”Better Than Nothing” Privacy with Bloom Filters: To What Extent?

  • Giuseppe Bianchi
  • Lorenzo Bracciale
  • Pierpaolo Loreti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7556)


Bloom filters are probabilistic data structures which permit to conveniently represent set membership. Their performance/memory efficiency makes them appealing in a huge variety of scenarios. Their probabilistic operation, along with the implicit data representation, yields some ambiguity on the actual data stored, which, in scenarios where cryptographic protection is unviable or unpractical, may be somewhat considered as a better than nothing privacy asset. Oddly enough, even if frequently mentioned, to the best of our knowledge the (soft) privacy properties of Bloom filters have never been explicitly quantified. This work aims to fill this gap. Starting from the adaptation of probabilistic anonymity metrics to the Bloom filter setting, we derive exact and (tightly) approximate formulae which permit to readily relate privacy properties with filter (and universe set) parameters. Using such relations, we quantitatively investigate the emerging privacy/utility trade-offs. We finally preliminary assess the advantages that a tailored insertion of a few extra (covert) bits achieves over the commonly employed strategy of increasing ambiguity via addition of random bits.


Hash Function Bloom Filter Differential Privacy Privacy Property Private Information Retrieval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bloom, B.H.: Space/time trade-offs in hash coding with allowable errors. Commun. ACM 13(7), 422–426 (1970)zbMATHCrossRefGoogle Scholar
  2. 2.
    Stonebraker, M., Keller, K.: Embedding expert knowledge and hypothetical data bases into a data base system. In: Proc. of the 1980 ACM SIGMOD Int. Conf. on Management of Data, pp. 58–66 (1980)Google Scholar
  3. 3.
    Maryanski, F.J.: An architecture for fault tolerance in database systems. In: Proceedings of the ACM 1980 Annual Conference, pp. 389–398. ACM (1980)Google Scholar
  4. 4.
    Gremillion, L.L.: Designing a bloom filter for differential file access. Commun. ACM 25(9), 600–604 (1982)CrossRefGoogle Scholar
  5. 5.
    Mullin, J.K.: Accessing textual documents using compressed indexes of arrays of small bloom filters. Comput. J. 30(4), 343–348 (1987)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Broder, A., Mitzenmacher, M.: Network applications of bloom filters: A survey. In: Internet Mathematics, pp. 636–646 (2002)Google Scholar
  7. 7.
    Cai, H., Ge, P., Wang, J.: Applications of bloom filters in peer-to-peer systems: Issues and questions. In: Proceedings of the 2008 Int. Conf. on Networking, Architecture, and Storage, NAS 2008, pp. 97–103 (2008)Google Scholar
  8. 8.
    Tarkoma, S., Rothenberg, C., Lagerspetz, E.: Theory and practice of bloom filters for distributed systems. IEEE Communications Surveys Tutorials 14(1), 131–155 (2012)CrossRefGoogle Scholar
  9. 9.
    Stranneheim, H., Kaller, M., Allander, T., Andersson, B., Arvestad, L., Lundeberg, J.: Classification of dna sequences using bloom filters. Bioinformatics 26(13), 1595–1600 (2010)CrossRefGoogle Scholar
  10. 10.
    Bellovin, S.M., Cheswick, W.R.: Privacy-enhanced searches using encrypted bloom filters. IACR Cryptology ePrint Archive,  22 (2004)Google Scholar
  11. 11.
    Raykova, M., Vo, B., Bellovin, S.M., Malkin, T.: Secure anonymous database search. In: Proc. of the 2009 ACM Workshop on Cloud Computing Security, CCSW 2009, pp. 115–126 (2009)Google Scholar
  12. 12.
    Goh, E.J.: Secure indexes. Cryptology ePrint Archive, Report 2003/216 (2003),
  13. 13.
    Nojima, R., Kadobayashi, Y.: Cryptographically secure bloom-filters. Trans. Data Privacy 2(2), 131–139 (2009)MathSciNetGoogle Scholar
  14. 14.
    Boneh, D., Kushilevitz, E., Ostrovsky, R., Skeith III, W.E.: Public Key Encryption That Allows PIR Queries. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 50–67. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Rottenstreich, O., Keslassy, I.: The bloom paradox: When not to use a bloom filter? In: Proc. 31th IEEE Int. Conf. on Computer Communications, INFOCOM, Orlando, Fl, USA (2012)Google Scholar
  16. 16.
    Sweeney, L.: k-anonymity: a model for protecting privacy. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10(5), 557–570 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Lodha, S.P., Thomas, D.: Probabilistic Anonymity. In: Bonchi, F., Malin, B., Saygın, Y. (eds.) PInKDD 2007. LNCS, vol. 4890, pp. 56–79. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Gross, P., Parekh, J., Kaiser, G.: Secure selecticast for collaborative intrusion detection systems. In: 3rd International Workshop on Distributed Event-Based Systems, DEBS 2004 (2004)Google Scholar
  19. 19.
    Shanmugasundaram, K., Brönnimann, H., Memon, N.: Payload attribution via hierarchical bloom filters. In: Proceedings of the 11th ACM Conference on Computer and Communications Security, CCS 2004, pp. 31–41. ACM, New York (2004)CrossRefGoogle Scholar
  20. 20.
    Gorai, M., Sridharan, K., Aditya, T., Mukkamala, R., Nukavarapu, S.: Employing bloom filters for privacy preserving distributed collaborative knn classification. In: 2011 World Congress on Information and Communication Technologies (WICT), pp. 495–500 (December 2011)Google Scholar
  21. 21.
    Siegenthaler, M., Birman, K.: Sharing private information across distributed databases. In: IEEE International Symposium on Network Computing and Applications, pp. 82–89 (2009)Google Scholar
  22. 22.
    Parekh, J.J., Wang, K., Stolfo, S.J.: Privacy-preserving payload-based correlation for accurate malicious traffic detection. In: Proceedings of the 2006 SIGCOMM Workshop on Large-Scale Attack Defense, LSAD 2006, pp. 99–106 (2006)Google Scholar
  23. 23.
    Bawa, M., Bayardo Jr., R.J., Agrawal, R., Vaidya, J.: Privacy-preserving indexing of documents on the network. The VLDB Journal 18(4), 837–856 (2009)CrossRefGoogle Scholar
  24. 24.
    Lai, P.K.Y., Yiu, S.M., Chow, K.P., Chong, C.F., Hui, L.C.K.: An efficient bloom filter based solution for multiparty private matching. In: Proc. of the, Int. Conf. on Security and Management, SAM 2006, Las Vegas, Nevada, USA, June 26-29, pp. 286–292 (2006)Google Scholar
  25. 25.
    Kuzu, M., Kantarcioglu, M., Durham, E., Malin, B.: A Constraint Satisfaction Cryptanalysis of Bloom Filters in Private Record Linkage. In: Fischer-Hübner, S., Hopper, N. (eds.) PETS 2011. LNCS, vol. 6794, pp. 226–245. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  26. 26.
    Schnell, R., Bachteler, T., Reiher, J.: Private record linkage with bloom filters. In: Proc. of Statistics Canada Symposium 2010: Social Statistics: The Interplay among Censuses, Surveys and Administrative Data, pp. 304–309 (2010)Google Scholar
  27. 27.
    Goodrich, M.T., Mitzenmacher, M.: Invertible bloom lookup tables. CoRR abs/1101.2245 (2011)Google Scholar
  28. 28.
    Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M.: L-diversity: Privacy beyond k-anonymity. ACM Trans. Knowl. Discov. Data 1(1) (2007)Google Scholar
  29. 29.
    Li, N., Li, T.: t-closeness: Privacy beyond k-anonymity and l-diversity. In: Proc. of IEEE 23rd Int’l Conf. on Data Engineering, ICDE 2007 (2007)Google Scholar
  30. 30.
    Dwork, C.: Differential Privacy: A Survey of Results. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  31. 31.
    Bose, P., Guo, H., Kranakis, E., Maheshwari, A., Morin, P., Morrison, J., Smid, M., Tang, Y.: On the false-positive rate of bloom filters. Inf. Process. Lett. 108(4), 210–213 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Giuseppe Bianchi
    • 1
  • Lorenzo Bracciale
    • 1
  • Pierpaolo Loreti
    • 1
  1. 1.DIEUniversitá di Roma “Tor Vergata”RomeItaly

Personalised recommendations