## 3 The PPBR Key Management Scheme  
### Network Model and Hypothesis  
This article assumes that sensor nodes can temporarily store the sensed data, all the data is managed by the network server in the base station, and MS node is dispatched to retrieve and collect the data regularly. In marine environment monitoring, a surveillance ship can be regarded as a MS which can converge the monitoring data. In battlefield reconnaissance, a mobile communication vehicle can also be regarded as a MS which can collect the battlefield information from the nodes of sensor networks in the future informatization war. The MS contains the sole _ID_ identifier of the whole network, and it has more abundant computation, storage, and energy resources than ordinary sensor nodes. However, the traditional scheme with fixed sink nodes, usually requires a large number of sink nodes distributed in the network. In addition, the heterogeneity on storage space, energy and computational ability between fixed sink nodes and the ordinary sensor nodes is not so very different from the heterogeneity between a MS node and ordinary sensor nodes. A schematic diagram of a wireless sensor network with MS is shown in Figure 1.  
There are mainly three kinds of moving patterns for sink nodes, which includes random route movement [31], fixed route movement [32], and controlled route movement [33; 34]. In this article, the sink node moves among fixed sensor nodes, and collects the monitoring data uploaded by the ordinary sensor nodes within their communication range, and the sensor nodes which are out of the communication range will be in the sleep mode. In fact, when the MS broadcasts the information within its communication range, it does not need to know whether the sensor node \(S_{i}\) is its neighbor node or not. Many sensor nodes in the network are limited in storage space, communication distance and energy supplies, and they will remain in a static state after deployment. Nevertheless, the MS node has relatively more abundant resources and is equipped with tamper-proof hardware and safety detection equipment, so it is reasonable to assume that generally a MS node would not be captured. This kind of network system can implement more complex data fusion, data access, data transmission, data forwarding and routing service by using a MS with its abundant resources. This manner can greatly reduce the communication overhead, and energy consumption in the ordinary nodes and effectively avoid generating isolated nodes in the network.  
Figure 1: A schematic diagram of a wireless sensor network with a mobile sink.  
The proposed PPBR scheme includes the initialization phase, direct key establishment, path key establishment, the key revocation, update, and the joining in of new nodes. The process of the scheme is shown in Figure 2, and the main steps of key establishment are shown in Figure 3.  
The proposed PPBR key management scheme is a combination of the Polynomial Pool-based key predistribution and Basic Random key predistribution scheme. The scheme combines the advantages of  
Figure 3: The steps of key establishment for the PPBR scheme.  
Figure 2: The main process of the PPBR scheme.  
the two protocols, utilizes the \(t\)-degree property of polynomial to improve the security of the traditional random key predistribution scheme. In detail, we use the Polynomial Pool-based key predistribution scheme to create the polynomial pool F which includes \(S_{p}\)\(t\)-degree bivariate polynomials and use the Basic Random key pre-distribution scheme to create the key pool K which contains \(S_{k}\) keys. Regardless of the establishments of direct session keys or path keys, they are all need to be calculated by the hash function using shared keys and shared polynomials. It makes the adversary need to capture a large number of nodes in the network to decode the keys, since it has to compromise the polynomial coefficients and random keys at the same time in order to capture the uncompromised nodes.