In the era of big data, there has been a significant surge in the volume of data generated from diverse sources such as social media platforms, e-commerce websites, and Internet of Things (IoT) devices. This increase has led to an uptick in the dimensionality of the data. High-dimensional data escalates the costs associated with storage and processing and presents formidable challenges for data analysis and machine learning model training. Concurrently, most data encompasses personal privacy and ethical considerations and is dispersed across various institutions. Consequently, devising efficient and secure methods for joint high-dimensional data dimension reduction has emerged as a pivotal technology for addressing these issues. This paper proposes a novel CKKS-based homomorphic encryption dimensionality reduction scheme(HE-DR), which combines the Rank-Revealing(RR) method's computational efficiency and homomorphic encryption's security to achieve fast and secure dimension reduction for high dimensional data. Our proposed scheme circumvents the necessity for data matrix encryption and the computation and transmission of ciphertext matrices. Consequently, compared with recent dimension reduction schemes based on fully or partially homomorphic encryption, our approach demonstrates nearly 60–200 times faster computational efficiency and less than 1/3 of the communication overhead previously observed in similar schemes. Furthermore, we demonstrate that our scheme maintains its computational efficiency even when dealing with high-dimensional data, requiring only five times the plaintext calculation time.