The staircase mechanism in differential privacy

Quan Geng, Peter Kairouz, Sewoong Oh, Pramod Viswanath

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


Adding Laplacian noise is a standard approach in differential privacy to sanitize numerical data before releasing it. In this paper, we propose an alternative noise adding mechanism: the staircase mechanism, which is a geometric mixture of uniform random variables. The staircase mechanism can replace the Laplace mechanism in each instance in the literature and for the same level of differential privacy, the performance in each instance improves; the improvement is particularly stark in medium-low privacy regimes. We show that the staircase mechanism is the optimal noise adding mechanism in a universal context, subject to a conjectured technical lemma (which we also prove to be true for one and two dimensional data).

Original languageEnglish (US)
Article number7093132
Pages (from-to)1176-1184
Number of pages9
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number7
StatePublished - Oct 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Data privacy
  • Randomized algorithm


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