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.

In this section, we review the two existing methods—SEF and PSM—and then explain the motivations of this paper.

A wireless sensor network is composed of a base station and large number of sensor nodes. The network can be represented as a digraph (or directed graph) G. The graph G is defined as follows: (1) G = ( V , E ) where , V = { v 1 , v 2 , … , v n } E = { e 1 , e 2 , … , e m } E ⊂ V × V

In Equation (1), V is a set of vertices and each vertex denotes a sensor node. E is a set of edges and each edge denotes a link between vertices (i.e., sensor nodes). For two arbitrary integers i and j, where i and j are less than n, e_ij (∈E) indicates a communication link between vertex v_i and v_j (v_i,v_j ∈ E). An in-degree (and out-degree) is the number of inward (and outward) graph edges from a given graph vertex in the directed graph. Figure 1 shows the in-degree and out-degree.

In the figure, the in-degree and out-degree of v₀ are 3 and 1, respectively. We denote that v₀ is the super-node for nodes v₁, v₂ and v₃. Also, nodes v₁, v₂ and v₃ are sub-nodes of v₀, respectively. Additionally, the number of the in-degree can be represented as an amount of communications.

In this paper, we propose a path renewal method to uniformly consume energy resources. In our proposal, each sensor node can know the amount of communications and remaining energy. In the figure, if the remaining energy of v₀ is less than a threshold value, one of the sub-nodes searches a new super-node. Our proposal is briefly illustrated in the next section.

In our network model, routing paths are established by the flooding of a control message. This fashion is commonly used in most routing protocols at the initial establishment of routing path. Similar to PSM, a control message includes information on the partition of the keys (PIK) and on hop counts from the base station (HC). Also, each node can know its own in-degree.

Figure 2 shows a propagation of a flooding message. In the figure, the node that received the message inserts its PIK to the message and forwards it to the next hop (toward terminals). Suppose N₂ receives the control message including PIK of 1 and 7 from N₁. When N₂ sends the message to the next node, it inserts its PIK to the message. Here, given N₁, N_1.PIK(5) implies that N₁ stores PIK that is 5. N₃ does not need to insert the PIK to the message since PIK in the message already has PIK(7).

After the paths are established, all nodes store their in-degree and the list of the sub-nodes by elapsed time. Each node manages the list. The list is comprised of IDs of sub-nodes and the number of data transmissions of each sub-node. For an arbitrary super-node N_sup and three sub-nodes N_sub.1, N_sub.2 and N_sub.3, the process of path renewal is as follows:

In the table, TE, EM, and FM are threshold energy, eviction message, and fare message, respectively. Let N_sub.3 have the highest number of the transmissions in the list. If the remaining energy of N_sup is less than TE, N_sup sends EM to N_sub.3. EM includes the fitness value of N_sup. N_sub.3 finds a new super-node in the neighboring nodes. Each of the neighboring nodes sends its own fitness value to N_sub.3. If N_sub.3 finds a new super-node that has the highest fitness value, N_sub.3 sends FM to N_sup and migrates to other super-node. After N_sup receives the RM from N_sub.3, N_sup removes N_sub.3 in the list.

To elect a new super-node, we define an evaluation function by considering HC, ID, EC and diversity of PIK. The evaluation function is defined as follows: (2) F ( n ) = EC ( n ) + α ⋅ DPIK ( n )

In Equation (2), the evaluation function consists of EC and DPIK. EC is energy consumption and DPIK is a diversity of PIK. Alpha is a security weight factor determined by the user. So, for an arbitrary sensor node n, EC and DPIK are defined as follows: (3) EC ( n ) = HC + ID + RE = 1 n HC ⋅ E t + ( n HC − 1 ) ⋅ E r + n ID ⋅ ( E t + E r ) + n RE DPIK ( n ) = | PKI ( n ) | where , E t  is energy consuption by a transmission . E r    is energy consumption by receiving data . | PKI ( n ) |  is a number of elements of  PKI ( n )

In Equation (3), n_HC, n_ID and n_RE are a hop count, in-degree and remaining energy of the node n respectively. It is clear that energy consumption is affected by hop count and in-degree. So, we can represent energy consumption of the node with consideration of n_HC and n_ID. DPIK implies a diversity of partition information of key. In the equation, DPIK is a number of elements of PIK.

A simulation was performed to compare the proposed PRM method with the existing SEF and PSM ones. A performance criterion is balanced energy consumption and success rate of data transmission. We also analyze the detection power of proposed method. In the simulation, the network consists of 1,000 nodes spread over a territory whose size is 100 ×120 m. The nodes are randomly deployed in the territory and the base station is placed at the end of the territory. Each sensor node takes 16.56 μJ/12.5 μJ to transmit/receive a byte, and each MAC generation consumes 15 μJ. The size of original report and of MAC is 24 and 1 bytes, respectively. There are 1,000 keys in the key pool, which is divided into 10 partitions.

Figure 3 shows a filtering rate for false reports with a security weight in case that the number of forged MACs per a report is 1, 4, 10 and 16. For the same network topology, routing paths on SEF, PSM and PRM are established, respectively. Then we generate false reports in the network. Assigned keys in each node are randomly generated with various seed values from 0 to 9. We calculate an average dropping rate for the false report.

In the figure, the proposed method is better than SEF but less efficient than PSM in terms of dropping ratio. The figure illustrates a similar performance for PRM and PSM. In PSM, each node chooses a super-node by considering information of keys on incoming path from the base station. In PRM, each node only has partition information of nodes within five hop counts, so the performance of the proposed method is a little less efficient than PSM.

Figure 4 shows an average number of traveled nodes to filter the false report. The reports are generated with 1, 4, 10, 16 forged MACs. The number of traveled nodes in the original SEF approach is the highest since routing paths are chosen with consideration of only hop counts. Though PSM detects the false reports earlier than PRM, the performance gap is acceptable.

Figure 5 shows the number of alive node that can send a data to next node or base station in SEF, PSM and PRM. We generate false reports that include eight forged MACs and inject the report into the network.

When the routing paths are established, each node considers hop counts or hop counts and partition information of keys. Therefore, the path would make the most secure paths in heavy traffic so that the nodes along the paths would consume more energy resources. Also, the super-node that has high in-degree (i.e., many sub-nodes) would consume more energy resources. That is, the communication traffic of the super-node is more than others that have a low in-degree and the node should be consumes much energy than others. In other hand, PRM considers communication traffic when a sub-node selects a super-node. For these reasons, the network life time of PRM is better than that of either SEF and PSM.

There are many security issues including false data injection attacks in WSNs. SEF [9] is the first solution that can alleviate the impacts of the attacks. While a sensing report is being forwarded toward the base station, the report is verified by the forwarding nodes. PSM [12] can enhance the detection power of SEF. Every control message stores the information on the filtering keys of the nodes it traveled on, when paths are established by flooding. A sensor node has an evaluation function to choose the most secure path based on the information.

In this paper, we proposed a path renewal method to provide WSNs with load balancing. A network is represented as a digraph and a communication traffic model for the network is proposed. Base on the model, an evaluation function to choose a new super-node is defined. The effectiveness of the propose method is shown with the simulation results. As future works, some AI algorithms will be applied in order to find further optimal solutions.