## 7 Performance Analysis
### Efficiency Analysis
#### 7.2.2 Simulation Experiments
Although scheme [18] achieves faster execution, requiring only a single \(G_{0}\) operation, it does so by modifying only the \(D\) component while keeping other components unchanged, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Operator** & **Hash** & \(\mathbf{G_{0}}\) & \(\mathbf{G_{T}}\) & \(\mathbf{C_{e}}\) \\ \hline Execution Time & 21.752 ms & 13.006 ms & 1.088 ms & 7.82 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Execution time of different cryptographic operations. Figure 4: Comparison of computational overhead among different schemes [18; 29; 30; 31]: (**a**) Key generation. (**b**) Encryption. (**c**) Proxy key generation. (**d**) Decryption. which increases a potential risk of key leakage. In contrast, both our scheme and the study of [29] introduce randomness into each component, significantly enhancing security. This added security measure results in a decryption time that is higher than that of [18] but lower than that of [29], achieving a balance between performance and security. In Figure 4d, our scheme exhibits superior efficiency in decryption time, achieving lower computational overhead compared to other schemes while maintaining strong security guarantees. Although its decryption time is comparable to that of scheme [18], as shown in Figure 3c, it is important to note that the decryption time includes both the CN's and CR's decryption processes. In our scheme, the majority of the decryption workload is offloaded to the CN, thereby significantly reducing the burden on resource-constrained devices. Moreover, our scheme optimises bilinear pairing operations, further enhancing decryption efficiency without compromising access control security. It is also observed that the decryption time of [29] increases sharply, primarily due to the introduction of an additional pairing computation for each element in the set \(|S|C_{e}\). This extra operation, designed to enable outsourced decryption and enhance key security, results in a noticeably higher decryption overhead compared to our scheme. Figure 5 illustrates the relationship between the number of attributes and the size of attribute keys across various schemes. As shown, our proposed scheme, along with [18; 29; 30], exhibits relatively low key storage overhead, maintaining compact key sizes as the number of attributes increases. In contrast, the study of [31] incurs notably higher storage overhead due to its key structure comprising two distinct components: one for attribute-based access control, and the other for the keyword matching key. This dual structure significantly increases the overall storage requirements. In summary, although our scheme may not afford the fastest execution time, it offers significant advantages in terms of security, flexibility, and scalability. By incorporating randomness, it reduces the risk of key leakage, while its architecture, which is designed to operate without a CA, simplifies key management and reduces costs. Traditional CA-based systems often face challenges such as centralised control, single points of failure, scalability issues, and increased operational overhead, making them less suitable for dynamic and distributed environments. In contrast, our scheme eliminates these limitations, serving as an adaptable and efficient multi-scenario framework for strategic alliances or conglomerates. It enables secure and efficient access control and resource sharing across organisations. Under multi-attribute conditions, it effectively addresses the complexities of environments such as joint ventures and shared services, making it a robust solution for scenarios requiring both security and operational efficiency. Figure 5: Comparison of key storage overhead across schemes with varying numbers of attributes [18; 29; 30; 31].