# Public Key-Based Authentication and En-Route Filtering Scheme in Wireless Sensor Networks
## 5 Performance Analysis
### Security Analysis  
The authors will compare the security performance of DSEDA, PDF, and PKAEF according to the following aspects: (1) security of private key; (2) resilience to false report injection attacks; (3) resilience to report disruption attacks launched by a non-CH node (a cluster node which is not a CH node); (4) resilience to report disruption attacks launched by a CH node; (5) resilience to selective forwarding attacks; (6) malicious nodes detection and isolation. **Theorem 1**. : _PKAEF has a more secure private key than DSEDA and PDF, and PDF has a more secure private key than DSEDA._  
**Proof. ** Regarding DSEDA, each CH node holds a private key used for signing the event reports. The adversary just needs to compromise a CH to obtain its private key and it is easy for the adversary to find and capture a CH because the CHs and sensor nodes are heterogeneous in DSEDA. Concerning PDF, all nodes in the network share a unique system private key based on the [PERSON]'s secret sharing technique. Thus, the adversary needs to compromise \(t\) nodes to derive the system private key. Therefore, PDF has a more secure private key than DSEDA, however, the adversary just needs to compromise any \(t\) nodes anywhere in the network to derive the system private key in PDF. Looking at PKAEF, each cluster private key is shared by the sensor nodes in the cluster. Thus, to derive a cluster private key, the adversary has to compromise \(t\) sensor nodes in that cluster rather than in the whole network. Therefore, PKAEF has a more secure private key than PDF. Finally, PKAEF has a more secure private key than DSEDA and PDF, and PDF has a more secure private key than DSEDA. \(\square\)  
**Theorem 2. **_PKAEF is more resilient to false report injection attacks than PDF and DSEDA, and PDF is more resilient to such attacks than DSEDA._  
**Proof. ** Regarding PDF, the adversary has to compromise at least \(t\) sensor nodes in the network to deduce the system private key; therefore, PDF can resist false report injection attacks when less than \(t\) sensor nodes in the network are compromised. Looking at PKAEF, the adversary has to compromise at least \(t\) sensor nodes in the same cluster to derive the cluster private key; therefore, PKAEF can resist false report injection attacks when less than \(t\) sensor nodes in the same cluster are compromised. It is generally more difficult for the adversary to capture \(t\) sensor nodes in the same cluster than to capture \(t\) sensor nodes in the whole network; therefore, PKAEF is more resilient to false report injection attacks than PDF. Concerning DSEDA, if a CH node is compromised it can successfully forge false reports with legitimate signatures using its private key. Since the CHs are fixed after deployment and the CHs and sensor nodes are heterogeneous, the adversary easily can find and capture the CHs; therefore, DSEDA is generally more vulnerable to false report injection attacks than PDF and PKAEF. To conclude, PKAEF is more resilient to false report injection attacks than PDF and DSEDA, and PDF is more resilient to such attacks than DSEDA. \(\square\)  
**Theorem 3. **_PKAEF is more resilient to report disruption attacks launched by a non-CH node than DSEDA, and PDF cannot resist such attacks._  
**Proof. ** Regarding DSEDA, if a compromised non-CH node participating in report generation provides a secret share with an incorrect MAC, or refuses to provide a secret share, then an alternative secret share from a non-participating node will be sent to the CH. The CH cannot verify the correctness of a secret share, however. Thus, a compromised non-CH node participating in report generation might forge a wrong secret share and generate a correct MAC for it to pass the MAC verification of the CH. When the report with wrong secret shares reaches the BS, the BS will recover the wrong event information. To summarize, DSEDA only can combat report disruption attacks launched by a non-CH node to a certain extent.