Communication-Efficient Private Protocols for Longest Common Subsequence

  • Matthew Franklin
  • Mark Gondree
  • Payman Mohassel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5473)


We design communication efficient two-party and multi-party protocols for the longest common subsequence (LCS) and related problems. Our protocols achieve privacy with respect to passive adversaries, under reasonable cryptographic assumptions. We benefit from the somewhat surprising interplay of an efficient block-retrieval PIR (Gentry-Ramzan, ICALP 2005) with the classic “four Russians” algorithmic design. This result is the first improvement to the communication complexity for this application over generic results (such as Yao’s garbled circuit protocol) and, as such, is interesting as a contribution to the theory of communication efficiency for secure two-party and multiparty applications.


Communication Complexity Homomorphic Encryption Oblivious Transfer Longe Common Subsequence Private Diff 
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.
    Are guarantees of genome anonymity realistic (2008),
  2. 2.
    CODIS: Combined DNA index system (2008),
  3. 3.
    deCODE genetics (2008),
  4. 4.
    The genomic privacy project (2008),
  5. 5.
    HapMap: International HapMap project (2008),
  6. 6.
    Aho, A., Hirschberg, D., Ullman, J.: Bounds on the complexity of the longest common subsequence problem. J. of the ACM 23(1), 1–12 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Aiello, B., 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
  8. 8.
    Altman, R., Klein, T.: Challenges for biomedical informatics and pharmacogenenomics. Annu. Rev. of Pharmacology and Toxicology 42, 113–133 (2002)CrossRefGoogle Scholar
  9. 9.
    Arlazarov, V.L., Dinic, E.A., Kronod, M.A., Faradzev, I.A.: On economic consruction of the transitive closure of a directed graph. Doklady Akademii Nauk SSSR 194, 487–488 (1970)MathSciNetGoogle Scholar
  10. 10.
    Atallah, M.J., Kerschbaum, F., Du. Secure, W.: private sequence comparisons. In: Proc. of WPES, pp. 39–44 (2003)Google Scholar
  11. 11.
    Brickell, J., Shmatikov, V.: Privacy-preserving graph algorithms in the semi-honest model. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 236–252. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. of Cryptology 13, 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Chor, B., Kushilevitz, E., Goldreich, O., Sudan, M.: Private information retrieval. J. of the ACM 45(6), 965–981 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  15. 15.
    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
  16. 16.
    Damgård, I., Jurik, M.: A length-flexible threshold cryptosystem with applications. In: Information Security and Privacy, pp. 350–364 (2003)Google Scholar
  17. 17.
    Franklin, M.K., Gondree, M., Mohassel, P.: Multi-party indirect indexing and applications. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 283–297. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Franklin, M., Gondree, M., Mohassel, P.: Communication-efficient private protocols for longest common subsequence. Cryptology ePrint Archive, Report 2009/019 (2009),
  19. 19.
    Fraser, C.: Subsequences and supersequences of strings. PhD thesis, University of Glasgow (1995)Google Scholar
  20. 20.
    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
  21. 21.
    Gentry, C., Ramzan, Z.: Single-database private information retrieval with constant communication rate. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 803–815. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  22. 22.
    Goldreich, O.: Foundations of Cryptography. Cambridge University Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  23. 23.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  24. 24.
    Ishai, Y., Malkin, T.G., Strauss, M.J., Wright, R.N.: Private multiparty sampling and approximation of vector combinations. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 243–254. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Jha, S., Kruger, L., Shmatikov, V.: Towards practical privacy for genomic computation. In: IEEE Symposium on Security and Privacy (2008)Google Scholar
  26. 26.
    Kiltz, E., Mohassel, P., Weinreb, E., Franklin, M.K.: Secure linear algebra using linearly recurrent sequences. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 291–310. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  27. 27.
    Malin, B., Sweeney, L.: Re-identification of dna through an automated linkage process. In: AMIA Annual Symposium, pp. 423–427 (2001)Google Scholar
  28. 28.
    Masek, W.J., Paterson, M.S.: A faster algorithm for computing string edit distances. J. of Computer and System Sciences 20, 18–31 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Melchor, C.A., Deswarte, Y.: Single-database private information retrieval schemes : Overview, performance study, and usage with statistical databases. In: Domingo-Ferrer, J., Franconi, L. (eds.) PSD 2006. LNCS, vol. 4302, pp. 257–265. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  30. 30.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proc. of STOC, pp. 590–599 (2001)Google Scholar
  31. 31.
    Naor, M., Pinkas, B.: Oblivious transfer and polynomial evaluation. In: Proc. of STOC, pp. 245–254 (1999)Google Scholar
  32. 32.
    Department of Health and Human Services. 45 CFR (Code of Federal Regulations), parts 160–164. Standards for privacy of individually identifiable health information, final rule. Federal Register 67(157), 53182–53273 (August 12, 2002)Google Scholar
  33. 33.
    The GPL Violations project (2008),
  34. 34.
    Szajda, D., Pohl, M., Owen, J., Lawson, B.G.: Toward a practical data privacy scheme for a distributed implementation of the Smith-Waterman genome sequence comparison algorithm. In: Proc. of NDSS, pp. 253–265 (2006)Google Scholar
  35. 35.
    Vaszar, L.T., Cho, M.K., Raffin, T.A.: Privacy issues in personalized medicine. Pharmacogenomics 4(2), 107–112 (2003)CrossRefGoogle Scholar
  36. 36.
    Yao, A.C.: How to generate and exchange secrets. In: Proc. of FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Matthew Franklin
    • 1
  • Mark Gondree
    • 1
  • Payman Mohassel
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaDavisUSA

Personalised recommendations