## 7 Evaluation
### Performance and Security Tradeoff  
In this section, we evaluate the different measures proposed in Section 5 and conduct the tradeoff analysis using the model analysis methods. The parameters for the model are taken from the implementation, and we use normalization. It is assumed that the attack rate on the system is \(\lambda_{2}=1\). We also assume it takes an average of 0.5 time units for the gateway node to carry out a rekeying process, and the rate at which the system is brought back to the good state by the rekeying process is \(\lambda_{4}=2\). The rate at which the attacker successfully breaks the key, while failing at accessing the data or he or she just fails to conduct a successful timing attack, is assumed to be \(\lambda_{6}=1\). Firstly, the effect of the rekeying rate \(\lambda_{1}\) and the weighting parameter \(w\) on the system cost measure \(\Theta\) is analyzed in Figure 5. The marginal values are investigated firstly. It is shown from the figure that when \(w=0\), where only the costs of losing sensitive information in the compromised system are considered, the system cost decreases monotonically with the rekeying rate \(\lambda_{1}\). Intuitively, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Shape Para** & **Scale Para** & **Variance** & **n (Sample)** & **Optimal Rate** \\ \hline no padding & & & 375 & 0.4348 \\ wei 0.40 & 0.05 & 0.2725 & 830 & 0.3000 \\ wei 0.37 & 0.05 & 0.5642 & 1070 & 0.2653 \\ wei 0.35 & 0.05 & 0.9980 & 1400 & 0.2326 \\ wei 0.34 & 0.05 & 1.6151 & 1750 & 0.2084 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimum rekeying rate for the WSN with different parameter sets of the Weibull distribution. Figure 4: The mitigation effectiveness of different random delay paddings. in this case, when we trigger the rekeying process more often, the security cost will decrease because the WSN is more likely to be brought back to the good working state. When we put all weight on the rekeying effort (\(w=1\)), the cost increases with the rekeying rate. The light color in the middle of the figure shows the optimum rekeying rate. For the middle values of the weighting parameter \(w\), the optimum rekeying rate for the lowest cost decreases when we put more weight on rekeying effort cost. For each specific rekeying rate \(\lambda_{1}\), the system cost is a straight line weighting the two kinds of cost. In this figure, we get the largest rekeying effort cost and lowest security cost at rate \(\lambda_{1}=2.0\). Figure 6 shows the system performance and security measures, i.e., system confidentiality \(\Lambda\) (defined in Equation (2)) and throughput \(X\) (defined in Equation (3)), changing with the rekeying rate \(\lambda_{1}\). It can be seen that the confidentiality measure monotonically increases with growing rekeying rate \(\lambda_{1}\), because the security improves when the system launches the rekeying process more frequently, as the system is more likely to be brought back to the good state from the timing attack state and the compromised state. While for the throughput measure, at small values of the rekeying rate, it is pretty low, because more time is spent in the compromised state when the throughput is not contributing. After obtaining the maximum throughput, the more often the gateway node triggers the rekeying act, the more often the gateway node denies sensor requests. As a result, the system throughput decreases with the rekeying rate. For a certain value of the rekeying rate \(\lambda_{1}\), the performance and security of WSNs are both improved when random paddings are interposed. At last, we present the security and performance tradeoff analysis for WSNs in Figure 7. The tradeoff measure \(T\), defined in Equation (4), increases with the rekeying rate \(\lambda_{1}\) at its low values, as the WSN security improves quickly. The rekeying rate \(\lambda_{1}\) indicates how often the system launches the rekeying process.