## 5 System Simulation
### Energy Calculations
In these phases the average node communicated as low as 85 bytes of activity reports, with the worst case being 564 bytes for node 42; normal for a direct neighbor of the BS. The subpaths sent by the BS to disseminate the routing paths and teach every node its DL and ULs, show close number of communicated bytes in both phases, initial and subsequent. Averaging around 45 bytes per node, the overhead is very minimal for one of the main steps in the model. Therefore the total communication OH per node from CENTERA's blocks, when authentication is not added, reached 1691.9 communicated bytes in the initial phase, and settled at around 130-140 communicated bytes per node in subsequent phases. Considering the normal date packet containing sensor readings constitute of 28 bytes (as set by TinyOS), the communication overhead of CENTERA range from 12% in normal periods to 17% in periods where the keep-alive message is sent. Note that these percentages are calculated in our simulations where the activity period is take to be as low as 6. For relatively stable networks the activity period may be chosen by the administrator to be 50, decreasing the communication overhead to less than 2%. Figure 9a, shows the different percentages of the communication energy dissipated by the blocks of CENTERA and the normal data packets exchanged. It is obvious that, with the exception of the first activity period, CENTERA is adding little overhead (12% to 17%) to the normal function of the WSN. Using the energy estimations found in [28], where the energy consumed in MICAz for transmission is 0.6 \(\upmu\)J/bit and for receipt is 0.67 \(\upmu\)J/bit, Table 6 contains the exact energy consumed per block per period. Figure 10a shows the proportion of the overhead incurred by CENTERA between the transmission energy to that of the reception energy. Two things can be noticed, (1) the reception energy is slightly higher  
Figure 9: **(a)** Communication overhead without authentication; **(b)** communication overhead with authentication. than transmission energy and (2) the energy consumption spikes at the first period to around 8 mJ and then averages to around 650 \(\upmu\)/period for the remaining network lifetime. Table 6 shows that the energy dissipated to transmit and receive normal sensor packets is around 4000 \(\upmu\) to 4500 \(\upmu\)/period. Thus, the communication energy overhead is minor when compared to the normal functioning of the sensor network. Note that, increasing the activity period from 6 to 50, for instance, decreases the overhead even further, as the number of normal packets sent per period is multiplied by 8 and thus the overhead ratio sinks from 650/4500 \(\approx\) 14% to around 1.7% overhead. As for the system with a proper authentication scheme incorporated, the overhead imposed by CENTERA will be higher due to the extended messages communicated and the cryptographic technique used. We include the Identity Based--PBC, due to its lightweight processing, short signature (160 bits) and most importantly zero energy and storage to communicate and store keys of every node. This is a direct advantage gained from using Identity based encryption. Tables 7 and 8 repeat the analysis of Tables 5 and 6 in showing the overhead of CENTERA when PBC is incorporated. Similar to the previous results, the overhead is still low as compared to the normal packets communicated by the sensors, as shown in Figure 9b. The overhead now remains at around 18% and rises to 28% in periods where keep alive messages are communicated. This raise is partly because of the additional transmissions and receipts incurred on the network, but majorly due to the fact that in such activity periods, there will be one less period of sending normal packets. Note that, similar to previous analysis, the overhead decreases drastically by increasing the activity period from 6 to 50 from 18% to around 2% and from 28% to around 2.8%.