Securely Solving Simple Combinatorial Graph Problems | SpringerLink
Skip to main content
Springer Nature Link
Log in

Securely Solving Simple Combinatorial Graph Problems

  • Conference paper
Financial Cryptography and Data Security (FC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7859))

Included in the following conference series:

Abstract

We investigate the problem of solving traditional combinatorial graph problems using secure multi-party computation techniques, focusing on the shortest path and the maximum flow problems. To the best of our knowledge, this is the first time these problems have been addressed in a general multi-party computation setting. Our study highlights several complexity gaps and suggests the exploration of various trade-offs, while also offering protocols that are efficient enough to solve real-world problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Yao, A.C.C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, pp. 160–164. IEEE (1982)

    Google Scholar 

  2. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC, pp. 1–10. ACM (1988)

    Google Scholar 

  3. Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC, pp. 11–19. ACM (1988)

    Google Scholar 

  4. Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)

    Google Scholar 

  5. Bogetoft, P., Damgård, I., Jakobsen, T.P., Nielsen, K., Pagter, J., Toft, T.: A practical implementation of secure auctions based on multiparty integer computation. In: Di Crescenzo, G., Rubin, A. (eds.) FC 2006. LNCS, vol. 4107, pp. 142–147. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Cramer, R., Franklin, M.K., Schoenmakers, B., Yung, M.: Multi-authority secret-ballot elections with linear work. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 72–83. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  7. Barni, M., Failla, P., Kolesnikov, V., Lazzeretti, R., Sadeghi, A.-R., Schneider, T.: Secure evaluation of private linear branching programs with medical applications. In: Backes, M., Ning, P. (eds.) ESORICS 2009. LNCS, vol. 5789, pp. 424–439. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Sadeghi, A.-R., Schneider, T., Wehrenberg, I.: Efficient privacy-preserving face recognition. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 229–244. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure two-party computation is practical. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 250–267. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Kocher, P.C.: Timing attacks on implementations of diffie-hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)

    Google Scholar 

  11. Damgård, I., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Toft, T.: Secure data structures based on multi-party computation. In: PODC, pp. 291–292. ACM (2011)

    Google Scholar 

  13. Ben-David, A., Nisan, N., Pinkas, B.: Fairplaymp: a system for secure multi-party computation. In: CCS, pp. 257–266. ACM (2008)

    Google Scholar 

  14. Burkhart, M., Strasser, M., Many, D., Dimitropoulos, X.: Sepia: privacy-preserving aggregation of multi-domain network events and statistics. In: Proceedings of the 19th USENIX Conference on Security, USENIX Security 2010. USENIX (2010)

    Google Scholar 

  15. Bogdanov, D., Laur, S., Willemson, J.: Sharemind: A Framework for Fast Privacy-Preserving Computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Geisler, M.: Cryptographic protocols: theory and implementation. PhD thesis, Aarhus University Denmark, Department of Computer Science (2010)

    Google Scholar 

  17. Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26(3), 362–391 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  18. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34(3), 596–615 (1987)

    Article  MathSciNet  Google Scholar 

  19. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  20. Toft, T.: Primitives and Applications for Multi-party Computation. PhD thesis, Department of Computer Science, Aarhus University (2007)

    Google Scholar 

  21. Kruger, L., Jha, S., Goh, E.J., Boneh, D.: Secure function evaluation with ordered binary decision diagrams. In: ACM CCS, pp. 410–420. ACM (2006)

    Google Scholar 

  22. Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  23. Brickell, J., Porter, D.E., Shmatikov, V., Witchel, E.: Privacy-preserving remote diagnostics. In: ACM CCS, CCS 2007, pp. 498–507. ACM (2007)

    Google Scholar 

  24. Barni, M., Failla, P., Lazzeretti, R., Sadeghi, A.R., Schneider, T.: Privacy-preserving ECG classification with branching programs and neural networks. IEEE TIFS 6(2), 452–468 (2011)

    Google Scholar 

  25. 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)

    Chapter  Google Scholar 

  26. Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious rams. J. ACM 43(3), 431–473 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  27. Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly secure oblivious RAM without random oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  28. Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  29. Damgård, I., Keller, M., Larraia, E., Miles, C., Smart, N.P.: Implementing AES via an actively/covertly secure dishonest-majority MPC protocol. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 241–263. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  30. Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012)

    Google Scholar 

  31. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press (2009)

    Google Scholar 

  32. Toft, T.: Solving linear programs using multiparty computation. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 90–107. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ICTEAM and IMMAQ institutes, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Abdelrahaman Aly, Edouard Cuvelier, Sophie Mawet, Olivier Pereira & Mathieu Van Vyve

Authors
  1. Abdelrahaman Aly
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edouard Cuvelier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sophie Mawet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Olivier Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mathieu Van Vyve
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technische Universität Darmstadt, Germany

    Ahmad-Reza Sadeghi

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aly, A., Cuvelier, E., Mawet, S., Pereira, O., Van Vyve, M. (2013). Securely Solving Simple Combinatorial Graph Problems. In: Sadeghi, AR. (eds) Financial Cryptography and Data Security. FC 2013. Lecture Notes in Computer Science, vol 7859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39884-1_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39884-1_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39883-4

  • Online ISBN: 978-3-642-39884-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation