## 6 Evaluation of the Proposed Protocol
### Communication and Computational Complexity Evaluation
This state takes place in the setup phase of the secure routing protocols and in the ESPDA protocol (no TDMA used). Therefore, if a node sends something via unicast or broadcast transmission, the other member nodes still receive the message even though further process may not take place. We count it as receiving cost. Based on these assumptions, we calculate the communication cost for each protocol by calculating how many bits of message get processed in each transmission. Radio energy consumption is proportional to the number of conveyed bits. Tables 8-13 provide details of the calculation  
In order to simplify our study on cluster expenditure for radio transmission in each protocol, we assume that both transmitting and receiving cost are equal. Note that their energy may differ significantly for different radio instruments. For comparison in the data aggregation phase, we assume a worst case where all cluster members get selected, so \(\mathbf{n_{s}=n}\). Since the transmission cost for ordinary node in Tables 8-13 is for individual cluster members, it should be multiplied by \(\mathbf{n}\) to capture the whole expenditure of cluster members. Therefore the cost of one cluster is cost of 1 CH plus its \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{**Step**} & \multicolumn{2}{c|}{**CH**} & \multicolumn{2}{c|}{**Ordinary Node**} \\ \cline{2-5}  & **Tx Cost (in bits)** & **Rx Cost (in bits)** & **Tx Cost (in bits)** & **Rx Cost (in bits)** \\ \hline
1 & \(1\times\text{adv}=80\) & — & — & \(1\times\text{adv}=80\) \\ \hline
2 & — & \(n\times\text{join\,reg}=256n\) & \(1\times\text{join\,reg}=256\) & \((n-1)\times\text{join\,reg}=256n-256\) \\ \hline
3 & \(1\times\text{sched}=80\) & — & — & \(1\times\text{sched}=80\) \\ \hline
**Total** & **160** & **256n** & **256** & **256n-96** \\ \hline \end{tabular}
\end{table} 
Table 10: Communication cost of SecLEACH in setup phase. \begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \multirow{2}{*}{**Step**} & \multicolumn{2}{c|}{**CH**} & \multicolumn{2}{c|}{**Ordinary Node**} \\ \cline{2-5}  & **Tx Cost (in bits)** & **Rx Cost (in bits)** & **Tx Cost (in bits)** & **Rx Cost (in bits)** \\ \hline
1 & \(1\times\text{adv}=560\) & — & — & \(1\times\text{adv}=560\) \\ \hline
2 & — & \(n\times\text{join\,req}=192n\) & \(1\times\text{join\,req}=192\) & \((n-1)\times\text{join\,req}=192n-192\) \\ \hline
3 & \(1\times\text{CK\_req}=16n+176\) & — & — & \(1\times\text{CK\_req}=16n+176\) \\ \hline
4 & — & \(1\times\text{CK\_rep}=80n+608\) & — & \(1\times\text{ck\_rep}=80n+608\) \\ \hline
6 & \(1\times\text{sched\_seed\_permt}=368\) & — & — & \(1\times\text{sched\_seed\_permt}=368\) \\ \hline
**Total (setup phase)** & **16n + 1104** & **272n + 608** & **192** & **288n + 1520** \\ \hline
7 & — & \(n\times\text{pattern\_code}=240n\) & \(1\times\text{pattern\_code}=240\) & — \\ \hline
8 & \(1\times\text{selected\_nodes}=16n_{s}+176\) & — & — & \(1\times\text{selected\_nodes}=16n_{s}+176\) \\ \hline
9 (within cluster) & — & \(n_{s}\times\text{data}=256n_{s}\) & \(1\times\text{data}=256\) if selected, otherwise 0 & — \\ \hline
10 (from CH to BS) & \(1\times\text{data}=80n_{s}+192\) & — & — & — \\ \hline
**Total (steady state)** & **96n + 368** & **240n + 256n + 256n + 368** & **496 if selected, otherwise 240** & **16n + 176** \\ \hline \end{tabular}
\end{table} 
Table 11: Communication cost of MS-LEACH in setup phase.