## 4 Our Proposed 5 GAKA-LCCO Protocol  
According to the above motivation, we propose a 5 GAKA-LCCO protocol, which is illustrated in Figure 5.  
Figure 4: DoS attacks against the HN for the 5G-IPAKA protocol. Figure 3: DoS attacks against both the SN and the HN for the 5G-IPAKA protocol. In Figure 5, the detail steps of the 5 GAKA-LCCO protocol are as follows:  
1. When the SEAF initiates an authentication with the UE, the SEAF generates \(RAND_{SN}\) and \(T_{SN}\), and then sends \(RAND_{SN}\) and \(T_{SN}\) to the UE, where \(T_{SN}\) is a timestamp generated by the SEAF. 2. Upon receiving \(RAND_{SN}\) and \(T_{SN}\), the UE sends \(SUCI=x\cdot G||\{SUPI\}_{EK}||MAC_{UE}\) to the SEAF, where \(EK||ICB||MK||K_{AUISF}=KDF(K,x\cdot y\cdot G||RAND_{SN}||T_{SN}||SNN)\) and \(MAC_{UE}=HMAC(MK,\{SUPI\}_{EK})\). Note that the time synchronization only needs to be maintained between the SN and the HN in the 5 GAKA-LCCO protocol, so the UE does not verify \(T_{SN}\). 3. Upon receiving \(SUCI\), the SEAF sends \(RAND_{SN}\), \(T_{SN}\), \(SUCI\), and \(SNN\) to the AUSF. 4. If the SEAF is entitled to use \(SNN\) and \(T_{SN}\) is valid, then the AUSF stores the received \(SNN\), and sends \(RAND_{SN}\), \(T_{SN}\), \(SUCI\), and \(SNN\) to the UDM. Otherwise, the AUSF aborts. If \(|T_{SN}-T_{AUISF}|<\Delta t_{AUISF}\), then \(T_{SN}\) is valid, where \(T_{AUISF}\) is the current time of the AUSF and \(\Delta t_{AUISF}\) is the time difference set by the AUSF. 5. The UDM first verifies \(T_{SN}\). If \(T_{SN}\) is invalid, then the UDM/ARPF aborts. Otherwise, the UDM invokes the SIDF when \(SUCI\) is received. Then, the SIDF de-conceals \(SUCI\) to gain \(SUPI\) before the UDM can process the request. After the de-concealing process, the SIDF sends \(MK\), \(K_{AUISF}\), and \(SUPI\) to the UDM. If \(|T_{SN}-T_{UDM}|<\Delta t_{UDM}\), then \(T_{SN}\) is valid, where \(T_{UDM}\) is the current time of the UDM and \(\Delta t_{UDM}\) is the time difference set by the UDM. 6. The UDM/ARPF generates \(RAND\) and calculates \(AUTN\), where \(AUTN=AMF||MAC\) and \(MAC=f_{1}(MK,RAND||AMF)\). 7. The UDM sends \(RAND_{SN}\), \(RAND\), \(AUTN\), \(K_{AUISF}\), and \(SUPI\) to the AUSF. When an AKMA subscription is used, the UDM also sends \(AKMA\) to the AUSF. 8. The AUSF calculates \(K_{SEAF}\) from \(K_{AUISF}\), then sends \(RAND_{SN}\), \(K_{SEAF}\), \(SUPIRAND\), and \(AUTN\) to the SEAF, where \(K_{SEAF}=KDF(K_{AUISF},SNN)\). 9. The SEAF stores \(K_{SEAF}\), and then sends \(RAND\), \(AUTN\), \(ngKSI\), and \(ABBA\) to the UE. 10. The UE verifies \(AUTN\) based on \(MK\). If the verification is successful, then the UE calculates \(K_{SEAF}\) from \(K_{AUISF}\), and stores \(K_{SEAF}\). Otherwise, the UE aborts. Compared with the latest version of the 5G AKA protocol, the main improvements of our proposed 5 GAKA-LCCO protocol are as follows:  
* Modify the key derivation process of the pre-shared key. In detail, \(EK||ICB||MK||K_{AUISF}=KDF(K,x\cdot y\cdot G||RAND_{SN}||T_{SN}||SNN)\), where \(EK\) and \(ICB\) are used to encrypt \(SUPI\), \(MK\) is used to calculate \(MAC_{UE}\) and \(MAC\), and \(K_{AUISF}\) is used to derivate \(K_{SEAF}\). Figure 5: Our proposed 5 GAKA-LCCO protocol. * Add the challenge-response mechanism for the UE. \(x\) is included in \(SUCI\) of the first sent message of the UE as a challenge, and \(x\) is added to \(AUTN\) of the third received message of the UE as a response. * Add the challenge-response mechanism for the SN. Firstly, \(RAND_{SN}\) is added to the first sent message of the SEAF as a challenge and \(RAND_{SN}\) is added to \(SUCI\) of the first received message of the SEAF as a response. Then, \(RAND_{SN}\) is added to the second sent message of the SEAF as a challenge and \(RAND_{SN}\) is added to the second received message of the SEAF as a response. * Add the timestamp mechanism for the SN and the HN. \(T_{SN}\) is added to the first four messages of the protocol, but \(T_{SN}\) is only verified by the AUSF and the UDM.