Title: Safeguarding Data Privacy During Causal Structure Learning via Fully Homomorphic Encryption

Abstract:

Maintaining data privacy remains a critical concern within the fields of structural data management and data mining. A significant, ongoing hurdle in this domain is the risk of privacy breaches during distributed causal structure learning, particularly when data must be transmitted and computed upon. This study introduces a methodology leveraging Fully Homomorphic Encryption (FHE) to conduct operations on ciphertexts, thereby ensuring that data remains encrypted throughout both transmission and processing phases.

Integrating FHE into causal structure learning presents substantial difficulties, primarily due to the high computational overhead and the limited native support for division and logarithmic functions within FHE frameworks. To address these obstacles, we introduce a suite of innovative techniques designed to optimize performance. These include: (i) circuit simplification to improve efficiency; (ii) approximations of division and logarithmic operations utilizing Newton-Raphson Reciprocal and Taylor expansion methods; and (iii) a batching strategy enhanced by SIMD acceleration to streamline the overall learning workflow.

Furthermore, the versatility of our approach is demonstrated through its adaptability to differential privacy, highlighting its potential for extension beyond FHE alone. Experimental findings indicate that our proposed method yields causal structures with high consistency and results comparable to those obtained using plaintext data across the tested datasets. Ultimately, the method proves to be both efficient and practical, capable of completing the learning of causal structures within tens of minutes while maintaining robust privacy protections via FHE.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC