Merging multi-source time series data in cloud servers significantly enhances the effectiveness of analyses. However, privacy concerns are hindering time series analytics in the cloud. Responsively, numerous secure time series analytics schemes have been designed to address privacy concerns. Unfortunately, existing schemes suffer from severe performance issues, making them impractical for real-world applications. In this work, we propose novel secure time series analytics schemes that break through the performance bottleneck by substantially improving both communication and computational efficiency without compromising security. To attain this, we open up a new technique roadmap that leverages the idea of mixed model. Specifically, we design a non-interactive secure Euclidean distance protocol by tailoring homomorphic secret sharing to suit subtractive secret sharing. Additionally, we devise a different approach to securely compute the minimum of three elements, simultaneously reducing computational and communication costs. Moreover, we delicately introduce a rotation concept, design a rotation-based hybrid comparison mode, and finally propose our fast secure top-$k$protocol that can dramatically reduce comparison complexity. With the above secure protocols, we propose a practical secure time series analytics scheme with exceptional performance and a security-enhanced scheme that considers stronger adversaries. Formal security analyses demonstrate that our proposed schemes can achieve the desired security requirements, while the comprehensive experimental evaluations illustrate that our schemes outperform the state-of-the-art scheme in both computation and communication.

A corpus of recent work has revealed that the learned index can improve query performance while reducing the storage overhead. It potentially offers an opportunity to address the spatial query processing challenges caused by the surge in location-based services. Although several learned indexes have been proposed to process spatial data, the main idea behind these approaches is to utilize the existing one-dimensional learned models, which requires either converting the spatial data into one-dimensional data or applying the learned model on individual dimensions separately. As a result, these approaches cannot fully utilize or take advantage of the information regarding the spatial distribution of the original spatial data. To this end, in this paper, we exploit it by using the spatial (multi-dimensional) interpolation function as the learned model, which can be directly employed on the spatial data. Specifically, we design an efficient SPatial inteRpolation functIon based Grid index (SPRIG) to process the range and kNN queries. Detailed experiments are conducted on real-world datasets. The results indicate that, compared to the traditional spatial indexes, our proposed learned index can significantly improve the index building and query processing performance with less storage overhead. Moreover, in the best case, our index achieves up to an order of magnitude better performance than ZM-index in range queries and is about 2.7 × , 3 × , and 9 × faster than the multi-dimensional learned index Flood in terms of index building, range queries, and kNN queries, respectively.