## 5 System Simulation
### Energy Calculations
In subsequent phases, this number dropped to around 88,000 bytes in the whole network, averaging to around 1100 bytes per node. Note that the last period, where there is one less period to send normal packets, the total is just 70,664 bytes to authenticate, the thing that clearly shows that the majority of the processing overhead is spent authenticating the normal sensor messages. One thing that can be noticed is that the worst case in the normal phases is much higher than that of the initial phase. This is clearly described by the absence of normal packets in the initial phase. This gives an indication of the huge load that the closer nodes to the BS have to endure due to the nature of such networks. The majority of the cryptographic overhead is due to the normal packets communicated and not due to the blocks of CENTERA. This conforms to the previously gathered results where we noticed that the additional number of packets sent by CENTERA is in the range of 12% to 17% for the chosen activity period. To further show the advantage of authentication in a trust based system for energy efficiency, we introduced into our system a broadcasting attacker node while changing its identity and calculated the cumulative number of bytes exchanged until each pass. In this scenario, node 11 broadcasts normal packets to its neighbors at a high rate while changing its identity, in order that its packets are forwarded by its neighbors into the system. As explained previously, CENTERA forces nodes to only forward the packets of their designated UL neighbors. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Pass** & & **SIGN** & **VERIFY** & **ENC** & **DEC** & **TOTAL** \\ \hline \multirow{4}{*}{2} & Network & 1340.00 & 132,280.00 & 0.00 & 2040.00 & 135,660.00 \\  & Av. Per Node & 16.75 & 1653.50 & 0.00 & 25.50 & 1695.75 \\  & Worst Case (42) & 2029.00 & 2029.00 & 7309.00 & 7309.00 & 18,676.00 \\ \hline \multirow{4}{*}{8} & Network & 9848.00 & 37,956.00 & 22,400.00 & 18,440.00 & 88,644.00 \\  & Av. Per Node & 123.10 & 474.45 & 280.00 & 230.50 & 1108.05 \\  & Worst Case (32) & 5989.00 & 725.00 & 10,969.00 & 1945.00 & 19,628.00 \\ \hline \multirow{4}{*}{14} & Network & 9848.00 & 37,760.00 & 22,400.00 & 18,340.00 & 88,348.00 \\  & Av. Per Node & 123.10 & 472.00 & 280.00 & 229.25 & 1104.35 \\  & Worst Case (50) & 8849.00 & 897.00 & 16,109.00 & 2477.00 & 28,332.00 \\ \hline \multirow{4}{*}{20} & Network & 7768.00 & 31,356.00 & 16,800.00 & 14,740.00 & 70,664.00 \\  & Av. Per Node & 97.10 & 391.95 & 210.00 & 184.25 & 883.30 \\ \cline{1-1}  & Worst Case (32) & 5098.00 & 814.00 & 9638.00 & 2294.00 & 17,844.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Total Number of Authenticated Bytes. We repeated this scenario while changing the broadcasting rate of node 11, from ten times the normal rate of normal packets, to 50 and 100 times. Table 10 shows the cumulative number of bytes exchanged for the whole network of 81 nodes, the average number of bytes per node, and the worst case, in each broadcasting rate and compares them to the normal case of CENTERA with authentication. It is clear from the table how the overhead of the authentication is offset by the broadcasting attacker in as low as three and four passes of the system for the 100 and 50 times broadcasting rate cases. Also in the low rate of ten times broadcasting rate, the overhead is closing up in four passes in the table. Figure 11 displays the network exchanged bytes and it is clear how the authentication overhead is overcome very quickly by one attacker. Note that in CENTERA this attack will be limited in time and space. In CENTERA and as a direct benefit of authentication, node 11 is unable to deceive its neighbors by using their UL node ID and thus those neighbors drop the packets of the attacker; the attack is limited in space. In the next pass, as the packets are authenticated, the BS detects the high sending rate of node 11, and isolates it to end its negative effect from the system; the attack is limited in time.