## 5 Performance Evaluation
### Communication Overhead  
In a wireless sensor network with battery-powered or self-charging node devices, to seamlessly monitor the environment, the nodes must be consistently active and periodically transmit data [32]. The proposed protocol aimed to assist the monitoring operation by lowering the complexity of establishing secure communication channels. At the minimum cost with level 1 security, the encapsulated material for session key generation was an identity of a node and a random point of the elliptic curve. This message \((ID_{N},C)\) cost \(8+32=40\) bytes. The communication overhead counted only the cost to establish the keys; thus, this message size excluded the size of the ciphertext. The computation overhead of a level 2 secure channel was higher compared with level 1, as it required two more messages. The request from a sensor node \((ID_{N},C^{\mathrm{f}},R_{n})\) was \(8+8+32=48\) bytes. The corresponding implicit certificate \((r,Cert_{N})\) was \(32+40=72\) bytes. In total, the handshake at level 2 security cost three exchange messages and 160 bytes. Note that the overall communication cost varied depending on the frequency of reissuing the key pairs.  
We compared our protocol with other existing key establishment schemes that also provide authentication properties in Table 3. In [14], the key establishment required two parties  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Features**} & **Proposed** & **Proposed** & **[14]** & **[28]** & **[29]** & **[30]** & **[31]** \\  & **Level 2** & **Level 1** & & & & & \\ \hline Mutual authentication & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Integrity & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\circ\) \\ Impersonation attack & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\circ\) \\ Session key attack & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\circ\) & \(\bullet\) & \(\bullet\) \\ Node capture attack & \(\bullet\) & \(\circ\) & \(\circ\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\circ\) \\ Perfect forward secrecy & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Replay attack & \(\bullet\) & \(\circ\) & \(\bullet\) & \(\bullet\) & \(\circ\) & \(\bullet\) & \(\circ\) \\ Message modification attack & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ Anonymity & \(\circ\) & \(\circ\) & \(\bullet\) & \(\bullet\) & \(\circ\) & \(\bullet\) & \(\circ\) \\ \hline \hline \end{tabular}  
* Secure against a particular attack or supports a particular feature. \(\circ\) Insecure against a particular attack or does not support a particular feature.  
\end{table}
Table 2: Comparison of functionality features of the proposed protocol with related protocols.  
to update information for consecutive communication. Excluding the registration phase, the protocol needed four exchange messages, with a total of 168 bytes. The research in [29] proposed two protocols, in which the handshake of the first protocol cost four exchange messages and 420 bytes, while the second one cost two messages and 142 bytes. In [28; 30], the size of messages to create an authenticated channel nearly doubled the cost of a proposed protocol at level 2 security with quantity.