## 6 Simulation Results
### Experimental Results
#### 6.6.1 Energy Efficiency Performance  
Figure 7 show the average energy cost of each transmission (from an arbitrary node to the observation point) at different malicious ratios ranging from 10-30%. **Remark 1**. : _The number of compromised nodes in the network is closely related to the attacker's subjective intention of paralyzing the network, and in some sense, it is unpredictable. The authors in [57] figured out that, for an unspecific (unknown) type of attack against WSNs, if no more than 20% of the nodes are malicious, the attack can be detected and confined, which is due to the fact that the great majority of nodes are still behaving properly and it is not complicated to distinguish misbehaving ones. In some other research studying the security of WSNs, the numbers of malicious nodes in their simulations are usually assumed to be 1-30% of the total number of sensor nodes in the network [58, 59, 60]._  
Figure 6: Route determination example. At a malicious ratio of 10%, it can be observed that both lines of RCPED and PLGPa fluctuate per number of nodes in the network. Notably, RCPED consistently has less average transmission cost than PLGPa because RCPED requires no additional hardware (means no extra energy consumption) to ensure security. Compared to PLGPa, the energy cost reduced by RCPED can hit values up to 87.93%. The average transmission cost of AODV-EHA tends to drop as the number of nodes goes up, even if it indeed fluctuates dramatically. The cost seems to be less than that of PLGPa when nodes number in the network exceeds a certain value (130 or higher), this is due to the increment of nodes density that offers more choices of nodes, and a route with better energy efficiency is more likely to be found. Even though compromised nodes are occasionally included on the route (this is the cause of violent fluctuation in the green line), the damage can still be offset to some extent. Therefore, when the choices of nodes are more than enough (exceeding 130), the compensation can be sufficient to make AODV-EHA provide better performance than that of PLGPa. When malicious ratio rises to 20%, even though RCPED has the least average transmission cost, its relative advantage over PLGPa begins to weaken, and this is because as the malicious ratio rises, it becomes more difficult for RCPED to remove compromised nodes in route discovery. The aforementioned saved energy brought by the independence of additional hardware could be partially counteracted to some extent. The tendency of AODV-EHA keeps still at a malicious ratio at 10%, but the transmission cost appears to be less than PLGPa only after node number exceeds 170, which is more than a node number of 130 at a malicious ratio of 10%. It attributes to the fact that a larger malicious ratio makes it more likely for AODV-EHA to encounter compromised nodes in route discovery. Hence, the aforementioned energy compensation brought by the increment in choices of nodes is partially offset. As the malicious ratio reaches up to 30%, energy cost reduced by RCPED compared to PLGPa continues to decrease and sometimes can be as low as 28.34%. AODV-EHA retains the same line tendency similarly to what was previously shown at malicious ratios at 10% and 20%, but its performance never surmount PLGPa in the provided nodes number ranged from 60 to 200. The reason is that as the malicious ratio continues to drop, it becomes increasingly difficult for protocols that are without cryptographic encryption (for example, RCPED and AODV-EHA) to eliminate the damage reflected as extra energy cost (caused by malicious nodes). By contrast, the performances of PLGPa are relatively stable regardless of the malicious ratio since it is equipped with cryptography. Figure 7: Average end to end overall transmission cost (Joule). Based on all the above results gathered from overall energy cost performance evaluations, it can be concluded that RCPED has advantages in terms of overall energy cost in transmissions under different malicious ratios.