An Effective Group-Based Key Establishment Scheme for Large-Scale Wireless Sensor Networks using Bivariate Polynomials

Key establishment in sensor networks is a challenging problem because of the resource limitations of the sensors. Due to resource constraints as well as vulnerable to physical capture of the sensor nodes, the traditional public-key routines are not feasible to apply in most sensor network architectures. Several symmetric key establishment mechanisms are proposed in the literature to establish symmetric keys between communicating sensor nodes for their secret communications in a sensor network, but most of them are not scalable. In this paper, we propose a deterministic group-based key pre-distribution scheme based on a hierarchical wireless sensor networks using bivariate polynomials over a finite field. This scheme guarantees that a direct key is always established between any two neighbor sensors in any deployment group. Our proposed scheme also guarantees that no matter how many sensor nodes are compromised, the non-compromised nodes can still communicate with $100\%$ secrecy, i.e., our scheme is always unconditionally secure against node capture attacks. Moreover, it provides significantly better trade-off between communication overhead, network connectivity and security against node capture compared to the existing key pre-distribution schemes. Finally, it also supports dynamic node addition after the initial deployment of the nodes in the network.