g., smart homes, healthcare, power plants, homeland security, smart buildings, etc.). In a sensor network, numbers of wireless sensors collect and (partially) process the application raw data anytime and wirelessly forward the collected data through relay nodes to anywhere (e.g., a remote server). In practice, a real WSN application consists of heterogeneous sensor nodes (i.e., low-capacity nodes and high-capacity nodes) [1�C7]. A low-capacity node, i.e., L-node, is a resource-constrained node (e.g., Telos [8], MicaZ [9], etc.) that has low bandwidth, less computation power, less memory, and low battery power [3]. A high-capacity node, i.e., H-node, is a much more resource-rich node (e.g., stargate node [10]) that has high transmission range and directional antenna, more computation power and memory.

Recently, many researchers have shown the heterogeneous sensor networks are very suitable for real-time applications, and have better performance, reliability, scalability, transparency, load-balancing, network life-time, and cost-efficiency [11�C15] etc. Thus, heterogeneous sensor networks are more efficient and practical in real-time applications.The deployment of heterogeneous WSNs promises reliable data transmission, scalability, load-balancing and application efficiency [12�C15]; however, it bring a plethora of security related issues (such as mutual authentication and session-key establishment, confidentiality, and message freshness) that must be introduced at the application design time. The resource-hungry sensor nodes are deployed in open environments, where they are susceptible to attacks by global adversaries using compromised nodes.

Furthermore, there is no denying that wireless channels are more vulnerable than wired networks. In a mission-critical application, if the technology Batimastat fails due to the lack of strong and adequate security then it will affect (people’s) day-to-day life or damage its long-term application’s viability. Therefore, to protect WSNs from unauthorized access (e.g., the compromised nodes and/or the global adversary), all the sensor nodes in a network should perform the following: (i) mutual authentication to establish a common trust; (ii) two communicating nodes should establish a dynamic session key after performing the authentication; and (iii) all the wireless data must be secured (i.e., confidential) while in transit.

Thus, the mission-critical applications require an efficient and adaptive mutual authentication framework that can establish a common trust within the network and protect the network from unauthorized access and security threats.During the last decade, a number of security protocols have been proposed for homogeneous WSNs [16�C26], and for heterogeneous WSNs [27�C38]. Indeed, each protocol has advantages and disadvantages. However, in the existing researches (see Section 3), the focus is on unilateral authentication (i.e.