Privacy Probability Computation for Privacy-Preserving Statistical Analysis Under Multisource Real-Valued Data

Privacy-preserving statistical analysis (PSA) over distributed datasets is essential for achieving a balance between data utility and privacy protection. This process requires supporting diverse queries on sensitive data while ensuring both data and queries confidentiality. However, the existing Privacy Probability Computation (PPC) methods are typically restricted to discrete point queries due to their reliance on interpolation techniques. Consequently, how to effectively support range queries over continuous, real-valued datasets in distributed systems, e.g., IoT, remains an open and challenging research problem. To address this challenge, we introduce an AQF-PPC method on real-valued data. This method employs Ideal Counting Functions (ICFs) on closed and half-closed intervals to construct Approximate Query Functions (AQFs), thereby facilitating the integration with existing fully homomorphic encryption (FHE) techniques. To accommodate varying precision requirements, translating-and-scaling operations can be applied on the AQFs, enabling flexible query processing. Furthermore, for multi-attribute dataset, the AQF-PPC can efficiently compute various probabilities, e.g., basic, joint and conditional probabilities, thereby supporting a wide range of statistical analysis. Accuracy should be guaranteed by the proposed method, while corresponding theorems are used to prove it. In security analysis, this method has been proven to be statistically secure against chosen element attack, protecting both data and query privacy. Performance evaluation exhibits a computational complexity ofO(nm)and a communication complexity ofO(n2m), for n service providers and a dataset of sizem. These properties make AQF-PPC a practical and scalable solution for PSA in IoT environments.