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

A commonly used metric for comparing the resilience of key predistribution schemes is fails, 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.