## 3 The Proposed 3-Tier-AKA Model
### Environment Characteristics  
Figure 1 illustrates the edge-fog-cloud 3-tier architecture. This section presents an in-depth analysis of each tier, elucidating their distinct characteristics using the notation presented in Table 2.  
The edge tier has the following characteristics:  
* Set of \(D\) mobile edge devices represented as \(\delta=\{\delta_{1},\delta_{2},\cdots,\delta_{d}\}\), where \(1\leq d\leq D\). * Mobility: Edge devices can move from one place to another [48]. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Study** & **Focus** & **Main Contributions** & **Limitations** & **Mobility** & **Domain** \\ \hline [PERSON] et al. [35] & Establishes secure communication while preserving privacy in vehicular ad hoc networks. & Minimizes computational and communication overhead. & Scalability and the impact of dynamic network conditions are not addressed. & Yes & Vehicular ad hoc networks \\ \hline [PERSON] et al. [36] & A mutual authentication based on elliptic curve cryptography and hash functions in fog computing. & Minimizes computation and communication overhead. Lightweight cryptographic. & Requires the edge user to store an extra identity, and no authentication between the fog and the cloud. & No & Generic \\ \hline [PERSON] et al. [37] & A lightweight authentication protocol designed for resource constrained devices in the Industrial Internet of Things (IIoT). & Minimizes communication overhead. Performance constrained IIoT devices. & Enhanced security for IoV for identity compromise and replay attacks. It stores a key pool for each sensor node. The storage cost is significant when the number of nodes increases. & No & Industrial Internet of Things \\ \hline [PERSON] et al. [41] & A mutual authentication for the edge-fog-cloud network utilizes a master secret key for new users to authenticate themselves to the fog server. & Computationally efficient, even in the existence of a large number of nodes. & Transmits a user’s identity over a public channel, compromising user anonymity. Reusing the same master password can pose a significant security risk. & No & Generic \\ \hline [PERSON] et al. [42] & Authentication key agreement protocol for fog-driven IoT healthcare system. The protocol involving three components: fog node, cloud server, and sensors. & Low latency. Leverages bilinear pairs to establish secure keys among the entities involved, ensuring authentication. & An attacker can perform a password guessing attack. Computationally expensive. & No & Healthcare \\ \hline [PERSON] et al. [43] & A mutual handover authentication in a vehicular network environment. It establishes mutual authentication between vehicles and fog nodes. & Ensure the integrity and privacy of vehicular network. Reduces the total message size. & It distributes user credentials to specific fog nodes. & Yes & Vehicular network \\ \hline [PERSON] et al. [44] & Anonymous handover authentication scheme for fog computing. & Lightweight. Low-latency authentication. & Improved communication and computation cost. & Yes & Generic \\ \hline [PERSON] et al. [45] & Threshold mutual authentication protocol that supports fast handover. & Reductions in authentication delays. & It increases the number of vehicles, leading to an increase in edge node storage. & Yes & Vehicular networks \\ \hline [PERSON] et al. [46] & Developed an access control in fog-assisted e-learning using cryptographic approaches. & High efficiency. Low complexity. Time efficient. & Large data size and hence high network cost. & No & eLearning \\ \hline [PERSON] et al. [47] & A lightweight, secure authentication key exchange AKE. & Computational efficiency. Low storage usage. Low communication costs. & Does not consider all the environment characteristics. & Yes & Generic \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Literature review summary. Interoperability: Edge devices may depend on their operation with other heterogeneous devices and service architectures.