Abstract—The subject of Key Management in Wireless

Sensor Networks has gained increased attention from the security community around the world in the last years. Several proposals were made concerning the peculiarities of resource constrains inherent to sensor devices. One of the most accepted proposals is based on random distribution of keys among the sensor nodes, which was followed by some variants in order to increase its security. In this paper we introduce the mathematical concepts behind this class of proposals through a step-by-step mathematical analysis. This leads to some practical concerns about its applicability to real world applications where the technological constrains strictly compromise the mathematical theoretical models. We demonstrate that the number of communication links needed to assure near 100 % network connectivity, is in fact, impractical in nowadays applications