Secure Error-Tolerant Graph Matching Protocols

  • Kalikinkar Mandal
  • Basel Alomair
  • Radha Poovendran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10052)


We consider a setting where there are two parties, each party holds a private graph and they wish to jointly compute the structural dissimilarity between two graphs without revealing any information about their private input graph. Graph edit distance (GED) is a widely accepted metric for measuring the dissimilarity of graphs. It measures the minimum cost for transforming one graph into the other graph by applying graph edit operations. In this paper we present a framework for securely computing approximated GED and as an example, present a protocol based on threshold additive homomorphic encryption scheme. We develop several new sub-protocols such as private maximum computation and optimal assignment protocols to construct the main protocol. We show that our protocols are secure against semi-honest adversaries. The asymptotic complexity of the protocol is \(O(n^5\ell \log ^*(\ell ))\) where \(\ell \) is the bit length of ring elements and n is the number of nodes in the graph.


Secure two-party computation Graph edit distance Privacy Graph algorithms 


  1. 1.
    Aggarwal, C.C., Wang, H.: Managing and Mining Graph Data. Springer, US (2010)CrossRefMATHGoogle Scholar
  2. 2.
    Aly, A., Cuvelier, E., Mawet, S., Pereira, O., Vyve, M.: Securely solving simple combinatorial graph problems. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 239–257. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39884-1_21 CrossRefGoogle Scholar
  3. 3.
    Atallah, M.J., Kerschbaum, F., Wenliang, D.: Secure and private sequence comparisons. In: Proceedings of the 2003 ACM Workshop on Privacy in the Electronic Society, WPES 2003, pp. 39–44. ACM, New York (2003)Google Scholar
  4. 4.
    Bellare, M., Hoang, V.T., Rogaway, P.: Foundations of garbled circuits. In: Proceedings of the 2012 ACM Conference on Computer and Communications Security, CCS 2012, pp. 784–796. ACM, New York (2012)Google Scholar
  5. 5.
    Blanton, M., Saraph, S.: Oblivious maximum bipartite matching size algorithm with applications to secure fingerprint identification. In: Pernul, G., Ryan, P.Y.A., Weippl, E. (eds.) ESORICS 2015. LNCS, vol. 9326, pp. 384–406. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24174-6_20 CrossRefGoogle Scholar
  6. 6.
    Blanton, M., Steele, A., Alisagari, M.: Data-oblivious graph algorithms for secure computation and outsourcing. In: Proceedings of the 8th ACM SIGSAC Symposium on Information, Computer and Communications Security, ASIA CCS 2013, pp. 207–218. ACM, New York (2013)Google Scholar
  7. 7.
    Cheon, J.H., Kim, M., Lauter, K.: Homomorphic computation of edit distance. In: Brenner, M., Christin, N., Johnson, B., Rohloff, K. (eds.) FC 2015. LNCS, vol. 8976, pp. 194–212. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48051-9_15 CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006). doi:10.1007/11681878_15 CrossRefGoogle Scholar
  9. 9.
    Fankhauser, S., Riesen, K., Bunke, H.: Speeding up graph edit distance computation through fast bipartite matching. In: Jiang, X., Ferrer, M., Torsello, A. (eds.) GbRPR 2011. LNCS, vol. 6658, pp. 102–111. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20844-7_11 CrossRefGoogle Scholar
  10. 10.
    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). doi:10.1007/978-3-540-24676-3_1 CrossRefGoogle Scholar
  11. 11.
    Gentry, C., Halevi, S., Jutla, C.S., Raykova, M.: Private database access with he-over-oram architecture. IACR Cryptology ePrint Archive 2014, 345 (2014)Google Scholar
  12. 12.
    Goldreich, O.: Foundations of Cryptography Volume II Basic Applications, vol. II. Cambridge University Press, New York (2004)CrossRefMATHGoogle Scholar
  13. 13.
    Hazay, C., Mikkelsen, G.L., Rabin, T., Toft, T.: Efficient RSA key generation and threshold paillier in the two-party setting. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 313–331. Springer, Heidelberg (2012). doi:10.1007/978-3-642-27954-6_20 CrossRefGoogle Scholar
  14. 14.
    Henecka, W., Stefan, K., Sadeghi, A.-R., Schneider, T., Wehrenberg, I.: Tasty: tool for automating secure two-party computations. In: Proceedings of the 17th ACM Conference on Computer and Communications Security, CCS 2010, pp. 451–462. ACM, New York (2010)Google Scholar
  15. 15.
    Huang, Y., Evans, D., Katz, J., Malka, L.: Faster secure two-party computation using garbled circuits. In: Proceedings of the 20th USENIX Conference on Security, SEC 2011, pp. 35–35. USENIX Association, Berkeley (2011)Google Scholar
  16. 16.
    Jha, S., Kruger, L., Shmatikov, V.: Towards practical privacy for genomic computation. In: Proceedings of the 2008 IEEE Symposium on Security and Privacy, SP 2008, pp. 216–230. IEEE Computer Society, Washington, DC (2008)Google Scholar
  17. 17.
    Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007). doi:10.1007/978-3-540-72540-4_4 CrossRefGoogle Scholar
  18. 18.
    Lipmaa, H., Toft, T.: Secure equality and greater-than tests with sublinear online complexity. In: Proceedings of the Automata, Languages, and Programming - 40th International Colloquium, ICALP 2013, Part II, Riga, Latvia, 8–12 July 2013, pp. 645–656 (2013)Google Scholar
  19. 19.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay–a secure two-party computation system. In: Proceedings of the 13th Conference on USENIX Security Symposium, SSYM 2004, vol. 13, p. 20. USENIX Association, Berkeley (2004)Google Scholar
  20. 20.
    Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S.: Handbook of Fingerprint Recognition, 2nd edn. Springer Publishing Company, London (2009)CrossRefMATHGoogle Scholar
  21. 21.
    Mandal, K., Alomair, B., Poovendran, R.: Secure error-tolerant graph matching protocols. Cryptology ePrint Archive, Report 2016/908 (2016).
  22. 22.
    Munkres, J.: Algorithms for the assignment and transportation problems. J. Soc. Ind. Appl. Math. 5(1), 32–38 (1957)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2001, pp. 448–457. Society for Industrial and Applied Mathematics, Philadelphia (2001)Google Scholar
  24. 24.
    Neuhaus, M., Bunke, H.: A graph matching based approach to fingerprint classification using directional variance. In: Kanade, T., Jain, A., Ratha, N.K. (eds.) AVBPA 2005. LNCS, vol. 3546, pp. 191–200. Springer, Heidelberg (2005). doi:10.1007/11527923_20 CrossRefGoogle Scholar
  25. 25.
    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). doi:10.1007/3-540-48910-X_16 CrossRefGoogle Scholar
  26. 26.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vision Comput. 27(7), 950–959 (2009)CrossRefGoogle Scholar
  27. 27.
    Toft, T.: Sub-linear, secure comparison with two non-colluding parties. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 174–191. Springer, Heidelberg (2011). doi:10.1007/978-3-642-19379-8_11 CrossRefGoogle Scholar
  28. 28.
    Yao, A.C.-C: How to generate and exchange secrets. In: Proceedings of the 27th Annual Symposium on Foundations of Computer Science, SFCS 1986, pp. 162–167. IEEE Computer Society, Washington, DC (1986)Google Scholar
  29. 29.
    Zeng, Z., Tung, A.K.H., Wang, J., Feng, J., Zhou, L.: Comparing stars: on approximating graph edit distance. Proc. VLDB Endow. 2(1), 25–36 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Kalikinkar Mandal
    • 1
  • Basel Alomair
    • 2
  • Radha Poovendran
    • 1
  1. 1.Network Security Lab, Department of Electrical EngineeringUniversity of WashingtonSeattleUSA
  2. 2.National Center for Cybersecurity TechnologiesKing Abdulaziz City for Science and Technology (KACST)RiyadhSaudi Arabia

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