A comprehensive guideline for choosing parameters in the Eschenauer-Gligor key predistribution

The Eschenauer-Gligor random key predistribution scheme is well known as the standard approach to secure communication in large-scale wireless sensor networks. The performance of the scheme has received considerable attention in the literature, yet there is still a lack of a comprehensive and rigorous guideline for identifying all possible combinations of scheme parameters to ensure an occurring probability p for the event that each sensor is directly connected to at least k neighboring sensors, for arbitrary k and p. This paper fills the gap and provides fundamental guidelines on choosing parameters of the scheme. We also significantly improve a recent result in [Zhao et al., IEEE Transactions on Automatic Control 2016].

[1]  Jun Zhao,et al.  On Resilience and Connectivity of Secure Wireless Sensor Networks Under Node Capture Attacks , 2017, IEEE Transactions on Information Forensics and Security.

[2]  Béla Bollobás,et al.  Random Graphs: Notation , 2001 .

[3]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[4]  Virgil D. Gligor,et al.  A key-management scheme for distributed sensor networks , 2002, CCS '02.

[5]  Jun Zhao,et al.  On Connectivity and Robustness in Random Intersection Graphs , 2017, IEEE Transactions on Automatic Control.

[6]  Mindaugas Bloznelis,et al.  Component evolution in a secure wireless sensor network , 2009 .

[7]  Osman Yagan.  Performance of the Eschenauer–Gligor Key Distribution Scheme Under an ON/OFF Channel , 2012, IEEE Transactions on Information Theory.

[8]  Jun Zhao,et al.  On k-Connectivity and Minimum Vertex Degree in Random s-Intersection Graphs , 2015, ANALCO.

[9]  Stefanie Gerke,et al.  Connectivity of the uniform random intersection graph , 2008, Discret. Math..

[10]  Katarzyna Rybarczyk.  The Coupling Method for Inhomogeneous Random Intersection Graphs , 2017, Electron. J. Comb..

[11]  Jun Zhao,et al.  $k$ -Connectivity in Random Key Graphs With Unreliable Links , 2015, IEEE Transactions on Information Theory.

[12]  P. Erd Os,et al.  On the strength of connectedness of random graphs , 1961 .

[13]  Peter Marbach.  A lower-bound on the number of rankings required in recommender systems using collaborativ filtering , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[14]  Dawn Xiaodong Song,et al.  Random key predistribution schemes for sensor networks , 2003, 2003 Symposium on Security and Privacy, 2003..

[15]  Virgil D. Gligor,et al.  Exact analysis of k-connectivity in secure sensor networks with unreliable links , 2015, 2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt).

[16]  Katarzyna Rybarczyk,et al.  Sharp threshold functions for the random intersection graph via coupling method , 2009, 0910.0749.

[17]  Katarzyna Rybarczyk,et al.  Diameter, connectivity, and phase transition of the uniform random intersection graph , 2011, Discret. Math..

[18]  Douglas R. Stinson,et al.  On the complexity of the herding attack and some related attacks on hash functions , 2012, Des. Codes Cryptogr..

[19]  Armand M. Makowski,et al.  Zero–One Laws for Connectivity in Random Key Graphs , 2009, IEEE Transactions on Information Theory.

[20]  Béla Bollobás,et al.  Random Graphs , 1985 .

[21]  Armand M. Makowski,et al.  Connectivity results for random key graphs , 2009, 2009 IEEE International Symposium on Information Theory.