## 6 Conclusions and Future Work  
This paper proposed a lightweight mutual authentication scheme for distributed MQTT architecture based on fog computing to establish scalable and secure M2M communications for the IIoT. Our proposed architecture is designed in a hierarchical structure with a multi-tier MQTT broker (Mu-TiMB). The authentication scheme is implemented by an authentication manager (AM) that is deployed in each broker to enable the independency of security management for each broker and its group of connected clients/brokers.  
Compared to the existing works, our proposed architecture mitigates security performance overhead by implementing a lightweight mutual authentication scheme between client-broker communication and broker-broker communication using hash function and XOR operation. The authentication scheme is characterized by low storage and communication overhead, which have been reduced to 89% and 23%, respectively, compared with the results given in the benchmark. Our system enables the management of the authentication for each broker and its group of connected clients/brokers independently. This decreases the possibility of security threats and facilitates security management. Our proposed architecture can avoid latency, network congestion, and bottlenecks due to clustering the clients  
Figure 13: Communication overhead for clients and brokers in Diro’s scheme, our scheme, and Amanlou’s scheme.  
into groups that connect to a single local broker as well as due to the flexibility of scaling the broker and its associated AM horizontally and vertically. In our proposed architecture, the hierarchical structure allows the MQTT client to obtain data from any broker, despite it being connected to a single local broker in the fog layer. One of the authentication scheme disadvantages is the lack of anonymity and untraceability.  
This paper can pave the way for the researchers to develop the proposed architecture with the other security properties, such as authorization, availability, and data confidentiality, so that there will be a comprehensive independent security manager for each broker that provides the required security properties for the group of connected clients/brokers. There are two limitations in this paper that could be addressed in future by conducting additional tests for the performance of the authentication scheme, including computation time and transmission time, and by presenting a formal security analysis using security verification tools such as AVISPA and Ban logic.  
In the future, we plan to implement an authorization system by deploying an authorization manager for each broker to enforce access control on topics. Moreover, we intend to achieve the availability and avoid the single point of failure for a broker and its associated AM by adding load-balancing solutions. In case any failures occur, another broker and AM can take over the load. In addition, we plan to achieve the confidentiality and integrity of publishing and subscribing to topics using lightweight encryption techniques.  
Conceptualization, H.K. and V.T.; methodology, H.K. and V.T.; software, H.K.; validation, H.K. and V.T.; writing--original draft preparation, H.K.; writing--review and editing, H.K. and V.T.; visualization, H.K. and V.T.; supervision, V.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.