# Mdpj _sciences_
## 6 Conclusions  
In this paper, we conducted a comprehensive security analysis of the DMRN Protocol using two representative formal verification tools SVO logic and ProVerif. The analysis evaluated key security requirements, including mutual authentication, secure key exchange, SUPI concealment, PFS, defense against attacks by compromised or malicious SNs, and quantum-safe properties. The verification research demonstrated that the protocol remains vulnerable to the following attack vectors depending on the attacker's capabilities. First, while the protocol enhances mutual authentication through PQC-powered and PFS-enabled keys, it faces challenges due to the lack of timeliness in the MAC value, making it vulnerable to HN masquerade attacks. Second, the key exchange mechanism leads to replay attacks on the SUPI and sophisticated attacks due to the non-freshness of the two keys, \(K_{S1}\) and \(K_{S2}\). Third, attacks by compromised SNs can expose critical information, such as \(K_{SEAF}\), earlier than in the standard 5G AKA process. To address these issues, we proposed the following countermeasures: (i) implementing anti-replay mechanisms to prevent SUCI replay attacks; (ii) including the UE's ephemeral public key in the generation process of \(K_{S2}\) to ensure the freshness of \(K_{S2}\), which is used for deriving the MAC value and important session keys; (iii) modifying the transmission of \(K_{SEAF}\) to occur after UE authentication to mitigate risks from compromised SNs; and (iv) adopting a hybrid PQC approach that combines traditional cryptography with PQC methods to maintain reliability while preparing for quantum threats. By evaluating the security properties of the DMRN protocol from various perspectives, this research provides crucial insights into the design of authentication and key exchange protocols for next-generation 6G networks. The findings of this study will significantly contribute to the standardization process of secure protocols, guiding future protocol design and verification efforts. Additionally, since mobile communication networks and IoT devices are closely related, future research will focus on evaluating the performance of the improved DMRN protocol, particularly in scenarios where PQC algorithms are applied. This will include performance metrics such as overhead and latency.  
Conceptualization, J.K. and I.Y.; methodology, I.Y.; validation, J.K., Y.K. and I.Y.; formal analysis, J.K. and Y.K.; investigation, I.W.A.J.P.; data curation, I.W.A.J.P.; writing--original draft preparation, I.Y., J.K., Y.K. and I.W.A.J.P.; writing--review and editing, Y.K. and I.Y.; visualization, I.W.A.J.P. and Y.K.; supervision, I.Y.; project administration, I.Y.; funding acquisition, I.Y. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (No. 2022-00207416, A study on PQC optimization and security protocol migration to neutralize advanced quantum attacks in Beyond 5G-based next-generation IoT computing environments, 100%).  
Not applicable  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Acknowledgments:** We acknowledge the use of ChatGPT, a large language model developed by OpenAI, for assistance in drafting and editing the manuscript. This model was employed to enhance the clarity and linguistic structure of the paper. All final decisions regarding the content were made by the authors.  
**Conflicts of Interest:** The authors declare no conflicts of interest.