## 2 Background and Related Work
### Related Work
The paper introduces the edge-assisted decentralized authentication (EADA) architecture, which delegates the authentication capability from the RS to distributed ENs. The proposed protocol consists of two authentication scenarios: Auth-I and Auth-II. In Auth-I, vehicles are collaboratively authenticated by a subset of ENs using identity-based signature techniques. The involved ENs are efficiently authenticated in batches by the vehicle. For Auth-II, a vehicle with a valid token can achieve fast handover authentication by utilizing the token as a private credential with the nearest EN, reducing authentication delays significantly. The evaluation of the proposed protocol's performance reports significant reductions in authentication delays. The proposed EADA architecture and threshold mutual authentication protocol address security requirements such as mutual authentication between vehicles and ENs, secure token generation, and resistance against attacks. However, increasing the number of vehicles will lead to an increase in EN storage. The previous works on authentication protocols in fog computing, vehicular ad hoc networks, Internet of Things (IoT), TLS 1.3, and 4G/5G networks provide valuable insights and inspiration for developing secure and efficient authentication mechanisms. These works highlight the importance of addressing different computing environments' unique challenges and requirements, such as resource constraints, mobility, privacy concerns, and scalability. They also demonstrate the application of various cryptographic techniques, including bilinear pairings, elliptic curve cryptography (ECC), one-way hash functions, and blockchain, to achieve secure authentication while minimizing computational and communication overhead. The study in [46] proposed a fog-computing-based e-learning architecture. The authors extended the learning environment from the cloud to the network edge. The approach enhanced the performance of learning data assessments and reduced the encryption burden on user devices by offloading part of the encryption tasks to fog nodes. It enforces specified policies for data access in the learning context by encrypting courses and exams using various cryptographic techniques. The proposed approach demonstrated that the architecture achieves data confidentiality, fine-grained access control, collusion resistance, and enforceability. Furthermore, the evaluations indicate that the solution is efficient, particularly regarding encryption computation costs. The work in [47] proposed a lattice-based incremental signature scheme to support an efficient gradational authentication approach for modified data in a fog environment. Fog nodes are allowed to authenticate changes without accessing the original message and signature. This eliminates the need for the edge device to store them locally. The approach supports multi-block and combined incremental operations. The proposed approach reduces computational overhead while maintaining reasonable key and signature lengths. The analysis of the proposed approach indicates that it can withstand known attacks and effectively conserves the limited resources of fog nodes. Overall, previous works provide a foundation for designing authentication protocols that address the specific challenges and requirements of fog computing, IoT, vehicular networks, and 5G environments. They emphasize the need for secure, lightweight, and efficient authentication mechanisms that ensure privacy, scalability, and resilience against various known attacks. A summary of the aforementioned related work is presented in Table 1. The table clearly shows the lack of security mechanisms that consider the characteristics of the three-tier architecture. Hence, this work aims to develop a secure and efficient method for mutual authentication and session key agreement in the edge-fog-cloud three-tier architecture, with a particular focus on enabling quick handover.