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

  • Kendall E
  • Kendall M
  • Kendall W
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Abstract

A commonly used metric for comparing the resilience of key predistribution schemes is $\text{fail}_s$, 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 challenging, difficult to compute 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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Kendall, E., Kendall, M. L., & Kendall, W. S. (2012). A Generalised Formula for Calculating the Resilience of Random Key Predistribution Schemes. Cryptology EPrint Archive. Retrieved from http://eprint.iacr.org/2012/426

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