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. This is the first time that a solution to this problem is presented.
|Title of host publication||Data and Applications Security and Privacy XXXII - 32nd Annual IFIP WG 11.3 Conference, DBSec 2018, Proceedings|
|Editors||Stefano Paraboschi, Florian Kerschbaum|
|Number of pages||17|
|State||Published - 2018|
|Event||32nd Annual IFIP WG 11.3 Conference on Data and Applications Security and Privacy, DBSec 2018 - Bergamo, Italy|
Duration: 16 Jul 2018 → 18 Jul 2018
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||32nd Annual IFIP WG 11.3 Conference on Data and Applications Security and Privacy, DBSec 2018|
|Period||16/07/18 → 18/07/18|
Bibliographical notePublisher Copyright:
© IFIP International Federation for Information Processing 2018.
- Distributed graphs
- Graph planarity
- Privacy-preserving distributed computations
- Secure multiparty computation