# A Communication-Efficient Secure Routing Protocol for IoT Networks +
## 6 Performance Evaluation
### Total byte performance  
In both the proposed and compared methods, the packets in the RREQ and its replies are updated hop-by-hop based on cryptographic processing. This feature changes the packet length depending on the network size. As packet length directly affects communication efficiency, we evaluate the total number of bytes in the packets flowing through the network when establishing a route. First, the total number of bytes in AODV and DSR can be expressed as [26; 30]  
\[B_{\text{AODV}} =(n+1)\times\text{Size}(\text{RREQ}_{\text{AODV}})+(n+1)\times \text{Size}(\text{RREP}_{\text{AODV}}) \tag{16}\] \[B_{\text{DSR}} =(n+1)\times\text{Size}(\text{RREQ}_{\text{DSR}})+(n+1)\times \text{Size}(\text{RREP}_{\text{DSR}}), \tag{17}\]  
where \(\text{Size}(a)\) (bytes) is the number of bytes in a packet \(a\). Furthermore, the total packet size of the SAODV can be expressed as [26]  
\[B_{\text{SAODV}}=B_{\text{AODV}}+2(n+1)\times\text{Size}(\text{IDB}_{\text{ Sig}})+2(n+1)\times\text{Size}(\text{Hash}), \tag{18}\]  
where \(\text{IDB}_{\text{Sig}}\) denotes the ID-based signature. The total packet size of ARAN can be defined as [30]  
\[B_{\text{ARAN}}=B_{\text{AODV}}+2(2n+1)\times\text{Size}(\text{IDB}_{\text{ Sig}}). \tag{19}\]  
The total packet size of ISDSR+ can be derived by [26]  
\[B_{\text{ISDSR+}}=B_{\text{DSR}}+2(n+1)\times\text{Size}(\text{IBSAS}_{\text{ Sig}}). \tag{20}\]  
where \(\text{IBSAS}_{\text{Sig}}\) is the digital signature based on the IBSAS. The packet format in the proposed method depends on whether the RREP is generated by an intermediate or destination node. Therefore, we evaluate the performance of each separately. When the destination node constructs an end-to-end route as part of the proposed method, it is expressed as  
Figure 2: Example of the network configuration for performance evaluation (where \(N=2\)). \[B_{\text{DR}}= B_{\text{AODV}}-2(n+1)\times\text{Size}(\text{HC})+2(n+1)\times \text{Size}(\text{LT})+2(n+1)\times\text{Size}(\text{LI})\] \[+2(2n+1)\times\text{Size}(\text{IDB}_{\text{Sig}})+2n\times\text{ Size}(\text{ID}). \tag{21}\]  
Next, we consider the total number of bytes when the intermediate nodes generate RREPs. This packet contains the RREP that the responder node previously received from the destination node D. First, the size of the RREP generated by the destination node D is calculated as follows:  
\[L_{\text{DR}}=\text{Size}(\text{RREP}_{\text{AODV}})-\text{Size}(\text{HC})+ \text{Size}(\text{LI})+\text{Size}(\text{LT})+\text{Size}(\text{ID})+2\times \text{Size}(\text{IDB}_{\text{Sig}}). \tag{22}\]  
To establish the route of the proposed method, the total number of bytes in the packets flowing in the network is expressed as  
\[B_{\text{IR}}=B_{\text{AODV}}-2(N+1)\times\text{Size}(\text{HC})+2(N+1) \text{Size}(\text{LT})+2(N+1)\times\text{Size}(\text{LI})\] \[B_{\text{DSR}} =(n+1)\times\text{Size}(\text{RREQ}_{\text{DSR}})+(n+1)\times \text{Size}(\text{RREP}_{\text{DSR}}), \tag{17}\]0  
where \(N\) denotes the number of nodes between the source node S and the responder generating the RREP. As indicated in Equation (23), when the intermediate nodes start to generate RREPs using the proposed method, the total number of bytes always increases with respect to the number of hops as compared to the other methods, which perform end-to-end communication with the same number of hops. This is because the packet size of a single message increases due to the previous packet being written in the RREP. However, in the proposed method the intermediate nodes can generate RREPs, making it possible to reduce the total packet size flowing in the entire network at the time of route construction. This is particularly applicable to large-scale end-to-end networks. By substituting the packet size values shown in Table 1 in Equations (18)-(23), the sum of the packet size with respect to the number of hops can be calculated. The results are presented in \[B_{\text{DSR}} =(n+1)\times\text{Size}(\text{RREQ}_{\text{DSR}})+(n+1)\times \text{Size}(\text{RREP}_{\text{DSR}}), \tag{17}\]1