Approximate Homomorphic Encryption for MLaaS by CKKS with Operation-Error-Bound

As data analysis often incurs significant communication and computational costs, these tasks are increasingly outsourced to cloud computing platforms. However, this introduces privacy concerns, as sensitive data must be transmitted to and processed by untrusted parties. To address this, fully homomorphic encryption (FHE) has emerged as a promising solution for privacy-preserving Machine-Learning-as-a-Service (MLaaS), enabling computation on encrypted data without revealing the plaintext. Nevertheless, FHE remains computationally expensive. As a result, approximate homomorphic encryption (AHE) schemes, such as CKKS, have attracted attention due to their efficiency. In our previous work, we proposed RP-OKC, a CKKS-based clustering scheme implemented via TenSEAL. However, errors inherent to CKKS operations—termed CKKS-errors—can affect the accuracy of the result after decryption. Since these errors can be mitigated through post-decryption rounding, we propose a data pre-scaling technique to increase the number of significant digits and reduce CKKS-errors. Furthermore, we introduce an Operation-Error-Estimation (OEE) table that quantifies upper-bound error estimates for various CKKS operations. This table enables error-aware decryption correction, ensuring alignment between encrypted and plaintext results. We validate our method on K-means clustering using the Kaggle Customer Segmentation dataset. Experimental results confirm that the proposed scheme enhances the accuracy and reliability of privacy-preserving data analysis in cloud environments.