## 1 Introduction  
Wireless Sensor Networks (WSN) are a collection of sensor nodes spatially dispersed to sense and collect data from the environment and collaborate with each other to deliver their readings to a base station (BS) for statistical analysis or merely data collection [1]. Sensor nodes are unattended devices that are severely constrained in terms of processing power, memory size, and energy levels; and thus security and energy consumption are major concerns for any WSN implementation or application. Several security attacks can be launched on a WSN to disrupt its routing scheme, to broadcast false or harmful information, to drain the node battery and thus decrease the network lifetime, among others [2]. There are several methods to detect malicious or misbehaving nodes, and to provide secure routing, which is another critical issue in WSNs, while accounting for energy consumption and hence lengthening the network lifetime. Among these are reputation-based and trust-based methods [3], location isolation [4], and behavior-based techniques [5]. For the proper functioning of these schemes, a secure and efficient authentication scheme is required to validate nodes to each other and to the base station with minimal processing power and data transmission overhead. Note that the term misbehavior or misbehaving node is used in this paper to reflect a node that willingly or unwillingly, due to a malfunction or defect, interrupts or abuses the functionality of the network in any way possible, except sending malicious packets. Misbehaviors include manipulating protocol-specific parameters, sending through improper neighbors, declaring erroneous data, or even broadcasting or dropping packets. In this paper, we present a CENTRalized Trust-based Efficient Routing protocol with an appropriate Authentication scheme (CENTERA) for WSNs. Utilizing the centralized approach, CENTERA, improving on our previous model CENTER [6], uses the more powerful and more knowledgeable BS to provide a more trusted network environment with more efficient and secure routing paths, while decreasing the load on the severely-constrained sensor nodes. In CENTERA, the sink BS periodically gathers minimal observations from the individual nodes about the number of packets sent through neighbors and then, it performs several checks and calculations to have a better and more accurate view of the network. The BS approximates the battery life of every node based on its presumed activity and calculates several quality metrics for every node, namely the maliciousness, cooperation, and competence levels. Then, the BS evaluates two trust values for each node--namely Data Trust and Forwarding Trust. Following the quality metrics calculations, the BS is able to detect several types of bad nodes: a malicious node sending false or illogical information, a non-cooperative node not reliably forwarding the packets of other nodes, or an incompetent node unable to correctly deliver packets to the sink BS, or a malfunctioned/malicious node broadcasting packets. Those \"bad\" nodes are isolated for a period of time that depends on their history. Thus the sink BS increments the bad or probation level of every node with repeated bad behavior, whereas decrements this level for repeated \"good\" behavior. Finally, the BS uses an efficient method to disseminate updated routing information to all the network nodes such that each node knows its uplink nodes to forward their packets to the BS, and its next hop downlink node to forward its own packets through it. CENTERA provides a trust-based routing protocol while accounting for the severely-constrained sensor nodes batteries and preserving energy in the presence of misbehaving nodes by detecting and isolating them.