Paper 2012/426

A Generalised Formula for Calculating the Resilience of Random Key Predistribution Schemes

Ed Kendall, Michelle Kendall, and Wilfrid S. Kendall


A commonly used metric for comparing the resilience of key predistribution schemes is $\fail_s$, which measures the proportion of network connections which are `broken' by an adversary which has compromised $s$ nodes. In `Random key predistribution schemes for sensor networks', Chan, Perrig and Song present a formula for measuring the resilience in a class of random key predistribution schemes called $q$-composite schemes. We present a correction to this formula for schemes where more than one key may be used to secure a link between a pair of nodes. Our corrected formula features an additional parameter which makes it applicable to a wider variety of random key predistribution schemes, including the original Eschenauer Gligor scheme. We also present a simplification of the formula for calculating connectivity. We refer to the recent paper by Yum and Lee which also claims to correct the original formula for the $q$-composite scheme. However the resulting formula is complicated, computationally demanding, and hard to understand. The formula which we propose and prove is easily computable and can be applied to a wider range of schemes.

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Publication info
Published elsewhere. Unknown where it was published
key predistribution schemeswireless sensor networks
Contact author(s)
michelle louise kendall @ gmail com
2012-08-05: received
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      author = {Ed Kendall and Michelle Kendall and Wilfrid S.  Kendall},
      title = {A Generalised Formula for Calculating the Resilience of Random Key Predistribution Schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2012/426},
      year = {2012},
      note = {\url{}},
      url = {}
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