## 6 Performance Evaluation
### Computational cost  
By altering the quantity of files and \(dg_{i}\) in Table 4, we used the cryptographic primitives and assessed the computational cost of the suggested algorithms. We can calculate the computing cost of the proposed design using this method. The proposed technique uses the Encrypt algorithm to construct keyword ciphertexts (\(k\)) and environmental data ciphertexts (\(E_{d_{i}}\)). To ascertain whether the keyword in the token (\(\tau\)) provided by the \(dr\) is a member of the keyword set (\(K\)), the \(dg_{i}\) performs a verification process.The \(dr\) can utilize the Trapdoor algorithm to obtain a trapdoor (\(T_{i}\)) if the verification is successful. The trapdoor (\(T_{i}\)) is then sent to the FS, enabling the Search algorithm to efficiently locate the desired keywords. Finally, the \(dr\) decrypts the environmental data ciphertexts (\(E_{d_{i}}^{\prime}\)) using the symmetric key (\(SS_{agg}\)) in the decryption and verification procedures. As shown in Table 4, we ran the algorithms with a file count of 100 and a total of 40 data generators (\(l=40\)) in each situation. We observe that the amount of files (\(n\)) affects the computational costs of all algorithms, as they all operate with the files. Additionally, we used 100 \(dg_{i}\)s to implement the algorithms while keeping the file count at \(n=100\). The findings show that when the number of \(dg_{i}\) rises, the computational costs of the encryption, trapdoor, decryption, and verification algorithms remain effective. The reason for this efficiency is that these algorithms use the \(dg_{i}\) values of information to execute pairing computations. Additionally, the computational cost analysis of each algorithm in the proposed scheme is compared with other relevant studies. While maintaining a fixed graph degree for the \(dg_{i}\), amounting to \(l=40\), the methods proposed by [PERSON] et al. [19] and [PERSON] et al. [25] are taken into consideration. As illustrated in Figure 2, the computation cost of encryption for each solution fluctuates in direct proportion to the quantity of files, denoted as \(n\). Among the three schemes, [PERSON] et al. 's [19] scheme incurs the highest computational cost. This is primarily due to its reliance on a greater number of bilinear operations in comparison with the other works. Additionally, the trapdoor algorithm in the scheme proposed by [PERSON] et al. [25] necessitates extra computations operations, further increasing its cost relative to that of [PERSON] et al. 's [19] scheme and the proposed scheme. \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Trapdoor** & **Search** & **Encryption** & **Encryption** \\ \hline \(n=100\) and \(l=40\) & 27 & 53 & 5160 & 9 \\ \hline \(l=100\) and \(n=100\) & 27 & 53 & 5160 & 9 \\ \hline \end{tabular}
\end{table} 
Table 4: Computational cost of the proposed scheme. With a file size of \(n=100\), we examine the computational cost of each procedure for different values of \(dg_{i}\) and \(l\). For the methods proposed by [PERSON] et al. [19] and [PERSON] et al. [25], the computational cost of encryption is significantly higher than that of the proposed approach, as illustrated in Figure 2. As the number of \(dg_{i}\)s increases, the computational cost exhibits a linear rise. This is due to the encryption technique employed in the proposed system, which requires relatively few hash functions and bilinear pairing computations. [PERSON] et al. [25] and [PERSON] et al. [19] indicated that the trapdoor algorithm incurs a greater computational cost than the proposed scheme, as it necessitates more complex calculations. According to [PERSON] et al. [25], each \(dg_{i}\) must perform several bilinear pairing operations during the search process. Consequently, the computational cost increases with the number of \(dg_{i}\)s because additional bilinear pairing operations are required. In contrast, the computational cost of the proposed strategy remains constant, as it is independent of the number of \(dg_{i}\)s. According [PERSON] et al.