Skip to main content

Key Predistribution Schemes Using Bent Functions in Distributed Sensor Networks

Part of the Lecture Notes in Computer Science book series (LNSC,volume 10143)

Abstract

Key management is an essential functionality for developing secure cryptosystems; particularly for implementations to low cost devices of a Distributed Sensor Networks (DSN)–a prototype of Internet of Things (IoT). Low cost leads to constraints in various resources of constituent devices of a IoT (e.g., sensors of a DSN); thereby restricting implementations of computationally heavy public key cryptosystems. This leads to adaptation of the novel key predistribution trick in symmetric key platform to efficiently tackle the problem of key management for these resource starved networks. After a few initial proposals based on random graphs, most key predistribution schemes (KPS) use deterministic (combinatorial) approaches to assure essential design properties. Combinatorial designs like a \((v,b,r,k)-\)configuration which forms a \(\mu (v,b,r,k)-\)CID are effective schemes to design KPS [20]. In this paper, we use bent Boolean functions to generate four combinatorial designs for the purpose of designing deterministic KPS. Of particular interest are our later (two) schemes that are constructed over Dillon’s bent Boolean function. Effectiveness of our solutions in term of crucial metrics in comparison to prominent schemes has been theoretically established.

Keywords

  • Bent functions
  • Partial spread
  • Combinatorial designs
  • Key predistribution scheme(s)
  • Internet of Things
  • Distributed Sensor Networks

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-54705-3_23
  • Chapter length: 19 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   79.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-54705-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   99.99
Price excludes VAT (USA)

Notes

  1. 1.

    Capture of this authority (sensor) acting as a TA makes the system vulnerable.

  2. 2.

    The definition of difference set can be found in the book by Stinson [26].

References

  1. Bag, S., Dhar, A., Sarkar, P.: 100% connectivity for location aware code based KPD in clustered WSN: merging blocks. In: Gollmann, D., Freiling, F.C. (eds.) ISC 2012. LNCS, vol. 7483, pp. 136–150. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33383-5_9

    CrossRef  Google Scholar 

  2. Bernasconi, A., Codenotti, B.: Spectral analysis of boolean functions as a graph eigenvalue problem. IEEE Trans. Comput. 48(3), 345–351 (1999)

    MathSciNet  CrossRef  Google Scholar 

  3. Bose, M., Dey, A., Mukerjee, R.: Key predistribution schemes for distributed sensor networks via block designs. Des. Codes Crypt. 67(1), 111–136 (2013)

    MathSciNet  CrossRef  MATH  Google Scholar 

  4. Blom, R.: An optimal class of symmetric key generation systems. In: Beth, T., Cot, N., Ingemarsson, I. (eds.) EUROCRYPT 1984. LNCS, vol. 209, pp. 335–338. Springer, Heidelberg (1985). doi:10.1007/3-540-39757-4_22

    CrossRef  Google Scholar 

  5. Cameron, P.J.: Strongly regular graphs. Preprint (2001). http://designtheory.org/library/preprints/srg.pdf

  6. Çamtepe, S.A., Yener, B.: Combinatorial design of key distribution mechanisms for wireless sensor networks. In: Samarati, P., Ryan, P., Gollmann, D., Molva, R. (eds.) ESORICS 2004. LNCS, vol. 3193, pp. 293–308. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30108-0_18

    CrossRef  Google Scholar 

  7. Çamtepe, S.A., Yener, B.: Key Distribution Mechanisms for Wireless Sensor Networks: a Survey. Technical report. Rensselaer Polytechnic Institute (2005)

    Google Scholar 

  8. Carlet, C.: More ps and h-like bent functions (2015). http://eprint.iacr.org/2015/168

  9. Chen, C.Y., Chao, H.C.: A survey of key predistribution in wireless sensor networks. Secur. Commun. Netw. (2011)

    Google Scholar 

  10. Cusick, T.W., Stănică, P.: Cryptographic Boolean Functions and Applications. Academic Press, Elsevier (2009)

    Google Scholar 

  11. Dhar, A., Sarkar, P.: Full Communication in a Wireless Sensor Network by Merging Blocks of a Key Predistribution Using Reed Solomon Code (2011)

    Google Scholar 

  12. Dillon, J.F.: A survey of bent functions. NSA Tech. J., 191–215, 1972

    Google Scholar 

  13. Dillon, J.F.: Elementary Hadamard Difference sets. Ph.D thesis, University of Maryland (1974)

    Google Scholar 

  14. Erdős, P., Rényi, A.: On the evolution of random graphs. In: Publication of the Mathematical Institute of the Hungarian Academy of Sciences, pp. 17–61 (1960)

    Google Scholar 

  15. Eschenauer, L., Gligor, V.: A key-management scheme for distributed sensor networks. In: 9th ACM Conference on Computer and Communications Security, pp. 41–47. ACM Press, New York (2002)

    Google Scholar 

  16. Henry, K., Paterson, M.B., Stinson, D.R.: Practical approaches to varying network size in combinatorial key predistribution schemes. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 89–117. Springer, Heidelberg (2014). doi:10.1007/978-3-662-43414-7_5

    CrossRef  Google Scholar 

  17. Kantor, W.M.: Bent functions and spreads (2005). http://pages.uoregon.edu/kantor/PAPERS/Bent+spreadsFinal.pdf

  18. Steiner, J.G., Neuman, B.C., Schiller, J.I.: Kerberos: an authentication service for open network systems. In: USENIX Winter, pp. 191–202 (1988)

    Google Scholar 

  19. Lee, J., Stinson, D.R.: Deterministic key predistribution schemes for distributed sensor networks. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 294–307. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30564-4_21

    CrossRef  Google Scholar 

  20. Lee, J., Stinson, D.R.: A combinatorial approach to key predistribution for distributed sensor networks. In: IEEE Wireless Communications and Networking Conference, WCNC 2005, pp. 1200–1205 (2005)

    Google Scholar 

  21. Lee, J., Stinson, D.R.: On the construction of practical key predistribution schemes for distributed sensor networks using combinatorial designs. ACM Trans. Inf. Syst. Secur. 11(2), 1–35 (2008)

    CrossRef  Google Scholar 

  22. Paterson, M.B., Stinson, D.R.: A unified approach to combinatorial key predistribution schemes for sensor networks. Des. Codes Crypt. 71(3), 433–457 (2014)

    MathSciNet  CrossRef  MATH  Google Scholar 

  23. Rothaus, O.S.: On bent functions. J. Comb. Theo. Ser. A 20, 300–305 (1976)

    MathSciNet  CrossRef  MATH  Google Scholar 

  24. Ruj, S., Pal, A.: Preferential attachment model with degree bound and its application to key predistribution in WSN. In: 30th IEEE International Conference on Advanced Information Networking and Applications, AINA 2016, Crans-Montana, Switzerland, 23–25, pp. 677–683, March 2016

    Google Scholar 

  25. Ruj, S., Roy, B.K.: Key predistribution schemes using codes in wireless sensor networks. In: 4th International Conference on Information Security and Cryptology, Inscrypt 2008, Beijing, China, December 14–17, Revised Selected Papers, pp. 275–288 (2008)

    Google Scholar 

  26. Stinson, D.R., Designs, C.: Constructions and Analysis. Springer, New York (2003)

    Google Scholar 

  27. Wu, B.: PS bent functions constructed from finite pre-quasifield spreads (2013). http://arxiv.org/pdf/1308.3355.pdf

  28. Wei, R., Wu, J.: Product Construction of Key Distribution Schemes for Sensor Networks. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 280–293. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30564-4_20

    CrossRef  Google Scholar 

Download references

Acknowledgement

This work was accomplished during Dr. Pinaki Sarkar’s tenure as a post doctoral fellow at Indian Institute of Science (IISc), Bangalore. The author would like to cordially thank Defense Research Development Organization (DRDO), India for funding his post doctoral research program at IISc, Bangalore.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Deepak Kumar Dalai .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Dalai, D.K., Sarkar, P. (2017). Key Predistribution Schemes Using Bent Functions in Distributed Sensor Networks. In: Chen, K., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2016. Lecture Notes in Computer Science(), vol 10143. Springer, Cham. https://doi.org/10.1007/978-3-319-54705-3_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-54705-3_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54704-6

  • Online ISBN: 978-3-319-54705-3

  • eBook Packages: Computer ScienceComputer Science (R0)