## 8 Conclusions  
This paper provided the syntax expression and security formulation of LR-SP-IBBE and proposed an LR-SP-IBBE construction. The proposed construction had continual leakage resilience. Based on the general subgroup decision hypothesis, our proved to be secure under STD. By comparing the efficiency of our proposed scheme and relevant ones, our scheme had a better performance. The relative leakage ratio could almost reach 1. The scheme had the following advantages.  
The scheme had a continuous leakage-resilient performance, which can better reflect real application scenarios. In real applications, adversaries generally have a long-term attack capability.  
The scheme had a good leakage-resilient performance, and the almost complete disclosure of the encapsulated symmetric key could also ensure the security of the scheme, which benefited from the use of the extractor. The entropy lost by the symmetric key could be supplemented through the extractor so that the symmetric key had enough entropy to continue to maintain confidentiality.  
The scheme had anonymity that well protected the privacy of users. Users are very sensitive to privacy. They all want to effectively protect their privacy while also making cloud storage convenient. Therefore, the scheme proposed in this paper is very suitable for applications such as cloud storage services.  
In a health diagnosis system, patient data are very large and usually needs to be stored on a cloud platform. In light of personal privacy, the data need to be secure and anonymous. This system is very suitable for such application scenarios.  
Generally speaking, the computational efficiency of schemes in prime order groups is better than that in composite order groups. A method for constructing an anonymous broadcast encryption scheme in a prime order group is a subject we will study in the future.  
Conceptualization and methodology, Q.Y. and J.L.; formal analysis, Q.Y. and S.J.; writing--original draft preparation, Q.Y.; writing--review and editing, Q.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant Numbers: 62172292, 62072104, 61972095, and U21A20465).  
**Institutional Review Board Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Schemes** & **Length of Public Key** & **Length of Private Key** & **Length of Ciphertext** \\ \hline
[16] & \(|G_{\mathcal{T}}|+t(|G_{1}|+|G_{2}|)\) & \(3d|G_{1}|\) & \(|G_{\mathcal{T}}|+|G_{1}|+|G_{2}|\) \\
[17] & \(|G_{\mathcal{T}}|+|G_{1}|+t|G_{2}|\) & \(d|G_{2}|\) & \(d|G_{1}|+|G_{\mathcal{T}}|\) \\
[19] & \(5|G_{0}|\) & \(|G_{0}|\) & \((1+d)|Z_{\star}^{\star}|+3|G_{0}|\) \\
[21] & \(3|G_{0}|\) & \(2|G_{0}|\) & \(2d\big{[}Z_{\star}^{\star}\big{]}+2|G_{0}|\) \\
[25] & \(2|G_{1}|+|G_{2}|+|H_{1}|\) & \(3|G_{1}|\) & \(2|G_{1}|+|G_{2}|\) \\
[26] & \((t+1)(|G_{1}|+|G_{2}|)\) & \((t+1)|G_{1}|\) & \(2|G_{1}|+|G_{2}|\) \\
[28] & \((2t+1)|G_{1}|\) & \((t+2)|G_{1}|\) & \(2|G_{1}|+|G_{2}|\) \\
[29] & \(nm|Z_{q}|\) & \(n|Z_{q}|\) & \(2m\) \\
[35] & \((3+t+n)|G_{1}|+|G_{2}|\) & \((n+2)|G_{1}|\) & \((n+2)|G_{1}|+|G_{2}|\) \\
[62] & \((3+t)|G_{1}|+|G_{2}|\) & \(2|G_{1}|\) & \(2|G_{1}|+|G_{2}|\) \\ Ours & \((3+t)|G_{1}|+|G_{2}|\) & \(4|G_{1}|\) & \(2|G_{1}|+|G_{2}|\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of Storage Efficiency.