## 1 Introduction  
The Internet of Things (IoT) has drawn attention from both industry and academic fields for years due to its advantages, such as efficiency and providing more secure communication environments. Among the various applications of IoT, online education has emerged as a significant application of Mobile IoT (MIoT). IoT provides the necessary technological support and infrastructure for online education to be conducted on mobile devices and over the Internet. English, being a globally universal language, is widely learned and considered a core subject in schools across most countries. Consequently, the application of MIoT in online English education has rapidly become an important method and primary tool for individual learning and communication. This is a novel education model that puts students at the center and relies on software platforms to deliver personalized learning experiences [1, 2]. Compared to traditional offline classroom education, online English education offers advantages such as higher efficiency [3, 4] and freedom from geographical constraints [5]. Here, online learning devices (OLDs) have the capability to communicate with other devices and infrastructure, such as roadside units in certain models, enablingaccess to the MIoT [6]. Thus, OLDs are allowed to report information and emergencies, which will be used to improve the quality of services [7; 8]. However, if OLDs are allowed to broadcast messages without any verification or limitation, the communication mechanism will become vulnerable and easy to compromise [9; 10; 11]. For example, if messages sent in MIoT are not signed with an online learning device's unique identities, then a malicious user can broadcast fraud messages or sign them with fabricated identities to bypass a weak system. To solve problems in secure communication, some studies have been dedicated to designing privacy-preserving authentication schemes [12; 13; 14]. However, due to the feature of changing topology, it is hard to balance efficiency and security in conventional MIoT. Then, a brand-new technology came into researchers' sights. Software-defined network (SDN) is an innovative technology that embodies a network structure distinct from traditional networks [15; 16]. In SDN, controlling and forwarding are separated and work in different layers [17; 18]. The control plane represents the centralized point as the brain of the whole architecture [19]. The data plane communicates with the control plane via southbound interfaces. It is mainly responsible for querying controllers for forwarding tables and forward packets. Using the programmability and scalability, the combination of VANETs and SDN offers a new approach to solve inherent problems in VANETs. Software-defined MIoT has been proposed for years and there have been many research efforts demonstrating the advantages of this new combination [20; 21]. Meanwhile, some schemes are proposed to cope with problems in quality of services (QoS) [22], heterogeneous network accessing [23], factory managing [24; 25] and so many others in different fields by combining with SDN [26]. Inspired by [27], we design a scheme that uses multicast technology to solve the driving direction and secure communication problems in software-defined MIoT. In traditional MIoT, OLDs mainly rely on broadcasting each other to receive network condition information, which lacks timeliness and overall planning [28; 29; 30]. By introducing multicast, the controller is allowed to manage OLDs and balance network throughputs more efficiently. In addition, some technology used not to be suitable for MIoT, like Steiner Tree, which is computation intense and scale sensitive [27]. But with SDN introduced, those algorithms can provide new methods for the development of MIoT [31; 32]. Thus, we propose a new secure communicating and device movement path scheme in this paper. By using multicast [33] and privacy-preserving authentication technologies, we aim to design a secure and efficient model in software-defined MIoT.