Robust Privacy-Utility Tradeoffs under Differential Privacy and Hamming Distortion

Kousha Kalantari, Lalitha Sankar, Anand D. Sarwate

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


A privacy-utility tradeoff is developed for an arbitrary set of finite-alphabet source distributions. Privacy is quantified using differential privacy (DP), and utility is quantified using expected Hamming distortion maximized over the set of distributions. The family of source distribution sets (source sets) is categorized into three classes, based on different levels of prior knowledge they capture. For source sets whose convex hull includes the uniform distribution, symmetric DP mechanisms are optimal. For source sets whose probability values have a fixed monotonic ordering, asymmetric DP mechanisms are optimal. For all other source sets, general upper and lower bounds on the optimal privacy leakage are developed and necessary and sufficient conditions for tightness are established. Differentially private leakage is an upper bound on mutual information leakage: the two criteria are compared analytically and numerically to illustrate the effect of adopting a stronger privacy criterion.

Original languageEnglish (US)
Pages (from-to)2816-2830
Number of pages15
JournalIEEE Transactions on Information Forensics and Security
Issue number11
StatePublished - Nov 2018


  • Differential privacy
  • Hamming distortion
  • information leakage
  • utility-privacy tradeoff

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Computer Networks and Communications

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