A key distribution technique for wireless sensor networks using spanning trees

Abstract

Protocols for encrypting communications in wireless sensor networks have rarely been addressed from a classical network optimization perspective. An underlying procedure of such protocols, known as key distribution, involves assigning cryptographic keys to sensors, which are then used to encrypt and decrypt transmitted data. In context of maximizing communications security objectives, the combinatorial nature of assigning keys to sensors with limited memory capacities exhibits properties conducive to developing methods for finding optimal key distributions. This work focuses on the q-Composite key distribution/assignment protocol, which requires that two sensors share at least q common keys to securely exchange data. As a means of reducing the likelihood of large-scale information breaches if a small number of keys are compromised, a security objective of maximizing the number of non-redundant (unique) keys assigned to the sensors is considered. It is demonstrated that node (sensor) degrees in a spanning tree, along with their memory capacities, can be used to exactly determine the maximum possible number of non-redundant keys assigned. Leveraging on these properties, our method reduces the problem of assigning a maximum number of keys to that of finding a degree-bounded spanning tree in a network. A polynomial time solution algorithm along with a linear time algorithm for assigning a maximum number of unique keys is introduced. Broadly, the proposed method provides a novel approach for designing, analyzing, or identifying secure key distributions in large-scale networks by using properties of the underlying graphs.