Threshold Key-Establishment in Distributed Sensor Networks Using a Multivariate Scheme

Key establishment in sensor networks is not a trivial task because of the scale of the network and resource limitations of the sensor nodes. Unfortunately, the previous solutions in general networks are inapplicable to sensor networks. In this paper, we propose a novel multivariate key pre-distribution scheme (MKPS) that simultaneously provides many nice features of previous schemes without any disadvantages such as additional memory. These features include node-to-node authentication, network scalability, key compositeness, perfect secrecy up to the capture of a fraction of nodes, and network connectivity. In this scheme, every node is assigned a unique ID that is an n tuple of positive integers. Based on these IDs, the shares of multivariate polynomials are stored in the memory of every sensor node prior to their deployment. After the deployment, those nodes that are at the communication range of each other and their IDs are at the Hamming distance of one from each other can establish n − 1 common keys. The secret key between such nodes is a symmetric combination of all these n − 1 keys. Hence, the proposed MKPS is in some sense an (n − 1)-composite scheme. We will show that this feature significantly improves the security of MKPS over previous schemes. The proposed method is in the category of threshold schemes, i.e., it remains perfectly secure up to the capture of a certain fraction of sensor nodes. For example, in some instances, the scheme remains almost perfectly secure until 90% of the nodes are captured. We will also propose a procedure to choose an optimal dimension n. In contrast to previous schemes, the design criteria in our scheme are both security and network connectivity. Hence, the proposed scheme provides an opportunity to the designer to adjust the network properties according to the desired application.