Wireless sensor networks (WSNs) are distributed collections of sensors with limited capabilities for computations and wireless communications. It is envisioned that such networks will be deployed in hostile environments where communications are

monitored, and nodes are subject to capture and surreptitious use by an adversary. Thus, cryptographic protection will be needed to ensure secure communications, as well as to support sensor-capture detection, key revocation and sensor disabling. Recently, random key predistribution schemes have been introduced to address these issues, and they are by now a widely accepted solution for establishing security in WSNs. The main goal of the dissertation is to investigate and compare two popular random

key predistribution schemes, namely the Eschenauer-Gligor (EG) scheme and the pairwise key distribution scheme of Chan, Perrig and Song. We investigate both schemes through their induced random graph models and develop scaling laws that corresponds to desirable network properties, e.g., absence of secure nodes that are

isolated, secure connectivity, resiliency against attacks, scalability, and low memory load - We obtain conditions on the scheme parameters so that these properties occur with high probability as the number of nodes becomes large. We then compare these

two schemes explaining their relative advantages and disadvantages, as well as their feasibility for several WSN applications. In the process, we first focus on the "full visibility" case, where sensors are all within communication range of each other. This assumption naturally leads to studying the random graph models induced by the aforementioned key distribution schemes,

namely the random key graph and the random pairwise graph, respectively. In a second step, we remove the assumption of full visibility by integrating a wireless communication model with the random graph models induced under full visibility. We study the

connectivity of WSNs under this new model and obtain conditions (for both schemes) that lead to the secure connectivity of the