Private Stream Search at Almost the Same Communication Cost as a Regular Search

  • Matthieu Finiasz
  • Kannan Ramchandran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7707)


Private Stream Search allows keyword-based search queries to be performed on streaming data (or on a database) without revealing any information about the keywords being searched. Using homomorphic encryption, Ostrovsky and Skeith proposed a solution to this problem in 2005. However, their solution requires the server to send an answer of size O(mSlogm) bits when m documents of S bits match the query, while a regular (non-private) query only requires mS bits. Following this work, some improved schemes have been proposed with the aim of keeping the reply from the server linear in mS. In this work we propose two new communication optimal constructions: both allow communication linear in mS, but they also offer an expansion factor (compared to a non-private query) asymptotically equal to 1 when m and S increase. More precisely, our first scheme requires m(S + O(logt)) bits (where t is the size of the database) and our second scheme m(S + C) where C is a constant depending only on the chosen computational security level.


privacy keyword search Reed-Solomon codes LDPC codes 


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  1. 1.
    Bethencourt, J., Song, D.X., Waters, B.: New constructions and practical applications for private stream searching (extended abstract). In: 2006 IEEE Symposium on Security and Privacy, pp. 132–139. IEEE Computer Society (2006)Google Scholar
  2. 2.
    Bethencourt, J., Song, D.X., Waters, B.: New techniques for private stream searching. ACM Trans. Inf. Syst. Secur. 12(3) (2009)Google Scholar
  3. 3.
    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
  4. 4.
    Danezis, G., Díaz, C.: Improving the decoding efficiency of private search. In: Anonymous Communication and its Applications. Dagstuhl Seminar Proceedings, vol. 05411. IBFI, Schloss Dagstuhl, Germany (2006)Google Scholar
  5. 5.
    Danezis, G., Diaz, C.: Space-Efficient Private Search with Applications to Rateless Codes. In: Dietrich, S., Dhamija, R. (eds.) FC 2007 and USEC 2007. LNCS, vol. 4886, pp. 148–162. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Gallager, R.G.: Low-density parity-check codes. M.I.T. Press, Cambridge (1963)Google Scholar
  7. 7.
    Luby, M.G.: LT codes. In: FOCS, pp. 271–280. IEEE (2002)Google Scholar
  8. 8.
    Luby, M.G., Mitzenmacher, M.: Verification codes. In: Proc. Allerton Conf. on Communication, Control, and Computing (2002)Google Scholar
  9. 9.
    Luby, M.G., Mitzenmacher, M., Shokrollahi, M.A.: Analysis of random processes via and-or tree evaluation. In: SODA, pp. 364–373 (1998)Google Scholar
  10. 10.
    Luby, M.G., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.A.: Analysis of low density codes and improved designs using irregular graphs. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, STOC 1998, pp. 249–258. ACM (1998)Google Scholar
  11. 11.
    Luby, M.G., Mitzenmacher, M., Shokrollahi, M.A., Spielman, D.A.: Efficient erasure correcting codes. IEEE Transactions on Information Theory 47(2), 569–584 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Ostrovsky, R., Skeith, W.E.: Private Searching on Streaming Data. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 223–240. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Ostrovsky, R., Skeith, W.E.: Private searching on streaming data. Journal of Cryptology 20(4), 397–430 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Reed, I.S., Solomon, G.: Polynomial codes over certain finite fields. Journal of the SIAM 8(2), 300–304 (1960)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Matthieu Finiasz
    • 1
  • Kannan Ramchandran
    • 2
  1. 1.CryptoExpertsFrance
  2. 2.UC BerkeleyUSA

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