Privacy-Preserving planarity testing of distributed graphs

Guy Barshap, Tamir Tassa

Research output: Contribution to journalArticlepeer-review


We study the problem of privacy-preserving planarity testing of distributed graphs. The setting involves several parties that hold private graphs on the same set of vertices, and an external mediator that helps with performing the computations. Their goal is to test whether the union of their private graphs is planar, but in doing so each party wishes to deny from his peers any information on his own private edge set beyond what is implied by the final output of the computation. We present a privacy-preserving protocol for that purpose which is based on the Hanani-Tutte theorem. That theorem enables translating the planarity question into the question of whether a specific system of linear equations over the field F2 is solvable. Our protocol uses a diverse cryptographic toolkit which includes techniques such as homomorphic encryption, oblivious Gaussian elimination, and private set intersection.

Original languageEnglish
Pages (from-to)117-144
Number of pages28
JournalTransactions on Data Privacy
Issue number2
StatePublished - Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, University of Skovde. All rights reserved.


  • Distributed graphs
  • Graph planarity
  • Privacy-preserving distributed computations
  • Secure multiparty computation


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