Privacy-Preserving String Edit Distance with Moves

  • Shunta Nakagawa
  • Tokio Sakamoto
  • Yoshimasa Takabatake
  • Tomohiro I
  • Kilho Shin
  • Hiroshi SakamotoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11223)


We propose the first two-party protocol for securely computing an extended edit distance. The parties possessing their respective strings x and y want to securely compute the edit distance with move operations (EDM), that is, the minimum number of insertions, deletions, renaming of symbols, or substring moves required to transform x to y. Although computing the exact EDM is NP-hard, there exits an almost linear-time algorithm within the approximation ratio \(O(\lg ^*N\lg N)\) for \(N=\max \{|x|,|y|\}\). We extend this algorithm to the privacy-preserving computation enlisting the homomorphic encryption scheme so that the party can obtain the approximate EDM without revealing their privacy under the semi-honest model.


  1. 1.
    Akgün, M., Bayrak, A.O., Ozer, B., Sağiroğlu, M.S.: Privacy preserving processing of genomic data: a survey. J. Biomed. Inform. 56, 103–111 (2015)CrossRefGoogle Scholar
  2. 2.
    Atallah, M.J., Kerschbaum, F., Du, W.: Secure and private sequence comparisons. In: WPES, pp. 39–44 (2003)Google Scholar
  3. 3.
    Aziz, M.M.A., Alhadidi, D., Mohammed, N.: Secure and efficient multiparty computation on genomic data. In: IDEAS, pp. 278–283 (2016)Google Scholar
  4. 4.
    Beck, M., Kerschbaum, F.: Approximate two-party privacy-preserving string matching with linear complexity. In: BigData Congress, pp. 31–37 (2013)Google Scholar
  5. 5.
    Belazzougui, D., Zhang, Q.: Edit distance: sketching, streaming, and document exchange. In: FOCS, pp. 51–60 (2016)Google Scholar
  6. 6.
    Blake, I.F., Kolesnikov, V.: Strong conditional oblivious transfer and computing on intervals. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 515–529. Springer, Heidelberg (2004). Scholar
  7. 7.
    Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005). Scholar
  8. 8.
    Catalano, D., Di Raimondo, M., Faro, S.: Verifiable pattern matching on outsourced texts. In: Zikas, V., De Prisco, R. (eds.) SCN 2016. LNCS, vol. 9841, pp. 333–350. Springer, Cham (2016). Scholar
  9. 9.
    Cheon, J.H., Kim, M., Lauter, K.E.: Homomorphic computation of edit distance. In: FCW, pp. 194–212 (2015)Google Scholar
  10. 10.
    Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves. ACM Trans. Algorithms 3(1) (2007). Article 2MathSciNetCrossRefGoogle Scholar
  11. 11.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)Google Scholar
  12. 12.
    Goldwasser, S., Kalai, Y., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: STOC, pp. 555–564 (2013)Google Scholar
  13. 13.
    Hach, F., Numanagić, I., Alkan, C., Sahinalp, S.C.: Scalce: boosting sequence compression algorithms using locally consistent encoding. Bioinformatics 28(23), 3051–3057 (2012)CrossRefGoogle Scholar
  14. 14.
    Inan, A., Kaya, S., Saygin, Y., Savas, E., Hintoglu, A., Levi, A.: Privacy preserving clustering on horizontally partitioned data. Data Knowl. Eng. 63(3), 646–666 (2007)CrossRefGoogle Scholar
  15. 15.
    Jowhari, H.: Efficient communication protocols for deciding edit distance. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 648–658. Springer, Heidelberg (2012). Scholar
  16. 16.
    Li, M., Chen, X., Li, X., Ma, B., Vitanyi, P.M.B.: The similarity metric. IEEE Trans. Inform. Theory 50(12), 3250–3264 (2004)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Maruyama, S., Tabei, Y.: Fully-online grammar compression in constant space. In: DCC, pp. 218–229 (2014)Google Scholar
  18. 18.
    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). Scholar
  19. 19.
    Patel, S., Persiano, G., Yeo, K.: Recursive orams with practical constructions. Cryptology ePrint Archive, Report 2017/964 (2017)Google Scholar
  20. 20.
    Rane, S., Sun, W.: Privacy preserving string comparisons based on Levenshtein distance. In: WIFS, pp. 1–6 (2010)Google Scholar
  21. 21.
    Rane, S., Sun, W., Vetro, A.: Privacy-preserving approximation of L1 distance for multimedia applications. In: ICME, pp. 492–497 (2010)Google Scholar
  22. 22.
    Samanthula, B.K.K., Chun, H., Jiang, W.: An efficient and probabilistic secure bit-decomposition. In: ACM SIGSAC Symposium on Information, Computer and Communications Security, pp. 541–546 (2013)Google Scholar
  23. 23.
    Shapira, D., Storer, J.A.: Edit distance with move operations. J. Discrete Algorithms 5(2), 380–392 (2007)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Starikovskaya, T.: Communication and streaming complexity of approximate pattern matching. In: CPM, pp. 13:1–13:11 (2017)Google Scholar
  25. 25.
    Stefanov, E., et al.: Path oram: an extremely simple oblivious ram protocol. In: CCS, pp. 299–310 (2013)Google Scholar
  26. 26.
    Takabatake, Y., I, T., Sakamoto, H.: A space-optimal grammar compression. In: ESA, pp. 67:1–67:15 (2017)Google Scholar
  27. 27.
    Toft, T.: Constant-rounds, almost-linear bit-decomposition of secret shared values. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 357–371. Springer, Heidelberg (2009). Scholar
  28. 28.
    Yao, A.C.: How to generate and exchange secrets. In: FOCS, pp. 162–167 (1986)Google Scholar
  29. 29.
    Zhu, R., Huang, Y.: Efficient privacy-preserving edit distance and beyond. IACR Cryptology ePrint Archive 2017: 683 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Shunta Nakagawa
    • 1
  • Tokio Sakamoto
    • 2
  • Yoshimasa Takabatake
    • 1
  • Tomohiro I
    • 1
  • Kilho Shin
    • 3
  • Hiroshi Sakamoto
    • 1
    Email author
  1. 1.Kyushu Institute of TechnologyIizukaJapan
  2. 2.ThomasLab Inc.IizukaJapan
  3. 3.University of HyogoKobeJapan

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