## 4 The Proposed 3-Tier AKA Mutual Authentication and Key Agreement (AKA) Protocol  
The 3-Tier AKA protocol is structured into four main phases:  
1. Initialization: Responsible for generating the temporary secret key and master key.
2. Registration: Identifies edge devices, fog nodes, and cloud data centers within the 3-tier architecture.
3. Authentication and Key Agreement: Ensures the verification process between edge devices, fog nodes, and cloud data centers, and facilitates the creation and distribution of session keys for secure communication.
4. Handover verification: Focuses on validating the edge user and the new fog node during the handover process. This phase ensures seamless and secure transitions during handovers.  
Table 3 complements the modeling notation presented in Table 2 and displays the extended notation utilized in the protocol design.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Notation** & **Description** \\ \hline \(S_{\xi_{x}}\) & A temporary secret key \(S\) for edge device \(\delta_{x}\) \\ \hline \(S_{\chi_{x}}\) & A temporary secret key \(S\) for fog node \(\xi_{z}\) \\ \hline \(S_{\gamma_{x}}\) & A temporary secret key \(S\) for cloud data center \(\gamma_{z}\) \\ \hline \(K_{\xi_{x}}\) & A secret key \(K\) generated by 5G service provider during the registration phase for edge device \(\delta_{x}\) \\ \hline \(K_{\zeta_{z}}\) & A secret key \(K\) generated by 5G service provider during the registration phase for fog node \(\zeta_{z}\) \\ \hline \(K_{\gamma_{x}}\) & A secret key \(K\) generated by 5G service provider during the registration phase for cloud data center \(\gamma_{z}\) \\ \hline \(O_{\lambda_{d}}\) & A security token \(O\) generated by 5G service provider during the registration phase of the edge device \(\delta_{d}\) \\ \hline \(O_{\zeta_{z}}\) & A security token \(O\) generated by 5G service provider during the registration phase of the fog node \(\zeta_{z}\) \\ \hline \(O_{\gamma_{x}}\) & A security token \(O\) generated by 5G service provider during the registration phase of cloud data center \(\gamma_{z}\) \\ \hline \(MS_{\omega_{x}}\) & The master secret key of the 5G service provider \(u_{x}\) \\ \hline \(T\) & A timestamp \(T\) is the current time that both participants record during the session. \\ \hline \(SK_{\delta_{d}\xi_{x}}\) & A generated session key to be used by the edge device \(\delta_{d}\) and the fog node \(\zeta_{z}\) \\ \hline \(SK_{\delta_{d}\gamma_{x}}\) & A generated session key to be used by the edge device \(\delta_{d}\) and the cloud data center \(\gamma_{z}\) \\ \hline \(SK_{\zeta_{z}\gamma_{x}}\) & A generated session key to be used by the fog node \(\xi_{z}\) and the cloud data center \(\gamma_{z}\) \\ \hline \(R_{\delta_{d}}\) & Response message from 5G service provider to edge device \(\delta_{d}\) \\ \hline \(R_{\zeta_{z}}\) & Response message from 5G service provider to fog node \(\zeta_{z}\) \\ \hline \(R_{\gamma_{x}}\) & Response message from 5G service provider to cloud data center \(\gamma_{z}\) \\ \hline \(M_{\delta_{d}\xi_{z}}\) & Messages between edge device \(\delta_{d}\) and the fog node \(\zeta_{z}\) \\ \hline \(M_{\delta_{d}\gamma_{x}}\) & Messages between edge device \(\delta_{d}\) and the cloud data center \(\gamma_{z}\) \\ \hline \(M_{\gamma_{x}\zeta_{z}}\) & Messages between fog node \(\zeta_{z}\) and the cloud data center \(\gamma_{z}\) \\ \hline \(E(p,k)\) & The encryption of the plaintext \(p\) with the encryption key \(k\) using the AES-128 encryption technique. \\ \hline \(D(c,k)\) & The decryption of the ciphertext \(c\) with the encryption key \(k\) using the AES-128 encryption technique. \\ \hline \(||\) & Concatenates two or more strings, sequences, or values together in a specific order to create a longer string. \\ \hline \hline \end{tabular}
\end{table}
Table 3: The edge–fog-cloud 3-Tier AKA protocol notation.