## 5 System Simulation
### Energy Calculations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Pass** & **Hello** & **Reports** & **SUB** & **Total OH** & **Normal** & **TOTAL** \\ \hline \multirow{3}{*}{2} & Network & 14,608.00 & 476,434.00 & 8030.00 & 499,072.00 & 0.00 & 499,072.00 \\  & Av. Per Node & 182.60 & 5955.43 & 100.38 & 6238.40 & 0.00 & 6238.40 \\  & Worst Case (42) & 220.00 & 6663.00 & 426.00 & 7309.00 & 0.00 & 7309.00 \\ \hline \multirow{3}{*}{8} & Network & 0.00 & 19,656.00 & 8274.00 & 27,930.00 & 128,880.00 & 150,810.00 \\  & Av. Per Node & 0.00 & 245.70 & 103.43 & 349.13 & 1536.00 & 1885.13 \\  & Worst Case (32) & 0.00 & 1456.00 & 489.00 & 1945.00 & 9024.00 & 10,969.00 \\ \hline \multirow{3}{*}{14} & Network & 0.00 & 19,656.00 & 7939.00 & 27,595.00 & 122,880.00 & 150,475.00 \\  & Av. Per Node & 0.00 & 245.70 & 99.24 & 344.94 & 1536.00 & 1889.94 \\ \cline{1-1}  & Worst Case (50) & 0.00 & 2204.00 & 273.00 & 2477.00 & 13,632.00 & 16,109.00 \\ \hline \multirow{3}{*}{20} & Network & 8008.00 & 19,656.00 & 9476.00 & 37,140.00 & 92,160.00 & 129,300.00 \\ \cline{1-1}  & Av. Per Node & 100.10 & 245.70 & 118.45 & 464.25 & 1152.00 & 1616.25 \\ \cline{1-1}  & Worst Case (32) & 110.00 & 1584.00 & 600.00 & 2294.00 & 7344.00 & 9638.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Bytes Transmitted and Received with PBC Authentication. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Pass**} & & \multicolumn{2}{c}{**Hello**} & \multicolumn{2}{c}{**Reports**} & \multicolumn{2}{c}{**SUB**} & \multicolumn{2}{c}{**OH**} & \multicolumn{2}{c}{**Normal**} \\ \cline{2-13}  & & **tx** & **rx** & **tx** & **rx** & **tx** & **rx** & **tx** & **rx** & **tx** & **rx** \\ \hline  & Network & 38,438.40 & 35,376.00 & 758,342.40 & 1,706,870.56 & 19,564.80 & 21,193.44 & 816,345.60 & 1,763,440 & 0.00 & 0.00 \\
2 & Av. Per Node & 480.48 & 442.20 & 9479.28 & 21,335.88 & 244.56 & 264.92 & 10,204.32 & 22,043.00 & 0.00 & 0.00 \\  & Worst Case (42) & 528.00 & 589.60 & 10,310.40 & 24,200.40 & 1132.80 & 1018.40 & 11,971.20 & 25,808.40 & 0.00 & 0.00 \\ \hline  & Network & 0.00 & 0.00 & 53,145.60 & 46,010.24 & 20,102.40 & 21,900.96 & 73,248 & 67,911.20 & 331,776. & 288,153.60 \\
8 & Av. Per Node & 0.00 & 0.00 & 664.32 & 575.13 & 251.28 & 273.76 & 915.60 & 848.89 & 4147.20 & 3601.92 \\  & Worst Case (32) & 0.00 & 0.00 & 3571.20 & 3186.32 & 1296.00 & 1173.84 & 4867.20 & 4909.16 & 22,118.40 & 23,669.76 \\ \hline  & Network & 0.00 & 0.00 & 53,145.60 & 46,010.24 & 19,401.60 & 20,887.92 & 27,547.20 & 66,898.16 & 3317.76 & 288,153.60 \\
14 & Av. Per Node & 0.00 & 0.00 & 664.32 & 575.13 & 242.52 & 261.10 & 906.84 & 836.23 & 4147.20 & 3601.92 \\  & Worst Case (50) & 0.00 & 0.00 & 5366.40 & 5820.96 & 720.00 & 659.28 & 6086.40 & 6480.24 & 33,177.60 & 36,019.20 \\ \hline  & Network & 8448.00 & 33,489.28 & 53,145.60 & 46,010.24 & 22,771.20 & 25,363.52 & 84,364.80 & 104,863.04 & 248,832 & 216,115.20 \\
20 & Av. Per Node & 105.60 & 418.62 & 664.32 & 575.13 & 284.64 & 317.04 & 1054.56 & 1310.79 & 3110.40 & 2701.44 \\  & Worst Case (32) & 105.60 & 471.68 & 3878.40 & 4159.36 & 1574.40 & 1457.92 & 5558.40 & 6088.96 & 17,971.20 & 19,296.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Transmission Energy in (μJ) with PBC Authentication. In Table 9, we show the effect of the cryptographic techniques to perform the required authentication to secure the WSN in the most hostile environments. We divided the study as per the number of bytes signed and verified by each node to determine the initial sender of the packet. Also there is the number of bytes where the subsequent nodes have to encrypt and decrypt the source's signature in order to verify the direct hop-by-hop forwarder of the packet. Note that in the initial phase the major overhead is due to the verification of the broadcasted neighbor reports, which loaded the network by 132,288 bytes to verify, averaging 1653.5 verified bytes per node. The total number of bytes processed by cryptographic functions reached 135,660 bytes in the network averaging 1695.75 bytes per node in the initial phase.