On Private Scalar Product Computation for Privacy-Preserving Data Mining

  • Bart Goethals
  • Sven Laur
  • Helger Lipmaa
  • Taneli Mielikäinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3506)


In mining and integrating data from multiple sources, there are many privacy and security issues. In several different contexts, the security of the full privacy-preserving data mining protocol depends on the security of the underlying private scalar product protocol. We show that two of the private scalar product protocols, one of which was proposed in a leading data mining conference, are insecure. We then describe a provably private scalar product protocol that is based on homomorphic encryption and improve its efficiency so that it can also be used on massive datasets.


Privacy-preserving data mining private scalar product protocol vertically partitioned frequent pattern mining 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AIR01]
    Aiello, W., Ishai, Y., Reingold, O.: Priced Oblivious Transfer: How to Sell Digital Goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. [AMS+96]
    Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.I.: Fast Discovery of Association Rules. In: Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.) Advances in Knowledge Discovery and Data Mining, pp. 307–328. AAAI/MIT Press (1996)Google Scholar
  3. [BB00]
    Boulicaut, J.-F., Bykowski, A.: Frequent Closures as a Concise Representation for Binary Data Mining. In: Terano, T., Chen, A.L.P. (eds.) PAKDD 2000. LNCS, vol. 1805, pp. 62–73. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  4. [BBR03]
    Boulicaut, J.-F., Bykowski, A., Rigotti, C.: Free-Sets: A Condensed Representation of Boolean Data for the Approximation of Frequency Queries. Data Mining and Knowledge Discovery 7(1), 5–22 (2003)CrossRefMathSciNetGoogle Scholar
  5. [CGS97]
    Cramer, R., Gennaro, R., Schoenmakers, B.: A Secure and Optimally Efficient Multi-Authority Election Scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)Google Scholar
  6. [DA01a]
    Du, W., Atallah, M.J.: Privacy-Preserving Statistical Analysis. In: Proceedings of the 17th Annual Computer Security Applications Conference, New Orleans, Louisiana, USA, December 10–14, pp. 102–110 (2001)Google Scholar
  7. [DA01b]
    Du, W., Atallah, M.J.: Protocols for Secure Remote Database Access with Approximate Matching. Advances in Information Security, vol. 2, pp. 192. Kluwer Academic Publishers, Boston (2001),
  8. [DJ01]
    Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. [DZ02]
    Du, W., Zhan, Z.: A Practical Approach to Solve Secure Multi-party Computation Problems. In: Marceau, C., Foley, S. (eds.) Proceedings of New Security Paradigms Workshop, Virginia Beach, virginia, USA, September 23–26, pp. 127–135. ACM Press, New York (2002)Google Scholar
  10. [FNP04]
    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
  11. [Gol04]
    Goldreich, O.: Foundations of Cryptography: Basic Applications. Cambridge University Press, Cambridge (2004)zbMATHGoogle Scholar
  12. [LAN02]
    Lipmaa, H., Asokan, N., Niemi, V.: Secure Vickrey Auctions without Threshold Trust. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357, pp. 87–101. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. [Lip03]
    Lipmaa, H.: On Diophantine Complexity and Statistical Zero-Knowledge Arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. [Lip04]
    Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Total Communication. Technical Report 2004/063, International Association for Cryptologic Research, February 25 (2004)Google Scholar
  15. [LL04]
    Laur, S., Lipmaa, H.: On Private Similarity Search Protocols. In: Liimatainen, S., Virtanen, T. (eds.) Proceedings of the Ninth Nordic Workshop on Secure IT Systems (NordSec 2004), Espoo, Finland, November 4–5, pp. 73–77 (2004)Google Scholar
  16. [LL05]
    Laur, S., Lipmaa, H.: Additive Conditional Disclosure of Secrets (manuscript) (January 2005)Google Scholar
  17. [Pai99]
    Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)Google Scholar
  18. [PHM00]
    Pei, J., Han, J., Mao, R.: CLOSET: An efficient algorithm for mining frequent closed itemsets. In: 2000 ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery (2000)Google Scholar
  19. [Pin02]
    Pinkas, B.: Cryptographic Techniques for Privacy-Preserving Data Mining. KDD Explorations 4(2), 12–19 (2002)CrossRefGoogle Scholar
  20. [VC02]
    Vaidya, J., Clifton, C.: Privacy Preserving Association Rule Mining in Vertically Partitioned Data. In: Proceedings of The 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada, July 23–26, pp. 639–644. ACM, New York (2002)CrossRefGoogle Scholar
  21. [vLW92]
    van Lint, J.H., Wilson, R.M.: A Cource in Combinatorics. Cambridge University Press, Cambridge (1992)Google Scholar
  22. [WY04]
    Wright, R.N., Yang, Z.: Privacy-Preserving Bayesian Network Structure Computation on Distributed Heterogeneous Data. In: Proceedings of The Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Seattle, Washington, USA, pp. 713–718. ACM, New York (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bart Goethals
    • 1
  • Sven Laur
    • 2
  • Helger Lipmaa
    • 2
  • Taneli Mielikäinen
    • 1
  1. 1.HIIT Basic Research Unit, Department of Computer ScienceUniversity of HelsinkiFinland
  2. 2.Laboratory for Theoretical Computer Science,Department of Computer Science and EngineeringHelsinki University of TechnologyFinland

Personalised recommendations