CED2: Communication Efficient Disjointness Decision

  • Luciana Marconi
  • Mauro Conti
  • Roberto Di Pietro
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 50)


Enforcing security often requires the two legitimate parties of a communication to determine whether they share a secret, without disclosing information (e.g. the shared secret itself, or just the existence of such a secret) to third parties—or even to the other party, if it is not the legitimate party but an adversary pretending to impersonate the legitimate one. In this paper, we propose CED2 (Communication Efficient Disjointness Decision), a probabilistic and distributed protocol that allows two parties—each one having a finite set of elements—to decide about the disjointness of their sets. CED2 is particularly suitable for devices having constraints on energy, communication, storage, and bandwidth. Examples of these devices are satellite phones, or nodes of wireless sensor networks. We show that CED2 significantly improves the communication cost compared to the state of the art, while providing the same degree of privacy and security. Analysis and simulations support the findings.


sets disjointness test communication complexity privacy security probabilistic algorithms 


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  1. 1.
    Agrawal, R., Evfimievski, A., Srikant, R.: Information sharing across private databases. In: Proceedings of the 22th ACM SIGMOD international conference on Management of data (SIGMOD 2003), pp. 86–97 (2003)Google Scholar
  2. 2.
    Barbay, J., López-Ortiz, A., Lu, T., Salinger, A.: An experimental investigation of set intersection algorithms for text searching. Journal of Experimental Algorithmics 14, 3.7–3.24 (2009)Google Scholar
  3. 3.
    Demaine, E.D., López-Ortiz, A., Ian Munro, J.: Adaptive set intersections, unions, and differences. In: Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2000), pp. 743–752 (2000)Google Scholar
  4. 4.
    Eschenauer, L., Gligor, V.: A key-management scheme for distributed sensor networks. In: Proceedings of the 9th ACM Conference on Computer and Communications Security (CCS 2002), pp. 267–282 (2002)Google Scholar
  5. 5.
    Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Håstad, J., Wigderson, A.: The randomized communication complexity of set disjointness. Journal Theory of Computing 3(1), 211–219 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Kalyanasundaram, B., Schnitger, G.: The probabilistic communication complexity of set intersection. SIAM Journal on Discrete Mathematics 5(4), 545–557 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kiayias, A., Mitrofanova, A.: Testing disjointness of private datasets. In: S. Patrick, A., Yung, M. (eds.) FC 2005. LNCS, vol. 3570, pp. 109–124. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Kissner, L., Song, D.X.: Privacy-preserving set operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Kurtz, T.G., Manber, U.: A probabilistic distributed algorithm for set intersection and its analysis. Journal of Theoretical Computer Science 49(2-3), 267–282 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, New York (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
    Mitzenmacher, M., Upfal, E.: Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press, New York (2005)CrossRefzbMATHGoogle Scholar
  13. 13.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1997)zbMATHGoogle Scholar
  14. 14.
    Yao, A.C.-C.: Some complexity questions related to distributive computing. In: Proceedings of the eleventh annual ACM symposium on Theory of computing (STOC 1979), pp. 209–213 (1979)Google Scholar
  15. 15.
    Ye, Q., Wang, H., Pieprzyk, J., Mo Zhang, X.: Unconditionally secure disjointness tests for private datasets. International Journal of Applied Cryptography 1(3), 225–235 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2010

Authors and Affiliations

  • Luciana Marconi
    • 1
  • Mauro Conti
    • 2
  • Roberto Di Pietro
    • 3
  1. 1.Department of Computer Science“Sapienza” Università di RomaRomaItaly
  2. 2.Department of Computer ScienceVrije Universiteit AmsterdamAmsterdamThe Netherlands
  3. 3.Department of MathematicsUniversità di Roma TreRomaItaly

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