## 1 Introduction  
In most of the traditional key management schemes for wireless sensor network, the sink node is fixed, which may cause lots of data storage and forwarding among the sensor nodes, and the keys may have higher risks of being captured [1; 2; 3; 4]. Sometimes, with the random deployment, there exist some isolated sensor nodes which cannot communicate with any sink node. Thus, many more sink nodes are usually needed to guarantee reliable data collection, which increases the system cost and energy consumption [5; 6]. Mobile Sink (MS) nodes with abundant resources can move within the range of the whole network, which not only reduces the amount of data storage and forwarding, but also decreases the energy consumption and network communication overhead, and meanwhile, it can effectively avoid the appearance of isolated nodes [7; 8; 9; 10]. There are many constraints in wireless sensor networks because of the lack of energy resources, limited communication range, low transmission power and poor computing abilities [11; 12; 13; 14; 15; 16]. Thus, sometimes nodes cannot use an asymmetric key encryption mechanism during communications, or they cannot get the geographic information after node deployment, or the storage capacity to store more information is limited, and so on. MS nodes will persistently broadcast their own identities on the move, and sensor node within communication range will send data stored in itself to the MS node after receiving the handshaking messages. In case the nodes are captured by an adversary, the adversary can acquire the information transmitted in the network by attacks including forgery, modification, and replay. They can prevent the MS node from receiving date from the sensor nodes, or even reduce the lifetime of the network as well.  
Existing key management schemes proposed for WSNs cannot solve the problems mentioned above well. First, most schemes are designed for networks with fixed sink nodes, which is not applicable for future application environments. Secondly, the generation and establishment of the keys mostly depend on a single encryption method, so the keys are easily captured and identified, which leads to lower network security. In addition, research on path key establishment and maintenance based on multi-hop links is insufficient for the current key management schemes. Thus in most cases, when the system security is improved, at the same time the connectivity of the network will be decreased.  
This paper proposes a hybrid key management scheme (PPBR scheme) based on a polynomial pool-based key pre-distribution and basic random key pre-distribution. The scheme combines the advantages of the two protocols, utilizes the \(t\)-degree property of polynomials and improves the security of the traditional basic random key pre-distribution scheme. It makes the adversary need to capture a large number of nodes in the network to decode the keys, since it has to possess the polynomial coefficients and random keys at the same time in order to capture the uncompromised nodes. Therefore, the scheme improves the security of the network and enhances the network's ability to resist capture attacks. Furthermore, the proposed scheme puts forward a path key generation method based on the tree-based path key establishment, which regards the MS node as the root in the range of communication. This can deal with the problem of higher nodes' storage capacity requirements and poor network connectivity. Simulation and analysis prove that the proposed method has better storage efficiency, connectivity and resilience for WSNs with MS compared to other widely used key management schemes.  
The rest of this article is organized as follows: in Section 2, some background knowledge and related work on key management schemes are introduced. Then, in Section 3, we describe the PPBR key management scheme in detail. Section 4 presents the simulation and results analysis, and finally we conclude the article in Section 5.