## 1 Introduction  
Road accidents cause approximately 1.3 million fatalities and 20 to 50 million injuries globally [1]. Hence, the principal aim of intelligent transportation systems (ITSs) is to reduce the number of road accidents by offering transportation safety. One of the fundamental components of an ITS is to provide vehicular networks that connect vehicles, pedestrians, roadside devices, drivers, and passengers [1, 2]. The latest trend in the advent of wireless communication technologies is the application and development of fifth-generation (5G) cellular networks spurred by massive government investment in many regions [3, 4, 5]. A 5G network obtains a multiple-fold increase in speed compared with current fourth-generation (4G) networks due to the characteristic of 5G, increasing the mobile data per unit area by 1000 times and the transmission rate to up to 10 Gbps. Furthermore, 5G achieves a five times latency reduction and extends the battery life of devices tenfold, which opens up enormous possibilities for mobile ad hoc networks (MANET), especially for the Internet of vehicles (IOVs). For example, one type of vehicular ad hoc network (VANET) distribution relies on IOVs for inter-vehicle communication to share information with others through their on-board unit (OBU) in a wireless network environment. Vehicles can realize many types of infotainment and safety-related services by making use of the shared information [6]. VANET typically coexists with other networks, such as satellite, 2G/3G cellular, and long-term evolution (LTE). However, in VANET communications, these networks utilize different protocols and standards, which could lead to disjointed information interaction and inefficient data processing. For example, the literature [7; 8] has demonstrated that IEEE 802.11p and LTE standards do not effectively support latency and scalability for vehicular communications. Moreover, roadside units (RSUs) are usually required in these networks to participate in the authentication process, which increases the system's latency. Furthermore, a study [9] has shown that a compromised RSU leads to leakage of sensitive data stored in the RSU. Therefore, rendering the whole system exposed and insecure. Nevertheless, the advantages provided by the 5G mobile wireless system, such as wide-area coverage, high speed, and low latency, can make inter-vehicle communication in VANET more effective in terms of performance and cost. These 5G mobile wireless systems have a double-layer network: a macro and a device layer. The macro layer is responsible for the communication between terminal devices and the base station. On the other hand, the device layer, device-to-device (D2D) communication, is the crucial component of these 5G wireless systems, which realizes direct communication between terminal devices without involving or requiring additional infrastructure [10; 11]. Compared with the VANET architecture, 5G-enabled vehicular networks have longer communication ranges and can connect with more vehicles per base station. To the best of the authors' knowledge, this is the first password-guessing attack authentication scheme based on the Chinese remainder theorem (CRT) for 5G-enabled vehicular networks. To be specific, three primary contributions of the paper are summarized as follows. * First, a new authentication scheme based on CRT for 5G-enabled vehicular networks, which require neither RSU nor tamper-proof device (TPD);
* Second, a significant reduction in the computational complexity imposed on the trusted authorities (TAs) since vehicles joining or leaving a multicast domain execute one modulo division operation using CRT in the proposed scheme;
* Third, an authentication scheme that withstands password guess attacks, in which the driver holds two secret authentication parameters, preventing illegal users from taking control of a registered participating vehicle. The rest of the paper is structured as follows: Section 2 discusses the latest related work. Section 3 presents the preliminaries.