## 5 Performance Evaluation  
The 3-Tier AKA protocol performance analysis and evaluation are presented in this section. The primary objective of this evaluation is to assess the protocol's efficiency across the following metrics: computational, signaling, communication, and storage costs. A comparative analysis is also conducted against existing protocols to ascertain the protocol's superiority and identify areas for improvement. The computational cost is examined by identifying the resources required to execute the protocol's operations, evaluating the time complexity, and understanding the protocol's computational demands. Furthermore, the signaling cost of the protocol is assessed. This entails analyzing the overhead incurred during the signaling process, such as message exchanges. The communication cost of the protocol is examined, especially the amount of data exchanged between network nodes during protocol execution. An assessment is made to determine the protocol's efficiency in utilizing network resources. Lastly, the storage cost of the protocol is also examined. This involves analyzing the storage requirements to support the protocol's operation. To provide a robust evaluation, a comparative analysis is performed against existing well-established alternative protocols. This analysis enables the identification of areas where the protocol outperforms existing solutions and areas where further enhancements can be made. For the evaluation of costs, we suppose that the length of the random number \(L_{R}\) is 128 bits, the AES encryption/decryption block size \(L_{AES}\) is 128 bits, the key length of AES \(L_{K}\) is 128 bits, the key length of 5G-AKA/4G EPS-AKA \(L_{AKA-K}\) is 256 bits, the length of hash function \(SHA-256\)\(L_{H}\) is 256 bits, the identity, temporary identity and anonymous identity \(L_{ID}\) are all of length 128 bits, and the length of sequence number SQN in 5G-AKA \(L_{SQN}\) is 48 bits. The timestamp \(L_{TS}\) is 32 bits. The length of the symmetric polynomial \(L_{SP}\) is 384 bits. The NTRU encryption/decryption block size \(L_{NTRU}\) is 160 bits.  
In [55], identity \(L_{ID^{*}}\) and timestamp \(L_{TS^{*}}\) use 64 bits each. The elliptic curve point \(L_{ECCP}\) is 320 bits. The hash function \(L_{H^{*}}\) is 160 bits. The symmetric key \(L_{SyK}\) is 128 bits for encryption.  
In TLS 1.3, the master key size \(L_{MK}\) is 384 bits, the pre-master key size \(L_{PMK}\) is 256 bits, and the client/server random number \(L_{C/SR}\) has a size of 256 bits. During the ECDHE process, the client/server private key length \(L_{C/SPrK}\) is 256 bits, and the public key length \(L_{C/SPuK}\) is 520 bits. The session resumption key size \(L_{SRk}\) is 256 bits. In general, the size of the ClientHello or ServerHello messages depends on how many extensions the message has, such as the server name and session ticket. The maximum size of a ClientHello message or ServerHello message is limited to 524,280 bits. We suppose that the ClientHello message has one extension, and its size is 480 bits \(L_{CH}\). The ServerHello message also has one extension, and its size is 320 bits \(L_{SH}\). The finished message has a fixed length of 288 bits  
Figure 9: 3-Tier AKA: Handover authentication phase.  
\(L_{F}\). Also, the certificate has a length of 512 bits \(L_{Cert}\), the certificate verify length is 512 bits \(L_{CertV}\), and the signed certificate timestamp size is 64 bits \(L_{T}\).