## 1 Introduction  
Recent advances in wireless communications and electronics have enabled the development of low-cost, low-power and multi-functional sensors that are small in size and communicate over short distances [1]. A wireless sensor network (WSN) is composed of a large number of small sensors with constrained energy, limited computation, communication range, and unchangeable battery power. Sensor nodes can be distributed in an outdoor environment to collect sensing data and forward it to base station via wireless channel [2-4]. Applications of WSNs range from indoor applications such as smart homes and health monitoring in a hospital to outdoor applications such as highway traffic monitoring, combat field surveillance, security and disaster management [5-8].  
In many applications, WSNs are deployed in outdoor environments. Consequently, they are vulnerable to false data injection attacks [9] in which an adversary inject false sensing reports into the network, through compromised nodes, with the goal of deceiving the base station or draining the constrained energy of the nodes [10]. The statistical en-route filtering scheme (SEF) [9] can filter out forged reports during the forwarding process. In the scheme, for an event, sensing nodes collaboratively generate a report which contains message authentication codes (MACs) so that each MAC is generated from a node using its symmetric keys and represents its agreement on the report [11]. As a report is forwarded towards the base station over multiple hops, each forwarding node verifies the MACs carried in the report, checking if it has any of the keys used to generate those MACs. If it does not have any of those keys, the report is forwarded without verification. Therefore, the detection power of the SEF is affected considerably by the choice of routing path [12].  
The path selection method (PSM) [12] was proposed to improve the detection power of SEF. In PSM sensor nodes evaluate the detection power of each incoming path from the base station and elect the most secure path for data transmission against false data injection attacks. In order to evaluate the path, each sensor node inserts additional information about filtering keys into a control message. However, such path selection based on the security power would make the most secure paths undergo heavy traffic so that the nodes along the paths would consume more energy resources. That is, the limited energy resources of the network would be spent in an unbalanced fashion, which could cause the decrease of the overall network lifetime.  
In this paper, we propose a path renewal method (PRM) to prolong a network lifetime. While the energy consumption of each sensor node is basically proportional to data transmissions, events do not uniformly occur on a sensor field. Thus, we cannot predict the energy consumption patterns in the network. In the paper, we represent a WSN as a digraph (directed graph), and define a communication traffic model. Based on the model, we propose a fitness function for the renewal of routing paths. To show the effectiveness, we have compared the proposed method with the two existing methods, SEF and PSM, in terms of balanced energy consumption and reliability of data transmission by providing simulation results.  
The remainder of the paper is organized as follows: Section 2 briefly explains the related works and the motivations of this work. Sections 3, 4, and 5 present a network model, the proposed path renewal method, and an evaluation function, respectively. Section 6 gives simulation results. Finally, conclusions and future works are covered in Section 7.