## 6 Evaluation of the Proposed Protocol
### Communication and Computational Complexity Evaluation
\begin{table}
\begin{tabular}{|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 & \(1\times\text{acc\_adv}=176\) & — & — & \(1\times\text{sec\_adv}=176\) \\ \hline
1.2 & — & \(1\times\text{Legitimate\,List}=320\) & — & \(1\times\text{Legitimate\,List}=320\) \\ \hline
1.3 & — & \(1\times\text{Group\_Key}=64\) & — & \(1\times\text{Group\_Key}=64\) \\ \hline
2 & — & \(n\times\text{join\,req}=32n\) & \(1\times\text{join\,req}=32\) & \((n-1)\times\text{join\,req}=32n-32\) \\ \hline
4 & \(n\times\text{sched}=224n\) & — & — & \(n\times\text{sched}=224n\) \\ \hline
**Total** & **224n + 176** & **32n + 384** & **32** & **256n + 528** \\ \hline \end{tabular}
\end{table} 
Table 12: Communication cost of the proposed protocol in setup phase and steady state phase. member nodes. Table 14 summarizes the comparison of the total expenditure for radio transmission within a cluster. From Table 14 we are able to see each protocols' radio communication cost in polynomial form. For radio communication cost, with the increasing number of member nodes, we find the following:  
* SLEACH is the cheapest secure routing protocol for the setup phase. Its radio communication expenditure is not much different from LEACH's. This is because its modified advertisement message adds a small number of bits to the transaction. Its transmission for the list of legitimate CH and group key (in step 1.2 and 1.3, Figure 2) add some more bits. However it is still the cheapest among secure routing protocols under evaluation. * Our protocol is the most expensive for the setup phase category. The size of the join request message and cluster key reply message are the main contributors to this cost. We have designed our protocol to have multiple steady-state phases in order to mitigate this costly setup phase. However our protocol is robust against all six possible attacks as shown in Table 3. We achieve these enhanced security features with some extra communication cost. * Though our protocol setup phase is the most expensive, its data aggregation cost is much cheaper than its baseline protocol, ESPDA. This is because we use TDMA scheduling in our protocol design. With about 40 times of \(n^{2}\) lesser transmissions than ESPDA, our scheme has three more enhanced security features than ESPDA as shown in Table 4. As the number of \begin{table}
\begin{tabular}{|c|c|c|c|} \hline \multirow{2}{*}{**Step**} & \multicolumn{2}{c|}{**CH**} & \multicolumn{2}{c|}{**Ordinary Node**} \\ \cline{2-4}  & **Tx Cost (in bits)** & **Rx Cost (in bits)** & **Tx Cost (in bits)** & **Rx Cost (in bits)** \\ \hline
1 & — & \(n\times\textbf{pattern\_code}=64n\) & \(1\times\textbf{pattern\_code}=64\) & \((n-1)\times\textbf{pattern\_code}=64n-64\) \\ \hline
3 & \(n_{s}\times\textbf{selected\_nodes}=32n_{s}\) & — & — & \(n_{s}\times\textbf{selected\_nodes}=32n_{s}\) \\ \hline
5 & — & \(n_{s}\times\textbf{data}=272n_{s}\) & \(1\times\textbf{data}=272\) if got selected, otherwise 0 & \((n_{s}-1)\times\textbf{data}=272n_{s}-272\) \\ (within cluster) & — & \(n_{s}\times\textbf{data}=272n_{s}\) & \(1\times\textbf{data}=272n_{s}\) \\ \hline
6 & \(n_{s}\times\textbf{data}=288n_{s}\) & — & — & \(n_{s}\times\textbf{data}=288n_{s}\) \\ (from CH to BS) & & & & \(64n+592n_{s}-336\) \\ \hline
**Total** & **320n\({}_{s}\)** & \(64n+272n_{s}\) & **336 if selected, otherwise 64** & **if selected, otherwise 64** \\ \hline \end{tabular}
\end{table} 
Table 13: Communication cost of ESPDA in data aggregation phase.