On the structure of the privacy hierarchy

Benny Chor*, Mihály Geréb-Graus, Eyal Kushilevitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


An N argument function f(x1,..., xN) is called t-private if a protocol for computing f exists so that no coalition of at most t parties can infer any additional information from the execution, other than the value of the function. The motivation of this work is to understand what levels of privacy are attainable. So far, only two levels of privacy are known for N argument functions which are defined over finite domains: functions that are N-private and functions that are ⌊(N - 1)/2⌋-private but not ⌈N/2⌉-private. In this work we show that the privacy hierarchy for N-argument functions which are defined over finite domains, has exactly ⌈(N + 1)/2⌉ levels. We prove this by constructing, for any ⌈N/2⌉ ≤ t ≤ N - 2, an N-argument function which is t-private but not (t + 1)-private.

Original languageEnglish
Pages (from-to)53-60
Number of pages8
JournalJournal of Cryptology
Issue number1
StatePublished - Dec 1994
Externally publishedYes


  • Distributed computing
  • Privacy hierarchy
  • Private functions


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