## 3 The Proposed 3-Tier-AKA Model
### Environment Characteristics
The edge tier exhibits heterogeneity due to variations in device architectures, communication, and network configurations [48]. The fog tier has the following characteristics:  
* Set of \(Z\) fog nodes, represented as \(\zeta=\{\zeta_{1},\zeta_{2},\cdots,\zeta_{z}\}\), where \(1\leq z\leq Z\). * Low latency and real-time interactions: Fog nodes close to the network edge collect, process, and store sensor and device data. This enables low latency and meets the needs of real-time interactions, particularly for latency-sensitive applications [14]. * Heterogeneity [14]: Fog nodes are available in various forms and can be deployed as physical or virtual nodes in diverse environments. They encompass high-performance servers, edge routers, gateways, access points, base stations, and more. These hardware platforms exhibit distinct computation and storage capabilities, run various operating systems (OSs), and support different software applications [14]. * Interoperability: Fog nodes are geographically distributed and interoperate in executing tasks to achieve the required quality of service. This includes interoperation among multiple fog nodes and devices with cloud computing [14]. The cloud tier has the following characteristics:  
* Set of \(C\) cloud data centers, represented as \(\gamma=\{\gamma_{1},\gamma_{2},\cdots,\gamma_{c}\}\), where \(1\leq c\leq C\). * Service-oriented: Cloud computing services are categorized into infrastructure as a service (IaaS), platform as a service (PaaS), and software as a service (SaaS). Users can utilize these services without owning hardware or knowing data locations. Examples include cloud storage, Google App Engine, and online gaming [49]. * On-demand self-service: Consumers can provision computing resources (such as virtual machines, storage, and applications) as needed without requiring human intervention from the service provider [50]. * Broad network access: Cloud resources are accessible over the network and can be accessed by various devices with Internet connectivity, such as laptops, smartphones, and tablets [50]. * Resource pooling: Cloud providers use multi-tenant models to pool and share resources among multiple users, with resources dynamically allocated based on demand. Users typically do not have control over the physical location of the resources [50]. * Rapid elasticity: Cloud resources can be scaled up or down quickly to accommodate changes in demand. This elasticity allows users to access additional resources during peak periods and release them when no longer needed [50]. * Measured service: Cloud systems automatically monitor and track resource usage, enabling users to be billed based on their consumption. \begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(\delta\) & A set of edge devices \\ \hline \(D\) & Number of edge devices represented as \(\delta=\{\zeta_{1},\zeta_{2},\cdots,\zeta_{z}\}\), where \(1\leq d\leq D\) \\ \hline \(\zeta\) & A set of fog nodes \\ \hline \(Z\) & Number of fog nodes represented as \(\zeta=\{\zeta_{1},\zeta_{2},\cdots,\zeta_{z}\}\), where \(1\leq z\leq Z\) \\ \hline \(\gamma\) & A set of cloud data centers \\ \hline \(C\) & Number of cloud data centers used as \(\gamma=\{\gamma_{1},\gamma_{2},\cdots,\gamma_{c}\}\), where \(1\leq c\leq C\) \\ \hline \(u\) & A set of 5G service providers \\ \hline \(S\) & A temporary secret key for each entity \\ \hline \(k\) & A secret key generated by 5G service provider during the registration phase for each entity \\ \hline \(O\) & A security token generated by 5G service provider during the registration phase for each entity \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notation for 3-Tier AKA model. The entities within the 5G network environment have the following assumptions:  
* The 5G network backhaul establishes a connection between fog nodes and the cloud data center. To ensure communication, a temporary secret key is assigned for the cloud's initial entry into the environment.