitivity in private data analysis. In: Proceedings of the third theory of cryptography conference, New York, NY, pp 265–284Google Scholar
  5. Dwork C et al (2006b) Our data, ourselves: privacy via distributed noise generation. In: Proceedings of the 24th annual international conference on the theory and applications of cryptographic techniques (EUROCRYPT), St. Petersburg, Russia, pp 486–503Google Scholar
  6. Dwork C et al (2010) Differential privacy under continual observations. In: Proceedings of the ACM symposium on the theory of computing (STOC), Cambridge, MAGoogle Scholar
  7. Hart GW (1992) Nonintrusive appliance load monitoring. Proc IEEE 80(12):1870–1891Google Scholar
  8. Le Ny J, Mohammady M (2018) Differentially private MIMO filtering for event streams. IEEE Trans Autom Control 63(1)Google Scholar
  9. Le Ny J, Pappas GJ (2014) Differentially private filtering. IEEE Trans Autom Control 59(2):341–354Google Scholar
  10. Molina-Markham A et al (2010) Private memoirs of a smart meter. In: Proceedings of the 2nd ACM workshop on embedded sensing systems for energy-efficiency in building, New York, NY, USA, pp 61–66Google Scholar
  11. Pyrgelis A, Troncoso C, De Cristofaro E (2017) What does the crowd say about you? evaluating aggregation-based location privacy. In: Proceedings of privacy enhancing technologiesGoogle Scholar
  12. Xu F et al (2017) Trajectory recovery from ash: user privacy is not preserved in aggregated mobility data. In: Proceedings of the 26th international conference on world wide web, pp 1241–1250Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Electrical EngineeringPolytechnique MontréalMontrealCanada

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