An integer programming formulation of the key management problem in wireless sensor networks

Abstract

With the advent of modern communications systems, much attention has been put on developing methods for securely transferring information between constituents of wireless sensor networks. To this effect, we introduce a mathematical programming formulation for the key management problem, which broadly serves as a mechanism for encrypting communications. In particular, an integer programming model of the q-Composite scheme is proposed and utilized to distribute keys among nodes of a network whose topology is known. Numerical experiments demonstrating the effectiveness of the proposed model are conducted using using a well-known optimization solver package. An illustrative example depicting an optimal encryption for a small-scale network is also presented.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. 1.

    Note that Gurobi may produce a nonzero optimality gap even if the incumbent solution is optimal. In such cases, additional time is required to validate that the incumbent solution is optimal.

References

  1. 1.

    Blom, R.: An Optimal Class of Symmetric Key Generation Systems, pp. 335–338. Springer, Berlin (1985). https://doi.org/10.1007/3-540-39757-4_22

    Google Scholar 

  2. 2.

    Blundo, C., De Santis, A., Herzberg, A., Kutten, S., Vaccaro, U., Yung, M.: Perfectly-Secure Key Distribution for Dynamic Conferences, pp. 471–486. Springer, Berlin (1993). https://doi.org/10.1007/3-540-48071-4_33

    Google Scholar 

  3. 3.

    Campos-Naez, E., Garcia, A., Li, C.: A game-theoretic approach to efficient power management in sensor networks. Oper. Res. 56(3), 552–561 (2008). https://doi.org/10.1287/opre.1070.0435

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Camtepe, S.A., Yener, B.: Combinatorial design of key distribution mechanisms for wireless sensor networks. IEEE/ACM Trans. Netw. 15(2), 346–358 (2007). https://doi.org/10.1109/TNET.2007.892879

    Article  Google Scholar 

  5. 5.

    Carvalho, M., Sorokin, A., Boginski, V., Balasundaram, B.: Topology design for on-demand dual-path routing in wireless networks. Optim. Lett. 7(4), 695–707 (2013). https://doi.org/10.1007/s11590-012-0453-0

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Chen, C.Y., Chao, H.C.: A survey of key distribution in wireless sensor networks. Secur. Commun. Netw. 7(12), 2495–2508 (2014). https://doi.org/10.1002/sec.354

    Article  Google Scholar 

  7. 7.

    Didla, S., Ault, A., Bagchi, S.: Optimizing AES for embedded devices and wireless sensor networks. In: Proceedings of the 4th International Conference on Testbeds and Research Infrastructures for the Development of Networks and Communities, TridentCom’08, pp. 4:1–4:10. ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), ICST, Brussels, Belgium (2008)

  8. 8.

    Eschenauer, L., Gligor, V.D.: A key-management scheme for distributed sensor networks. In: Proceedings of the 9th ACM Conference on Computer and Communications Security, CCS’02, pp. 41–47. ACM, New York (2002). https://doi.org/10.1145/586110.586117

  9. 9.

    He, T., Vicaire, P., Yan, T., Cao, Q., Zhou, G., Gu, L., Luo, L., Stoleru, R., Stankovi, J.A., Abdelzaher, T.: Achieving real-time target tracking using wireless sensor networks. In: Technical Report (2006)

  10. 10.

    Kim, S., Pakzad, S., Culler, D., Demmel, J., Fenves, G., Glaser, S., Turon, M.: Health monitoring of civil infrastructures using wireless sensor networks. pp. 254–263 (2007). https://doi.org/10.1145/1236360.1236395

  11. 11.

    Li, X., Aneja, Y.P.: A branch-and-cut approach for the minimum-energy broadcasting problem in wireless networks. INFORMS J. Comput. 24(3), 443–456 (2012). https://doi.org/10.1287/ijoc.1110.0463

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Liu, D., Ning, P.: Establishing pairwise keys in distributed sensor networks. In: Proceedings of the 10th ACM Conference on Computer and Communications Security, CCS’03, pp. 52–61. ACM, New York (2003). https://doi.org/10.1145/948109.948119

  13. 13.

    Rossi, A., Singh, A., Sevaux, M.: Column generation algorithm for sensor coverage scheduling under bandwidth constraints. Networks 60(3), 141–154 (2012). https://doi.org/10.1002/net.20466

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Rossi, A., Singh, A., Sevaux, M.: An exact approach for maximizing the lifetime of sensor networks with adjustable sensing ranges. Comput. Oper. Res. 39(12), 3166–3176 (2012). https://doi.org/10.1016/j.cor.2012.04.001

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Rossi, A., Singh, A., Sevaux, M.: Lifetime maximization in wireless directional sensor network. Eur. J. Oper. Res. 231(1), 229–241 (2013). https://doi.org/10.1016/j.ejor.2013.05.033

    Article  Google Scholar 

  16. 16.

    Ruj, S., Nayak, A., Stojmenovic, I.: Pairwise and triple key distribution in wireless sensor networks with applications. IEEE Trans. Comput. 62(11), 2224–2237 (2013). https://doi.org/10.1109/TC.2012.138

    MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Shin, I., Shen, Y., Thai, M.T.: On approximation of dominating tree in wireless sensor networks. Optim. Lett. 4(3), 393–403 (2010). https://doi.org/10.1007/s11590-010-0175-0

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Simplício Jr., M.A., Barreto, P.S.L.M., Margi, C.B., Carvalho, T.C.M.B.: A survey on key management mechanisms for distributed wireless sensor networks. Comput. Netw. 54(15), 2591–2612 (2010). https://doi.org/10.1016/j.comnet.2010.04.010

    Article  MATH  Google Scholar 

  19. 19.

    Waltenegus, D., Poellabauer, C.: Fundamentals of Wireless Sensor Networks: Theory and Practice—Waltenegus Dargie, Christian Poellabauer. Wiley, Hoboken (2010)

    Google Scholar 

  20. 20.

    Werner-Allen, G., Lorincz, K., Ruiz, M., Marcillo, O., Johnson, J., Lees, J., Welsh, M.: Deploying a wireless sensor network on an active volcano. IEEE Internet Comput. 10(2), 18–25 (2006). https://doi.org/10.1109/MIC.2006.26

    Article  Google Scholar 

  21. 21.

    Wu, W., Gao, X., Pardalos, P.M., Du, D.Z.: Wireless networking, dominating and packing. Optim. Lett. 4(3), 347–358 (2010). https://doi.org/10.1007/s11590-009-0151-8

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Maciej Rysz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, G., Semenov, A. & Rysz, M. An integer programming formulation of the key management problem in wireless sensor networks. Optim Lett 14, 1037–1051 (2020). https://doi.org/10.1007/s11590-019-01465-2

Download citation

Keywords

  • Key management
  • Wireless sensor networks
  • q-Composite method
  • Integer linear programming
  • Optimization