# Supervised Blockchain Anonymous Transaction Model Based on Certificateless Signcryption
## 7 Experimental Analysis
### Computational Overhead Analysis  
In this study, a bilinear pairing \(e:G_{1}\times G_{1}\to G_{2}\) was selected to achieve an 80-bit security level. Here, \(G_{1}\) is a supersingular elliptic curve defined over the finite field \(F_{q}\) with the equation \(E:y^{2}=x^{3}+x\) mod \(q_{1}\), where \(p_{1}\) is a 512-bit large prime number and \(q_{1}\) is a 160-bit large prime number. For the elliptic curve scheme, an elliptic curve \(E:y^{2}=x^{3}+ax+b\) mod \(q_{2}\) was chosen, with \(a,b\in Z_{q}^{*}\). The execution time of cryptographic operations was calculated using the C language under the PBC library, with each operation executed 1000 times. The average time consumption for each operation is presented in Table 4.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Time/ms** \\ \hline Setup & 1.591 \\ CreateAddr & 3.464 \\ CreateRkey & 0.014 \\ SetPartialKey & 1.616 \\ SetKey & 1.577 \\ CreateTx & 1.406 \\ VerifyTx & 0.032 \\ RenewalTx & 0.036 \\ TraceTx & 1.824 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time consumption of algorithms in CLSC_SAT.  
To evaluate the computational complexity, the computational overhead of the signature and verification algorithms in the CLSC_SAT model was compared with that of reference [21; 22; 23; 24; 25], focusing on the time consumption for signing and verifying signatures, as shown in Table 5. The results indicate that the CLSC_SAT model performs better in terms of computational cost. The signing algorithm time of reference [21] is close to that of the CLSC_SAT model, but its verification algorithm time is approximately three times that of the CLSC_SAT model. The signing and verification algorithm times of reference [22] are the same but are higher than those of the CLSC_SAT model. Reference [23], based on bilinear pairing operations, has the highest time consumption for both signing and verification algorithms. Although the verification algorithm time of reference [24] is the same as that of the CLSC_SAT model, its signing time is approximately three times that of the CLSC_SAT model. The signing and verification algorithm times of reference [25] are almost identical, but all of them are higher than the CLSC_SAT model. Therefore, the CLSC_SAT model improves signing efficiency by 33.18%, 45.29%, 33.22% and 33.5% compared to references [22; 23; 24; 25], respectively, and improves verification efficiency by 66.81%, 66.64%, 94.29%, and 66.88% compared to references [21; 22; 23; 24; 25], respectively. The experiments demonstrate that the CLSC_SAT model achieves higher signing and verification efficiency while protecting identity privacy compared to other schemes.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Operation** & **Description** & **Running Time/ms** \\ \hline \(T_{bp}\) & Bilinear pair pairing operation & 3.049 \\ \(T_{bp}^{\text{sh}}\) & Scalar multiplication based on pairing & 1.136 \\ \(T_{bp}^{\text{sh}}\) & Point addition based on pairing & 0.007 \\ \(T_{bp}^{\text{sh}}\) & Scalar multiplication on elliptic curves & 0.928 \\ \(T_{occ}^{\text{sh}}\) & Point addition on elliptic curves & 0.006 \\ \(T_{mpf}\) & Map\_to\_point hash function & 2.440 \\ \(T_{h}\) & One-way hash function & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average runtime for cryptographic operations in PBC library.  
Figure 3: Time in different transactions under the account model.  
The calculation cost of CLSC_SAT model with references [21; 22; 23; 24; 25] signature and verification is shown in Figure 4.