# Public Key-Based Authentication and En-Route Filtering Scheme in Wireless Sensor Networks
## 5 Performance Analysis
### Overhead Analysis  
#### 5.2.1 Communication Overhead  
1 Communication overhead for report generation  
The communication overhead for report generation is measured as the message overhead during the report generation phase. A 160-bit elliptic curve is chosen for DSEDA, PDF, and PKAEF. Then, the lengths of the base point, public key, private key, and the order are 40 bytes, 40 bytes, 20 bytes, and 20 bytes respectively. During the report generation phase in DSEDA, each of the \(T\) participating sensor nodes needs to send its {\(E_{u}\), \(u\), MAC\({}_{Ku,CH}\)(\(E_{u}\), \(u\))} to the CH. Suppose that the lengths of node ID, \(E_{u}\), and MAC are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Security Performance** & **PKAEF** & **PDF** & **DSEDA** \\ \hline Security of private key & High & Moderate & Low \\ Resilience to false report injection attacks & High & Moderate & Low \\ Resilience to report disruption attacks launched by a & High & Poor & Low \\ non-cluster head (CH) node & High & Poor & Poor \\ Resilience to report disruption attacks launched by a CH node & High & Poor & Poor \\ Resilience to selective forwarding attacks & High & Poor & Poor \\ Malicious nodes detection and isolation & Yes & No & No \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of security performance. 1 byte, 8 bytes, and 8 bytes, respectively, and (\(T\), \(t\)) = (6, 5). Then, the total message overhead for report generation in DSEDA is 102 bytes. Regarding PDF, the message overhead for report generation includes four parts: (a) to share a random \(k\), each of the \(t\) participating nodes needs to send a share of secret \(f_{si}\)(\(S_{j}\)) to each of the other \(t-1\) participating nodes. The message overhead is \(t\times(t-1)\times 20\) bytes. (b) The \(t-1\) participating nodes except the CH, need to send \(k_{i}l_{i}P\) to the CH. The message overhead is (\(t-1\)) \(\times\) 40 bytes. (c) The CH needs to broadcast \(R\). The message overhead is 40 bytes. (d) The \(t-1\) participating nodes, except the CH, need to send their partial signatures to the CH. The message overhead is (\(t-1\)) \(\times\) 20 bytes. When \(t\) = 5, as set in DSEDA, then the total message overhead for report generation in PDF is 680 bytes. When PDF uses pre-computation to reduce the communication overhead for \(k\) sharing, then the message overhead in part (a) can be saved, and the total message overhead for report generation will be 280 bytes. Regarding PKAEF, the message overhead for report generation includes four parts: (a) a cluster node broadcasts its observed event values {\(E\), \(L_{e}\), \(t_{e}\)} for selecting participating nodes. (b) The \(t-1\) participating nodes except the CH, need to send \(k_{j}P\) to the CH. The message overhead is (\(t-1\)) \(\times\) 40 bytes. (c) The CH needs to broadcast \(X(R)\). The message overhead is 20 bytes. (d) The \(t-1\) participating nodes, except the CH, need to send their partial signatures to the CH. The message overhead is (\(t-1\)) \(\times\) 20 bytes. When the lengths of \(E\), \(L_{e}\), and \(t_{e}\) are 4 bits, 20 bits, and 4 bytes respectively, and \(t\) = 5 as set in DSEDA, then the total message overhead for report generation in PKAEF is 267 bytes. It can be seen that the message overhead for report generation in PDF is the highest, most of which is incurred by the sharing of \(k\). PKAEF reduces the message overhead for report generation by making each participating node pick a random \(k_{j}\) rather than \(k\) sharing and, by making the CH broadcast \(X(R)\) rather than \(R\). The message overhead for report generation in DSEDA is the lowest, since the event report in DSEDA is signed by the CH rather than the \(t\) participating nodes, however, that the private key is kept by a single node will result in poor security of the private key.