## 2 Related Works
### Five Types of Key Management Protocols  
(1) Random Key Pre-distribution Protocol  
This protocol has three steps: key pre-distribution, key sharing, and key establishment. Before the deployment of any sensor node, m sets of keys are selected from a large key pool. The m keys form a key chain which is sent to each sensor node. One key is selected from among the nodes and is used to transmit data within the group. However, each sensor node must store m keys. [PERSON]'s method [9] used a global matrix pool to replace the global key pool. In the key pre-distribution phase, each node randomly selects several matrices from the global matrices pool. In this case, any two adjacent nodes have a row of elements from the same matrix that can establish a pair-wise key. In 2003, [PERSON] _et al._[10] proposed a random key transmission protocol. The random keys are transmitted between the sensor nodes such that any two nodes can establish a secure communication channel. The shortcoming of this method is that each sensor node must store more than three sets of keys. In order to enhance security, the number of keys must be increased. However, an increase in the number of keys increases the load of the sensor nodes. Power consumption is also increased. (2) Group-based Key Pre-distribution Protocol  
The Group-based Key Pre-distribution Protocol is used to divide the area where the nodes are into several sections. Nodes are placed or dropped into a pre-defined area such that the sensor nodes have a higher probability of good communication. [PERSON] and [PERSON] [11] proposed a paired key protocol which uses a polynomial key pool and pre-distribution of a grid key. This protocol has higher elasticity in catch and attack. It also has superior sensor node communication. However, the key management algorithm is relatively complicated. More time is required to generate a key. (3) Hierarchical Key Pre-distribution Protocol  
The hierarchical key pre-distribution protocol's elements include a base station, a cluster header, and sensor nodes. Before deployment, each cluster header stores keys. After deployment, the nodes in a network will exchange identification codes. At the same time, that the identification codes are being exchanged, the cluster header will be informed of the identification codes of the sensor nodes. The sensor nodes in the whole network can then communicate with each other. However, if one of the nodes is caught, the information transmitted between the cluster header and the sensor nodes can be easily observed by an enemy. Therefore, the cluster header must increase the number of keys toimprove security. The resources of the sensor nodes are limited, however, making an increase in the number of keys impracticable. [PERSON] and [PERSON] [12] proposed an improved key distribution mechanism (IKDM) which makes use of bivariate polynomials to develop a secure wireless sensor network. In this scheme, each gateway does not directly store the gateway keys of the nodes. Instead, each gateway stores bivariate polynomial functions. After deployment, a node sends its identification code and the gateway numbers to the nearest gateway. Then the gateway receiving the data asks other gateways to obtain sub-keys. The nearest gateway can then compute the gateway keys of its neighboring nodes from these sub-keys. Other similar schemes, such as the one by [PERSON] _et al_. [13], are also based on the Identity-Based symmetric keying scheme. (4) Direct Communication Protocol  
In direct communication in WSNs [14,15], all sensor nodes both gather data and then as well as transmit the collected data directly to the base station. This is extremely energy inefficient, since path loss in wireless systems is proportional to \(R^{n}\), where \(R\) is the distance between a sensor node and the base station, and \(n\) typically ranges between 2 and 4. Therefore, because of energy inefficiency, long distance transmission in direct communication consumes more power.