Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption

2026-06-03

AI Summary

This work addresses the challenge of privacy leakage in distributed causal structure learning by proposing a privacy-preserving approach based on fully homomorphic encryption (FHE), which enables causal discovery directly on encrypted data. The method achieves efficient computation through circuit simplification and accurate approximations of division and logarithmic functions via Newton–Raphson iteration combined with Taylor series expansion. SIMD batch processing is further integrated to accelerate computation, and the framework seamlessly extends to support differential privacy. Experimental results demonstrate that the proposed approach recovers causal structures highly consistent with those obtained by plaintext algorithms across multiple datasets, while completing the learning task efficiently within tens of minutes, thereby achieving a strong balance among privacy preservation, accuracy, and scalability.

Abstract

Preserving data privacy is an important topic in structural data management and data mining. However, the issue of privacy leakage in distributed causal structure learning is a persistent challenge, especially in cases where data transmission and computation are required. In this paper, we propose a method based on fully homomorphic encryption (FHE) that performs calculations on ciphertexts, keeping data encrypted in transition and computation. Nevertheless, adopting FHE to causal structure learning is challenging due to the high computation cost and limited support on division as well as logarithm operations in FHE. To tackle this challenge, we propose a series of novel techniques including (i) circuit simplification for better efficiency, (ii) approximation of division and logarithm through Newton-Raphson Reciprocal and Taylor expansion, and (iii) a batching technique with SIMD-acceleration to enhance the whole learning process. Additionally, our method can be easily extended beyond FHE by demonstration of its portability to support differential privacy. Empirical results show that our method achieves high consistency and comparable causal structure with the plaintext version in the datasets tested. Last, our method is efficient and practical to complete learning causal structures in tens of minutes even under the privacy protection of FHE.

Problem

• data privacy
• causal structure learning
• privacy leakage
• distributed learning
• fully homomorphic encryption

Innovation

• Fully Homomorphic Encryption
• Causal Structure Learning
• Privacy-Preserving Computation
• SIMD Acceleration
• Numerical Approximation