Paper 2011/141

Fast and Private Computation of Cardinality of Set Intersection and Union

Emiliano De Cristofaro, Paolo Gasti, and Gene Tsudik


In many everyday scenarios, sensitive information must be shared between parties without complete mutual trust. Private set operations are particularly useful to enable sharing information with privacy, as they allow two or more parties to jointly compute operations on their sets (e.g., intersection, union, etc.), such that only the minimum required amount of information is disclosed. In the last few years, the research community has proposed a number of secure and efficient techniques for Private Set Intersection (PSI), however, somewhat less explored is the problem of computing the magnitude, rather than the contents, of the intersection - we denote this problem as Private Set Intersection Cardinality (PSI-CA). This paper explores a few PSI-CA variations and constructs several protocols that are more efficient than the state-of-the-art.

Note: This version presents modified constructions and new security model/proofs.

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Publication info
Published elsewhere. Minor revision.CANS 2012 - The 11th International Conference on Cryptology and Network Security
public-key cryptographycryptographic protocolsprivate set operationsprivate set intersectioncardinalitylinear complexity
Contact author(s)
pgasti @ nyit edu
2013-08-14: last of 6 revisions
2011-03-22: received
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      author = {Emiliano De Cristofaro and Paolo Gasti and Gene Tsudik},
      title = {Fast and Private Computation of Cardinality of Set Intersection and Union},
      howpublished = {Cryptology ePrint Archive, Paper 2011/141},
      year = {2011},
      note = {\url{}},
      url = {}
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