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Tham khảo tài liệu 'sustainable wireless sensor networks part 20', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Group Key Managements in Wireless Sensor Networks 561 Fig. 10. a afiY-tree and b the corresponding TKH key tree structure. b where m is the size of a unit rekeying message Ka kb 2 m for Ka Kb kc . It means that we need 25 transmissions and 31 receptions of a unit rekeying messages to update ST1 when node 3 is revoked. 5. Analysis of the Total Rekeying Cost In this section we analyze and compare the total rekeying costs of LKH OKD and TKH in multi-hop WSN environments. For the analysis we need to derive the average number of rekeying messages and the communication costs. The former is derived in Section 4.3 by employing the bins-and-balls problem. To calculate the latter we model a typical WSN topology as afiY-tree in Section 4.1. Both results are used to derive the total rekeying costs in Section 4.4 while the communication costs of the routing tree maintenance are calculated in Section 4.2. 5.1 afiY-tree Topology Model For the analysis of the communication cost we model a sensor network topology by using afiY-tree model. In the afiY-tree there are a subtree branches from the sink and each subtree has ft sibling sets and each sibling set has y sibling nodes. The resulting topology and the corresponding TKH key tree structure is depicted in Figure 10. a and b respectively. The total number of sensor nodes excluding a sink is N a fiY 1 and each subtree has fiY 1 nodes. Among N sensor nodes aft nodes are non-leaf parents and the rest a fiY 1 aft nodes are leaf children nodes. During the routing tree repair in afiY-tree we assume that a revoked non-leaf parent node is replaced by one of its siblings and a revoked subroot node is replaced by one of its children. 562 Sustainable Wireless Sensor Networks 5.2 Cost of Routing Tree Maintenance When there are N nodes in a network each node can be identified by using log2 N bits and the hop count value ranging from 0 to fi can be identified by log2 fi bits. Then the size of the CA message ImcAI and the PCR message mPCRI are .
