## 4 Proposed Protocol Procedure
### Registration Phase  
In the overarching steps of the provided protocol, the initial stage considered for the node is to successfully complete the registration phase. This phase must be completed at least one time by the node that intends to enter the network. In cases where a node has experienced prolonged disconnection to the network for a considerable time, it is required to repeat the registration phase steps and undergo authentication. During the initial step, the node picks a random number, referred to as \(\mathrm{r_{i}}\). The purpose of using random numbers is to ensure that the parameters generated in each step are unique and distinct. Following that, the subsequent node operation results in the calculation of the Ri value, which is derived from the fusion of random numbers and the node's private key. This value is an anonymous technique for utilizing the node's private key within the protocol process. The motivation behind the generation of this parameter is to utilize the node's private parameters indirectly in generating the \"authentication certificate\" parameter, allowing authentication to be implemented using the private parameters of both entities within the protocol process. It also contributes to the resilience of the showcased protocol against identity forgery attacks. By indirectly using the private keys, the protocol leverages their properties in generating secure parameters while maintaining the confidentiality of the private parameters.  
\[\mathrm{Ri}=\mathrm{H}(\mathrm{(PVNODE}^{*}\mathrm{ri)}\ |\ |\ \mathrm{ri}\ |\ \mathrm{PUNODE}) \tag{1}\]  
In the final step of the process, the node securely transmits the value \(\mathrm{R_{i}}\) and \(\mathrm{ID_{NODE}}\) to the server, along with its public key. Next, the server selects random numbers, \(\mathrm{f_{i}}\), and uses the technique of generating anonymous values for the indirect utilization of its private key, as described earlier. Subsequently, the server generates the value \"\(\mathrm{L_{i}}\)\" by combining these random numbers with its private key. Then, the server generates the required certificate of the node by generating the value of \"\(\mathrm{L_{i}}\)\" in the next operation. The \"\(\mathrm{AC_{i}}\)\" certificate is calculated using \"\(\mathrm{L_{i}}\)\" and \"\(\mathrm{R_{i}}\)\" values.  
\[\mathrm{L_{i}}=\mathrm{H}(\mathrm{(PV_{SERVERER}}^{*}\mathrm{f_{i}})\ |\ |\ \mathrm{f_{i}}\ |\ \mathrm{PU_{SERVER}}) \tag{1}\]  
\[\mathrm{AC_{i}}=\mathrm{H}(\mathrm{R_{i}}\ |\ |\ \mathrm{L_{i}}) \tag{2}\]  
Finally, the server sends the \(\mathrm{AC_{i}}\) parameter to the node using a secure channel. In Figure 2, the registration process is outlined alongside the values utilized in this process.  
\begin{table}
\begin{tabular}{c c} \hline
**Symbol** & **Definition** \\ \hline ID & Identity of the Node \\ \(\mathrm{PUNODE}\) & Public Key of The Node \\ \(\mathrm{PU_{SERVERER}}\) & Public Key of the Server \\ \(\mathrm{PV_{NODE}}\) & Private Key of the Node \\ \(\mathrm{PV_{SERVERER}}\) & Private Key of the Server \\ \(\mathrm{d_{i}}\), \(\mathrm{f_{i}}\), \(\mathrm{r_{i}}\), \(\mathrm{a_{i}}\), \(\mathrm{b_{i}}\), \(\mathrm{c_{i}}\) & Used Random Numbers in the protocol \\ \(\mathrm{H}\) & One-way Hash Function \\ \(\mathrm{P}\) & The Base Point \\ \(\mathrm{AC}\) & The Authentication Certificate \\ SK & The Session Key \\ \(\mathrm{E_{N(x)}}\) & Encrypted by Symmetric Key \\ \hline \end{tabular}
\end{table}
Table 1: The parameters utilized in the presented protocol.