## 5 Spatio-Temporal Big Data Collaborative Storage Mechanism
### Aggregation Proof Protocol
## 7 Conclusions

The proposed on-chain and off-chain collaborative storage system model architecture for processing large-scale spatio-temporal big data has important research significance. First, by utilizing incrementally aggregatable subvector commitments built on RSA, an efficient on-chain and off-chain collaborative storage scheme is implemented. This not only improves the communication efficiency of the system but also significantly reduces the computational overhead in the setup phase, providing a practical solution for the secure storage of large-scale spatio-temporal data. Secondly, the aggregation proof protocol designed in this study allows query set-based aggregation or decomposition proofs in the verification phase and is integrated with smart contracts. This design not only enhances the system's processing efficiency for update and verification transactions but also improves the overall operational performance and response speed of the system. In practical applications, these innovations not only help manage and protect large amounts of spatio-temporal big data containing time and geographic information tags, but also ensure the consistency and integrity of data storage. Future work prospects include further optimization of algorithms and protocols to improve the scalability and adaptability of the system, especially in the face of growing data size and complexity. In addition, more in-depth security analysis can be explored, including further research and testing of attack models to ensure the robustness and security of the system in the face of various threats. In summary, the research work proposed in this paper provides a solid theoretical foundation and practical application value for solving the security and efficiency challenges of large-scale spatio-temporal big data storage and, at the same time, lays the foundation for in-depth exploration and innovation in related fields in the future. Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON]; validation, [PERSON]; formal analysis, [PERSON] and [PERSON]; writing--original draft preparation, [PERSON] and [PERSON]; writing--review and editing, [PERSON] and [PERSON]; supervision, [PERSON]; project administration, [PERSON] and [PERSON]. 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 No. 62072249). No new data were created nor analyzed in this study. Data sharing is not applicable to this article. The authors declare no conflicts of interest. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Operation** & **Sending** & **Max** & **Min** & **Avg** & **Throughput/TPS** \\  & **Rate/TPS** & **Delay/s** & **Delay/s** & **Delay/s** & \\ \hline Verification & 376.58 & 24.99 & 10.9 & 13.11 & 17.06 \\ Verification & 379.43 & 24.94 & 11.09 & 13.04 & 17.07 \\ Verification & 383.42 & 24.98 & 11.01 & 12.87 & 17.01 \\ Aggregation & 302.18 & 45.38 & 19.12 & 42.28 & 10.98 \\ Aggregation & 299.84 & 44.70 & 18.94 & 42.10 & 11.07 \\ Aggregation & 300.36 & 44.56 & 18.98 & 42.33 & 10.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Execution efficiency of verification and aggregation. ## References

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