THC-DL: Three-Party Homomorphic Computing Delegation Learning for Secure Optimization
Ze Yang, Youliang Tian, Jinbo Xiong, Kun Niu, Mengqian Li, Xinyu Zhang, Jianfeng Ma · IEEE Internet of Things Journal · 2025
Delegation Learning(DL) flourishes data sharing, enabling agents to delegate data to the cloud for model training. To preserve privacy, homomorphic encryption (HE) offers an effective solution for privacy-preserving machine learning (PPML) in delegation learning, yet faces critical challenges in functionality (non-linear activation support), practicality (ciphertext blow-up from iterative computations), and security (data leakage risks caused by public knowledge of the mathematical principles applied in model training). To tackle these challenges, we propose THC-DL, a three-party HE framework addressing these challenges holistically for the first time. We elaborately design the ciphertext secure comparison (DL-CSC) protocol to satisfy secure comparison with private inputs, enabling efficient non-linear operations with O(1) communication complexity that reduces runtime to 12.5% of the DGK (Dolev-Greensmith-Kent protocol, the well-known comparison protocol). Second, we construct a Truncation-Mapping (Tru-Map) scheme, a mechanism that transforms input data by truncating and mapping it into a domain that facilitates more efficient processing, and the addition of truncated mapped data to resolve ciphertext blow-up by adaptively scaling ciphertexts during iterative training, ensuring correctness. Third, we formalize data leakage risks in HE-based quadratic convex optimization (standard in ML) and apply THC-DL to construct a secure optimization scheme. Theoretical analysis confirms THC-DL’s resilience against input recovery attacks, even when adversaries exploit public model parameters. Experiments on a real-world platform validate DL-CSC’s efficiency and scalability while reducing the computational complexity and communication complexity from O(n) to O(1) where n denotes the length of the input bits.