## 1 Introduction  
A WMN combines the advantages of wireless connections with the advantages of a mesh topology. A WMN provides better mobility, a lower cost of deployment, easier network expansion, and robust connections. A WMN is suitable for many applications, including broadband home networking, enterprise networking, building automation systems, and health and medical systems [1; 2]. Because the WMN was developed first for industrial purposes, each company had its own proprietary technology, and no industrial standard existed for WMNs. As a result, different WMN devices were incompatible with each other. In 2004, the Institute of Electrical and Electronics Engineering (IEEE) started the 802.11s Task Group (TG) to develop a standard for WMNs [3]. There are many standards related to WMN implementation, including 802.11s (Wi-Fi), 802.15.1 (wireless personal area network (WPAN) Bluetooth), 802.15.4 (WPAN ZigBee), and 802.16a (Worldwide Interoperability for Microwave Access (WiMAX)). The standard for 802.11s was finalized in July 2011 [3]. The widely deployed 802.11 wireless local area network (WLAN) infrastructure can be connected to a wireless sensor network (WSN) both to save on costs for deploying a new network and to utilize the advantages of 802.11 technologies [4]. A WMN can act as a scalable backbone by connecting separate sensor networks and even by connecting WMNs to a wired network. Initial research reported on the interconnection between WMN and WSN [5]. Subsequently, concerns over the power consumption related to 802.11 were also eliminated with power-efficient standards for the 802.11. Now, a sensor device is able to run for 5 to 10 years on a single AA battery [4]. Such a sensor device can then be used as a gateway for the WSN. The data rate for 802.11 is also very high compared to the common technologies used in a WSN, such as ZigBee, Bluetooth, or 802.15.4 [6]. IEEE 802.11s can be used to form the mesh topology or bridge networks for the WSN. 802.11s allows Wi-Fi devices to organize themselves and configure the network topology automatically. Wi-Fi devices with mesh functionality are referred to as mesh stations (or mesh STA). Mesh STAs that are far apart can still communicate with each other by utilizing wireless routing, where data packets are transmitted through intermediate mesh STAs. Hybrid Wireless Mesh Protocol (HWMP) is the default routing protocol for 802.11s, which must be implemented in layer 2. Thus, each 802.11s node is considered to be a layer 2 device. While the working principles and operations of HWMP have been defined in the drafted standard, the security features for the HWMP are not discussed in the drafted standard [7]. It is possible to treat the HWMP frames as normal management frames and to protect them with the same protocols as defined in 802.11w [8], but those protocols do not consider a multi-hopping environment. In this paper, we investigate how to protect routing messages, rather than data messages. In general, routing messages are sent to the immediate neighbors, at which point the neighbors process, possibly modify, and resend the messages. Therefore, some parts of these messages may be changed by the intermediate nodes during their propagation over the network. The most commonly changed parts of the routing message include the hop count and the metric of the path requested or provided. In terms of network security, we do not trust the intermediate node [9]. Thus, for the security of routing messages, the two types of message parts (_i.e._, the mutable and non-mutable fields) have different security requirements. The mutable fields (MFs) should be updated according to the routing rule as the message is propagated along the path. Each node requires a cryptographic scheme to detect illegal mutable information in the message. For the security of non-mutable fields (NMFs), the data integrity and data-origin authentication service for the field must be provided between the source and destination nodes.