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

*Ed Kendall and Michelle Kendall and Wilfrid S. Kendall*

**Abstract: **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.

**Category / Keywords: **applications / key predistribution schemes, wireless sensor networks

**Date: **received 27 Jul 2012

**Contact author: **michelle louise kendall at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20120805:141930 (All versions of this report)

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