## 10 Conclusions  
The AMI is one of the most important elements in the smart grid, and therefore, it was necessary to take care of the confidentiality of the transfer of information from it to monitoring and control centers. A new KMS that addresses common security concerns has been developed in order to overcome the primary problems with controlling and monitoring AMI systems. Three essential management techniques are supported by the KMS design for unicast, broadcast, and multicast modes of hybrid transmission.  
The storing and computation of keys and associated data can be simply implemented in SMs or UGs based on our system's performance and security evaluations. Additionally, in an AMI system, the distribution of keys and the data they are connected with do not obstruct normal network activity.  
After implementing the proposed strategy in our paper, the results were improved and indicated the stability of the AMI system and the security of the data. The storage cost was calculated according to the number of DR projects and SXs. The time required for conducting computations and the time cost for key distribution were calculated. The storage cost ranged from 0.448 to 1.4 Kbytes as the number of DR projects ranged from 5 to 20, which indicated that the storage cost increased when the DR increased. These values of storage cost are insignificant when compared with their improvement in storage devices.  
The time required for conducting computations was calculated for three transmission ways and for each SX and MS. The proposed key management algorithm consumed about 5 to 38 microseconds at each SX and consumed 0.3 to 5 microseconds at MS with unicast and broadcast transmission ways. The time consumed in MS for multicast should take NG and NP into consideration.  
The time cost for key distribution depends on the number of users in the DR project. Therefore, with 1000 users, the distribution time would be about 2.48 ms, and for 10,000 users, the distribution time would be about 24.77 ms.  
In future work, the energy-efficiency could be studied, and research could be conducted on energy-efficient cryptographic algorithms to minimize their impact on performance and battery life. Additionally, Real-World Deployment and Testing could be applied to evaluate its effectiveness in actual AMI systems. This could help identify practical challenges and fine-tune the scheme accordingly.  
Conceptualization, A.A.A. and B.M.E.-d.; methodology, K.M.A.-A.-E., software, A.A.A. and B.M.E.-d., validation, T.M.H.; formal analysis, K.M.A.-A.-E.; investigation, A.A.A.; resources, T.M.H.; data curation, B.M.E.-d.; writing--original draft preparation, A.A.A., and K.M.A.-A.-E.; writing--review and editing, K.M.A.-A.-E., and T.M.H.; visualization, B.M.E.-d.; supervision, K.M.A.-A.-E.; project administration, A.A.A.; funding acquisition, K.M.A.-A.-E. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Centre for Power Systems Research (CPSR), the Faculty of Engineering and the Built Environment, Cape Peninsula University of Technology, Cape Town, South Africa, and The APC was funded by Centre for Power Systems Research (CPSR), Faculty of Engineering and the Built Environment, Cape Peninsula University of Technology, Cape Town, South Africa.  
Not applicable.  
The authors declare no conflict of interest.