## 7 Conclusions  
In this paper, we provide overviews of both the latest version of the 5G AKA protocol and the 5G-IPAKA protocol, where the 5G-IPAKA protocol is a recently improved 5G AKA protocol. Then, we point out that one of the shortcomings of the 5G AKA protocol has not been completely overcome in the 5G-IPAKA protocol, leading to DoS attacks against the SN and HN. As a result, much of the energy of both the SN and HN is consumed. Additionally, the 5G AKA protocol has large communication and computation overhead. Thus, whether the authentication is successful or failed, this will lead to a great deal of energy consumption, while the 5G-IPAKA protocol has an even larger communication and computation overhead. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Protocols** & \begin{tabular}{c} **Communication** \\ **Overhead (Bits)** \\ \end{tabular} & \
\begin{tabular}{c} **Computation Overhead** \\ \end{tabular} &
\begin{tabular}{c} **Storage Overhead (Bits)** \\ \end{tabular} \\ \hline
5G AKA & 3120 & \(1 ECDH+1 ED+12F+2 XOR\) & 3328 \\
[23] & 3248 & \(4 PED+1 ED+10F+2 XOR\) & 7680 \\
[24] & 3472 & \(2 PED+1 ECDH+1 ED+13F+1 XOR\) & 5504 \\
[26] & 3664 & \(1 ECDH+1 ED+12F\) & 3392 \\
[28] & 3664 & \(1 ECDH+1 ED+16F+2 XOR\) & 3328 \\
5 GAKA-LCCO & 2656 & \(1 ECDH+1 ED+4F\) & 3392 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: A comparative analysis between the 5 GAKA-LCCO protocol and the recently improved 5G AKA protocols [23; 24; 26; 28] regarding the communication, computation, and storage overhead. To solve these problems, we propose a 5 GAKA-LCCO protocol. Compared with the latest version of the 5G AKA protocol, the main improvements of the 5 GAKA-LCCO protocol include the fact that the key derivation process of the pre-shared key is modified, the challenge-response mechanism for the SN is added, the challenge-response mechanism for the HN is added, the timestamp mechanism for the SN and HN is added, the synchronization failure procedure is removed, the MAC failure procedure is replaced with a timeout mechanism on the HN, and the communication and computation overhead of the authentication process is reduced. Finally, we use both the strand space model and the Scyther tool to formally analyze the security of the 5 GAKA-LCCO protocol. As a result, mutual authentication and injection among the UE, SN, and HN are established. Therefore, the 5 GAKA-LCCO protocol is secure in both the strand space model and the Scyther tool. Based on further discussion and comparative analysis, the 5 GAKA-LCCO protocol can completely overcome the above shortcomings of the latest version of the 5G AKA protocol and is better than the recently improved 5G AKA protocols in overcoming these shortcomings. In addition, the 5 GAKA-LCCO protocol has less communication and computation overhead than the 5G AKA protocol and the recently improved 5G AKA protocols. In the above protocols, the public key cryptography mechanism, which has large computation and storage overhead, is always used. To further reduce the computation overhead, we will further improve these protocols in the future so that they do not use the public key cryptography mechanism. Methodology, Y.X. ; formal analysis, S.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No.61741216, 61402367), Shaanxi Science and Technology Co-ordination and Innovation Project (No.2016 KTTSGY01-03), National Key Research and Development Program (No. 2018 YFC08242-04), and New Star Team Project of Xi'an University of Posts and Telecommunications. Not applicable.