# A Key Management Scheme for Mobile Wireless Sensor Networks
## 4 Evaluation and Comparison
### Resilience  
The resilience corresponds to the ability to cope with the presence of compromised secret material. If an adversary compromises a node of a WSN, he/she could exploit the information stored by the compromised node to attack other parts of the network. Tables 4-6 show the probability that an opponent eavesdrops on a link between uncompromised nodes (rows with label \"link\") and the probability that a false node passes an authenticity check (rows with label \"check\"). By comparing PCAT to the other schemes for mobile networks, it is observed that the best level of resilience against eavesdropping is provided by FPWK, SSL and PCAT. The poorest level of resilience, corresponding to the theoretical minimum, is provided by PGK and SKKE. EG, 2C and 1-5C provide an intermediate value. If \(x\) nodes are compromised within the working phase, LEAP+ and FLEAP reach the best theoretical level of resilience, that is equal to PCAT. RSDTMK reaches a high level of resilience. If \(x\) nodes are compromised within the initialization phase, LEAP+ and FLEAP provide the worst level of resilience, like PGK and SKKE. RSDTMK provides the same level of resilience as EG. \begin{table}
\begin{tabular}{c c c} \hline
**Effect** & **FPWK and PCAT** & **PGK and SKKE** \\ \hline link & 0 & 1 \\ check & 0 & 1 \\ \hline \end{tabular}
\end{table} 
Table 6: Resilience of other approaches for mobile networks when \(x\) nodes are compromised. \begin{table}
\begin{tabular}{c c c} \hline
**Scheme** & **Connectivity** \\ \hline FPWK, PGK, SKKE, LEAP+, FLEAP SSL and PCAT & 1 \\ EG, 1–5C RSDTMK & \(1-\frac{(r_{r}^{-})}{(r)}\) \\
2C & \(1-\frac{(r_{r}^{-})+r(r_{r}^{-})}{(r)}\) \\ \hline Initialization & link & 1 \\ check & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Connectivity. \begin{table}
\begin{tabular}{c c c} \hline
**Phase** & **Effect** & **LEAP+ and FLEAP** & **RSDTMK** \\ \hline Working & link & 0 \\ check & 0 & \(1-\left(1-\frac{p}{p-1}\left(1-\frac{(r_{r}^{-})}{(r)}\right)+\left(1-\frac{p} {n-1}\right)\left(1-\frac{(r_{r}^{2p}-r)}{(r)}\right)\right)^{x}\) \\ \hline Initialization & link & 1 \\ check & 1 & \(1-\left(\frac{(r_{r}^{-})}{(r)}\right)^{x}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Resilience of state-of-the-art approaches for static networks when \(x\) nodes are compromised. \begin{table}
\begin{tabular}{c c c} \hline
**Effect** & **EG** & **2C** & **1–5C** \\ \hline link & \(1-(1-\frac{r}{p})^{x}\) & \(\sum_{l=2}^{\frac{r}{(r)}(r_{r}^{-})-(r_{r}^{-})-x}\sum_{j=0}^{j}{(i)(-1)^{ \prime}(r_{r}^{-})}\) \\ \(\frac{(r_{r}^{-})-(r_{r}^{-})}-(r_{r-1}^{-})\) & \(\sum_{l=1}^{\frac{r}{(r)}(r_{r}^{-})(r_{r}^{-})-x}\sum_{j=0}^{\frac{\text{Min}( i)}{(r_{r}^{-})}(\frac{\text{Min}(i)S}{j})(-1)^{\prime}(r_{r}^{-})}\) \\ \(\frac{(r_{r}^{-})-(r_{r}^{-})}{(r_{r}^{-})}\) \\ \(\frac{(r_{r}^{-})-(r_{r}^{-})}\) \\ \(\frac{(r_{r}^{-})^Among the schemes for mobile networks, FPWK, SSL and PCAT provide the best resilience against false authentication. In addition, 2C and 1-5C provide a better resilience than EG, while PGK and SKKE provide no resilience. Among the schemes for static networks if the nodes are compromised in the working phase, LEAP+ and FLEAP provide the best resilience, like PCAT. RSDTMK reaches a level of resilience close to the optimum and better than 2C and 1-5C. If \(x\) nodes are compromised in the initialization phase, LEAP+ and FLEAP provide the worst level of resilience, like PGK and SKKE, while RSDTMK provides the same level of resilience as EG. Even in this case, FPWK, SSL and PCAT provide the best level of resilience. According to the described case study, and to the provided formulas, the limit of the network size of PCAT, according to (2), corresponds to 92 nodes, while the upper bound of FPWK, according to (1), is 33 nodes. Figures 6 and 7 show the probability of eavesdropping if \(x\) nodes are compromised within the working phase or in the initialization phase, respectively.