## 2 Related Work  
Most of the energy consumption in a WSN derives from the data transmission, and lots of research shows that the network can better support node movement, improve network coverage and extend the network lifetime by using some form of clustering technology [7]. The use of clustering technology was first put forward in WSNs with the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol [8]. In the algorithm, the cluster head is elected by the circulation mode, and every round is divided into two parts, which are cluster formation and stable operation. In the cluster formation stage, the sensor nodes in the monitoring area randomly generate a number within the range of \([0,1]\), and if the number is less than the threshold \(T(n)\), then the sensor node will be selected as the cluster head. The cluster head broadcasts the information and the sensor nodes choose their clusters according to the strength of the received signal, and finally the clustering for the monitoring area is completed. In the stable operation stage, the cluster head will deal with the information from sensor nodes and send the messages to the base station, and then start the next round of clustering until the energy is exhausted. In this method, the sensor nodes do not transmit data in multi-hops, and this can decrease the energy consumption in data transmission, but the selection of cluster heads is random, so it cannot realize uniform clustering, and it does not consider the factor of energy of the nodes, which may cause the early death of cluster heads. Actually, the cluster head selection is just suitable for static networks, and it does not apply to the movable nodes in MWSNs. Many researchers have proposed numerous improvements for LEACH, like Low-Energy Adaptive Clustering Hierarchy for Mobile nodes (LEACH-M) [9], which is an improved topology algorithm for node mobility. In the cluster head selection, it considers the mobility of the nodes and uses a wake mechanism based on a Time Division Multiple Address (TDMA) schedule. This allows the nodes to remain dormant in the TDMA time slot which is not theirs, so it can decrease the energy consumption. However the waking mechanism is complex, and it needs at least three TDMA frames for the mobile nodes to be rediscovered by the cluster head and establish a communication link with the cluster head. This may cause some parts of the transmitted data to be lost. The Adaptive LEACH-Mobile (ALM) algorithm [10] introduces the mobility metric on the base of LEACH-M, which considers both the mobility and energy consumption, and it improves the wake mechanism. When the sensor nodes do not receive data from the cluster head for two continuous TDMA time slots, they will automatically increase the communication range. This method maintains the links between sensor nodes and cluster head by increasing the communication range, so it will increase relatively the communication overhead of cluster heads. When the clustering is stable, it is necessary to consider the safe establishment of communication links between the sensor nodes and cluster head, which is a key step for data collection and transmission. Currently, there are not many research achievements on network security with changing topology, and most of these research achievements are based on static networks. Reference [11] proposed a new key management scheme for mobile heterogeneous WSNs based on asymmetric key pre-distribution and hash functions. It uses a seed key and hash function to realize the authentication of a mobile cluster head, but it only permits cluster heads move, and all the member nodes are static. Aiming at addressing the disadvantages of the Localized Encryption and Authentication Protocol (LEAP) [12] and Opaque Transitory Master Key (OTMK) [13], reference [14] helped the mobile nodes join the network safely in a mobile scenario by establishing pair keys and local broadcast keys with the new neighbor nodes.