# Supervised Blockchain Anonymous Transaction Model Based on Certificateless Signcryption
## 7 Experimental Analysis
### Communication Overhead Analysis  
The communication overhead of the CLSC_SAT model is primarily analyzed based on the size of the elements required for signature transmission, including the anonymous identity \(EID_{i}\), public key \(PK_{i}\), signature \(\sigma_{i}\), and timestamp \(t_{i}\). In the elliptic curve constructed in this paper, the sizes of \(q_{1}\) and \(q_{2}\) are 64 bytes and 20 bytes, respectively. Therefore, elements in \(G_{1}\) and \(G\) occupy 128 bytes and 40 bytes, respectively. Assuming that elements in \(Z_{q}^{*}\) occupy 20 bytes and the timestamp occupies 4 bytes, the space occupied by different types of data elements is shown in Table 6.  
To compare the commonalities of various schemes, this paper focuses solely on the size of the signatures. A comparison of communication overhead with the literature is presented in Table 7. It can be observed that the signature overhead in this study is the lowest, and the transmission overhead is only higher than that of reference [23].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Element** & **Size/Bytes** & **Description** \\ \hline \(|G_{1}|\) & 128 & Size occupied by elements in group \(G_{1}\). \\ \(|G_{i}|\) & 40 & Size occupied by elements in group G. \\ \(|Z_{q}^{*}|\) & 20 & Size occupied by elements in \(Z_{q}^{*}\). \\ \(|T|\) & 4 & Size occupied by timestamp. \\ \hline \hline \end{tabular}
\end{table}
Table 6: Different types of elements occupy the space size.  
Figure 4: Comparison of signature generation and verification time [21; 22; 23; 24; 25].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Scheme** & **Signature Algorithm/ms** & **Verification Algorithm/ms** \\ \hline
[21] & \(2T_{exc}^{sm}+2T_{h}\approx 1.858\) & \(3T_{exc}^{sm}+3T_{exc}^{pl}+3T_{h}\approx 2.805\) \\
[22] & \(3T_{exc}^{sm}+T_{exc}^{pl}+T_{h}\approx 2.791\) & \(3T_{exc}^{sm}+T_{exc}^{pl}+T_{h}\approx 2.791\) \\
[23] & \(3T_{exc}^{sm}+T_{h}\approx 3.409\) & \(3T_{bp}+T_{bp}^{2}+2T_{antp}+T_{h}\approx 16.3\) \\
[24] & \(3T_{exc}^{sm}+T_{bp}^{pl}+3T_{h}\approx 2.793\) & \(T_{exc}^{sm}+3T_{h}\approx 0.931\) \\
[25] & \(3T_{exc}^{sm}+T_{bp}^{pl}+4T_{h}\approx 2.806\) & \(3T_{exc}^{sm}+4T_{exc}^{pl}+3T_{h}\approx 2.811\) \\ CLSC\_SAT & \(2T_{exc}^{sm}+T_{exc}^{pl}+3T_{h}\approx 1.865\) & \(T_{exc}^{sm}+3T_{h}\approx 0.931\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of computational costs.  
In the CLSC_SAT model, \(tx_{send}=(EID_{i},PK_{i},\sigma_{i},t_{i})\), where \(EID_{i}\) occupies \(|G|+|Z_{q}^{*}|+|T|=64\) bytes, \(PK_{i}\) occupies \(2|G|=80\) bytes, \(\sigma_{i}\) occupies \(|G|+3|Z_{q}^{*}|=100\) bytes, and \(t_{i}\) occupies \(|T|=4\) bytes. Therefore, the total transmission signature overhead is \(4|G|+4|Z_{q}^{*}|+2|T|=248\) bytes. Similarly, taking references [22; 23] as examples, in reference [22], \(tx_{send}=(\sigma_{i},QID_{i},FID^{i},T_{i})\), where \(QID_{i}\) occupies \(|Z_{q}^{*}|=20\) bytes, \(FID^{i}\) occupies \(|G_{1}|+|Z_{q}|^{*}+|T|=152\) bytes, \(\sigma_{i}\) occupies \(|G_{1}|+|Z_{q}^{*}|=148\) bytes, and \(T_{i}\) occupies \(|T|=4\) bytes. Thus, the total transmission signature communication overhead is \(2|G_{1}|+3|Z_{q}^{*}|+2|T|=324\) bytes. In reference [23], \(tx_{send}=(PID_{i},vpk_{i},\sigma_{i},t_{i})\), where \(PID_{i}\) occupies \(|G_{1}|+|Z_{q}^{*}|+|T|=152\) bytes, \(\sigma_{i}\) occupies \(|G_{1}|=128\) bytes, \(|G_{1}|+|Z_{q}^{*}|=148\) bytes, and \(t_{i}\) occupies \(|T|=4\) bytes. Therefore, the total transmission signature overhead is \(3|G_{1}|+2|Z_{q}^{*}|+2|T|=432\) bytes. A comparison of communication overhead between this work and references [22; 23; 24; 25] is illustrated in Figure 5.