## 5 Performance Evaluation
### Authentication between Entities  
#### 5.2.1 Computational Cost  
The need to assess the efficiency and feasibility of the proposed protocol motivates the comparison of our designed protocol with established standards like 5G-AKA, 4G EPS-AKA, and TLS 1.3 in terms of computational costs. In the proposed authentication protocol, only AES-128 encryption technology is used. In the 5G-AKA protocol, the encryption technology used to encrypt user ID is the Elliptic Curve Integrated Encryption Scheme (ECIES). In 4G EPS-AKA, it uses a hash-based message authentication code key-derivation function (HCDF). In the Transport Layer Security (TLS 1.3) protocol, we chose \(TLS\_AES\_128\_GCM\_SHA256\) as the cipher suite. The CPU (Central Processing Units) running time simulation results are shown in Table 5. Figures 6, 8 and 10-12 show the Authentication and Key Agreement phase of each protocol. security anchor function (SEAF) in line 1. Moving to line 2, SEAF forwards the authentication message, along with the serving network ID, to the authentication server function (AUSF). In line 3, AUSF further sends the authentication message to either the unified data management (UDM) or the authentication credential repository and processing function (ARPF). Subsequently, in the next line, UDM/ARPF generates an authentication response message. Upon receiving the authentication response message after line 5, the edge user needs to compute the response, which involves performing seven hash functions. This computation adds to the total computational cost. On the other hand, the 5G network decrypts the SUCI and calculates the authentication messages using nine hash functions. The authentication process is in line 9, the edge user authenticates the 5G core network (SEAF, AUSF, UDM, ARPF). In lines 11 and 13, the SEAF and AUSF, respectively, authenticate the edge user, completing the mutual authentication between the entities involved in the 5G-AKA process. In the 4G EPS-AKA (Evolved Packet System Authentication and Key Agreement), presented in Figure 11, the process shares similarities with 5G-AKA, but there is a notable difference in the initial steps. Unlike 5G-AKA, there is no ID encryption process at the beginning of 4G EPS-AKA. Table 6 shows abbreviations used in the 5G-AKA protocol. Figure 10: 5G-AKA protocol. \begin{table}
\begin{tabular}{c c} \hline
**Operation** & **Time (ms)** \\ \hline Hash function \((T_{H})\) & 0.107 \\ \hline ECIES encryption \((T_{ECIES,E})\) & 1.166 \\ \hline ECIES decryption \((T_{ECIES,D})\) & 1.164 \\ \hline AES encryption \((T_{AAS,E})\) & 0.217 \\ \hline AES decryption \((T_{AAS,D})\) & 0.243 \\ \hline ECDHE processing \((T_{ECHE})\) & 1.535 \\ \hline HKDF processing \((T_{HKDF})\) & 0.578 \\ \hline Verify certificate \((T_{Vvc})\) & 0.138 \\ \hline \end{tabular}
\end{table} 
Table 5: The running time of each operation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline SUCI & Subscription Concealed Identifier \\ \hline GUTI & Globally Unique Temporary Identity \\ \hline SUPI & Subscription Permanent Identifier \\ \hline SNid & Serving network ID \\ \hline AV & Authentication vector \\ \hline AUTH & Authentication token \\ \hline RES & Response Token \\ \hline XRES & Expected response token \\ \hline HXRES & Hash of the expected response token \\ \hline \(K_{\textit{4}\textit  
In TLS 1.3, presented in Figure 12, the authentication and key exchange process involves several steps. First, the client computes the shared pre-master key, and then, calculates the master key. These pieces of information are then forwarded to the server in line 2. Upon receiving the ClientHello message from the client, the server computes the shared pre-master key and uses the HKDF (HMAC-based extract-and-expand key derivation function) to derive the master key. Lines 3, 4, and 5 represent optional steps for authentication, which may or may not be used depending on the specific configuration.