Due to the nature of wireless transmission, communication in wireless mesh networks (WMNs) is vulnerable to many adversarial activities including eavesdropping. Pairwise key establishment is one of the fundamental issues in securing WMNs. This paper presents a new matrix based pairwise key establishment scheme. Mesh client in our scheme only needs to prestore a key seed, which can be used to generate a column of secret matrix. It can establish pairwise keys with other clients after mesh routers broadcast public matrices. Our scheme is motivated by the fact that in WMNs, mesh routers are more powerful than mesh clients, both in computation and communication. Besides, we employ the pre deployment knowledge to reduce the computational cost of mesh clients. Security and complexity analysis show that the new scheme possesses several desirable features: 1) neighbor mesh clients can directly establish pairwise keys; 2) the new scheme is updatable, scalable, and robust against node capture attacks; and 3) communication and storage costs at mesh clients are significantly reduced. INDEX TERMS Pairwise key, matrix, deployment knowledge, wireless mesh networks, wireless sensor networks. et al.: Matrix-Based Pairwise Key Establishment Scheme FIGURE 1. Network architecture: Infrastructure/backbone WMNs presented in Akyildiz et at. scheme [2]. legitimate nodes, and even capture nodes in WMNs. Many security mechanisms have been proposed to countermeasure potential attacks in WMNs, and a non-exhaustive list includes location technology [3], [4], intrusion detection technology [5], [6], secure routing technology [7], [8] and key management technology [9]-[23].As a fundamental problem, key management has been both extensively and intensively studied in CPS and other similar situations. Taking wireless sensor networks (which are often integrated with WMNs) for example, asymmetric key cryptographic algorithms are generally considered infeasible for computing and communicating between energyconstrained sensor nodes [9]. Though such a constraint has been partially alleviated with the development of modern technology, it is still a fact that sensor nodes are not able to afford frequent asymmetric cryptographic operations. Other mechanisms, such as Kerberos, cannot be directly applied to sensor networks due to the lack of trusted infrastructure [10].According to its characteristics, key management can be classified by Self-enforcing Schemes, Arbitrated Keying Schemes and Key Pre-distribution Schemes [11], where Key Pre-distribution Schemes (hereinafter, KPS) is the focus of this paper. In KPS, a key management authority (also known as key distribution center) loads keys into nodes prior to deployment, then neighbor nodes can establish secure communication keys using their pre-loaded keys. Arguably the most straightforward KPS is to equip all nodes with a common master key, and any node can negotiate a session key with each other using the master key after deployment. However, an inherent weakness of this approach is that all communicatio...