## 7 Performance Evaluation
### Computation Overhead  
We consider computation overhead needed for each node to authenticate an entire code image. Computation overhead per node in each scheme is as follows:  
\[CP_{SecureDeluge}=C_{sig}\ +\ N_{pkt}^{basic}\cdot C_{hash} \tag{13}\]  
\[CP_{SPA}\ =\ C_{sig}\ +\ N_{pkt}^{basic}\cdot C_{hash} \tag{14}\]  
\[CP_{MBSA}\ =\ C_{sig}\ +\ N_{page}\cdot C_{hash}\ +\ 2\cdot N_{pkt}^{tx}\cdot C_{MAC} \tag{15}\]  
\[CP_{BFBSA}\ =\ C_{sig}\ +\ N_{page}\cdot C_{hash}\ +\ N_{pkt}^{basic}\cdot k \cdot C_{hash} \tag{16}\]  
where \(C_{sig}\), \(C_{hash}\) and \(C_{MAC}\) denote the computation overhead of digital signatures, hash operations and MAC operations, respectively. \(N_{page}\) is the number of pages, which is determined as [code image size / page size]. \(N_{pkt}^{basic}\) is the number of packets in the entire code image, which is computed as \(N_{page}\times\) [page size / packet size]. \(N_{pkt}^{tx}\) is the number of packets transmitted actually under the given link quality. \(k\) is the number of hash functions used in the Bloom filter. From Equations (13)-(16), we can derive the energy consumption due to computation overhead as follows:  
\[E_{mcu}^{SecureDeluge}=I_{mcu}\cdot V_{sup}\cdot T_{sig}+N_{pkt}^{basic}\cdot I _{mcu}\cdot V_{sup}\cdot T_{hash} \tag{17}\]  
\[E_{mcu}^{SPA}=I_{mcu}\cdot V_{sup}\cdot T_{sig}+N_{pkt}^{basic}\cdot I_{mcu} \cdot V_{sup}\cdot T_{hash} \tag{18}\]  
\[E_{mcu}^{MBSA}=I_{mcu}\cdot V_{sup}\cdot T_{sig}+N_{page}\cdot I_{mcu}\cdot V_{ sup}\cdot T_{hash}+2\cdot N_{pkt}^{tx}\cdot I_{mcu}\cdot V_{sup}\cdot T_{MAC} \tag{19}\]  
\[E_{mcu}^{BFBSA}=I_{mcu}\cdot V_{sup}\cdot T_{sig}+N_{page}\cdot I_{mcu}\cdot V_{ sup}\cdot T_{hash}+N_{pkt}^{basic}\cdot k\cdot I_{mcu}\cdot V_{sup}\cdot T_{hash} \tag{20}\]  
Since the computation overhead shows similar results in each link quality, we only present Figure 12 which shows the energy consumption for performing cryptographic operations in the bad channel condition. Obviously, computation overhead of the BFBSA scheme is the largest among all of schemes since BFBSA performs many more hash operations to verify the membership of each packet against the Bloom filter. It is worth noting that the computation overhead is constant in each hop regardless of the link quality because the lost packets can be retransmitted without computation.  
\begin{table}
\begin{tabular}{c c c c} \hline
**BER** & **Scheme** & _hdr_ **in Equation (12)** & **Payload Size (Bytes)** \\ \hline \multirow{4}{*}{\(9.44\times 10^{-6}\) (Excellent)} & Secure Deluge & 43 (header: 23, hash: 20) & 22 \\  & SPA & 63 (header: 23, hash: 40) & 44 \\  & MBSA & 43 (header: 23, MAC: 20) & 90 \\  & BFBSA & 23 (header: 23) & 110 \\ \hline \multirow{4}{*}{\(2.70\times 10^{-4}\) (Fair)} & Secure Deluge & 43 (header: 23, hash: 20) & 22 \\  & SPA & 63 (header: 23, hash: 40) & 44 \\  & MBSA & 43 (header: 23, MAC: 20) & 90 \\  & BFBSA & 23 (header: 23) & 92 \\ \hline \multirow{4}{*}{\(6.51\times 10^{-4}\) (Bad)} & Secure Deluge & 43 (header: 23, hash: 20) & 22 \\  & SPA & 63 (header: 23, hash: 40) & 22 \\ \cline{1-1}  & MBSA & 43 (header: 23, MAC: 20) & 72 \\ \cline{1-1}  & BFBSA & 23 (header: 23) & 56 \\ \hline \end{tabular}
\end{table}
Table 2: Optimal Payload Size.