The fusion of big data and cloud computing has established cloud services as the prime choice for data mining, making it a notable increase in individuals and organizations turning to cloud providers for data mining and storage needs. However, it raises significant concerns regarding data privacy. As a result, data owners commonly encrypt their data before sending it to the cloud, leading to complexities in balancing data privacy, result accuracy, and mining efficiency. To tackle these challenges, we introduce a set of privacy-preserving computational modules in a dual-cloud setup. Expanding on these modules, we present Apriori-based frequent itemset mining (FIM) and association rule mining (ARM) schemes, along with querying schemes, collectively designated as PrivARM. PrivARM caters to both cloud-defined and user-defined thresholds, ensuring strong privacy, result accuracy verification, and users’ offline. Theoretical analysis confirms the semi-honest security, while experiments in real transaction databases show practical feasibility. Moreover, comparative studies highlight the schemes’ advantages, including low computational overhead and minimal data transfer, achieving up to a 4 \(\times \) speedup.