The Composition Theorem for Differential Privacy

Peter Kairouz, Sewoong Oh, Pramod Viswanath

Research output: Contribution to journalArticlepeer-review


Sequential querying of differentially private mechanisms degrades the overall privacy level. In this paper, we answer the fundamental question of characterizing the level of overall privacy degradation as a function of the number of queries and the privacy levels maintained by each privatization mechanism. Our solution is complete: we prove an upper bound on the overall privacy level and construct a sequence of privatization mechanisms that achieves this bound. The key innovation is the introduction of an operational interpretation of differential privacy (involving hypothesis testing) and the use of a data processing inequality along with its converse. Our result improves over the state of the art, and has immediate connections to several problems studied in the literature.

Original languageEnglish (US)
Article number7883827
Pages (from-to)4037-4049
Number of pages13
JournalIEEE Transactions on Information Theory
Issue number6
StatePublished - Jun 2017


  • Differential privacy
  • hypothesis testing

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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