Brief Encounters with a Random Key Graph

  • Virgil D. Gligor
  • Adrian Perrig
  • Jun Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7028)


Random key graphs, also called uniform random intersection graphs, have been used for modeling a variety of different applications since their introduction in wireless sensor networks. In this paper, we review some of their recent applications and suggest several new ones, under the full visibility assumption; i.e., under the assumption that all nodes are within communication range of each other. We also suggest further research in determining the connectivity properties of random key graphs when limited visibility is more realistic; e.g., graph nodes can communicate only with a subset of other nodes due to range restrictions or link failures.


Sensor Network Wireless Sensor Network Mobile Node Hash Function Recommender System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Blackburn, S., Gerke, S.: Connectivity of the Uniform Random Intersection Graph. Discrete Mathematics 309(16), 5130–5140 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Eschenauer, L., Gligor, V.D.: A Key-Management Scheme for Distributed Sensor Networks. In: 9th ACM Conference on Computer and Communications Security, Alexandria, VA (2002)Google Scholar
  3. 3.
    Goehardt, E., Jaworski, J., Rybarczyk, K.: Random Intersection Graphs and Classification. In: Lens, H.J., Decker, R. (eds.) Studies in Classification, Data Analysis, and Knowledge Organization, vol. 33, pp. 67–74. Springer, Berlin (2007)Google Scholar
  4. 4.
    Marbach, P.: A Lower Bound on the Number of Rankings Required in Recommender Systems Using Collaborative Filtering. In: IEEE Conference on Information Sciences and Systems, pp. 292–297. Princeton University, NJ (2008)CrossRefGoogle Scholar
  5. 5.
    Blackburn, S.R., Stinson, D.R., Upadhyay, J.: On the Complexity of the Herding Attack and Some Related Attacks on Hash Functions. Report 2010/030 (2010),
  6. 6.
    Yağan, O., Makowski, A.: On the Random Graph Induced by a Random Key Predistribution Scheme under Full Visibility. In: IEEE International Symposium on Information Theory, Toronto, ON (2008)Google Scholar
  7. 7.
    Yağan, O., Makowski, A.: Zero-One Laws for Connectivity in Random Key Graphs. Technical Report, Institute for Systems Research, University of Maryland (February 2009)Google Scholar
  8. 8.
    Eschenauer, L., Gligor, V.D., Baras, J.: On Trust Establishment in Mobile Ad-Hoc Networks. In: Christianson, B., Crispo, B., Malcolm, J.A., Roe, M. (eds.) Security Protocols 2002. LNCS, vol. 2845, pp. 47–66. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Di Pietro, R., Mancini, L.V., Mei, A., Panconesi, A., Radhakrishnan, J.: Redoubtable Sensor Networks. ACM Transactions on Information and System Security (TISSEC) 11(3) (March 2008)Google Scholar
  10. 10.
    Wendlandt, D., Andersen, D., Perrig, A.: Perspectives: Improving SSH-style Host Authentication with Multi-Path Probing. In: USENIX Annual Technical Conference (June 2008)Google Scholar
  11. 11.
    Kelsey, J., Kohno, T.: Herding Hash Functions and the Nostradamus Attack. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 183–200. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Rybarczyk, K.: Sharp Threshold Functions for Random Intersection Graphs via a Coupling Method. The Electronic Journal of Combinatorics 18(1), 36–47 (2011)MathSciNetGoogle Scholar
  13. 13.
    Rybarczyk, K.: Diameter, Connectivity, and Phase Transition of the Uniform Random Intersection Graph. Submitted to Discrete Mathematics (July 2009)Google Scholar
  14. 14.
    Yağan, O., Makowski, A.: Random Key Graphs? - Can They Be Small Worlds? In: International Conference on Networks & Communications, pp. 313–318 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Virgil D. Gligor
    • 1
  • Adrian Perrig
    • 1
  • Jun Zhao
    • 1
  1. 1.ECE Department and CyLabCarnegie Mellon UniversityPittsburghPennsylvania

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