Privacy-preserving formal concept analysis: A homomorphic encryption-based concept construction

TL;DR

This work addresses the privacy risk of outsourcing Formal Concept Analysis by proposing PFCA, a framework that performs concept construction on encrypted data via fully homomorphic encryption. It introduces a two-stage workflow: encrypted concept processing to generate intermediate results and selective decryption to finalize the lattice, ensuring data confidentiality throughout the computation. The authors formalize encrypted operators and a ciphertext-based comparison mechanism, provide correctness and security analyses, and validate the approach experimentally on UCI datasets, showing exact concept counts and improved performance over traditional FCA methods. The results demonstrate PFCA's potential for privacy-preserving data mining and secure knowledge discovery in large-scale FCA applications, while noting scalability challenges and directions for more efficient algorithms.

Abstract

Formal Concept Analysis (FCA) is extensively used in knowledge extraction, cognitive concept learning, and data mining. However, its computational demands on large-scale datasets often require outsourcing to external computing services, raising concerns about the leakage of sensitive information. To address this challenge, we propose a novel approach to enhance data security and privacy in FCA-based computations. Specifically, we introduce a Privacy-preserving Formal Context Analysis (PFCA) framework that combines binary data representation with homomorphic encryption techniques. This method enables secure and efficient concept construction without revealing private data. Experimental results and security analysis confirm the effectiveness of our approach in preserving privacy while maintaining computational performance. These findings have important implications for privacy-preserving data mining and secure knowledge discovery in large-scale FCA applications.

Figures (7)

• Figure 1: The diagram of the privacy computing for concept.
• Figure 2: Generate the privacy-preserving concept by $\tilde{f}$ operator.
• Figure 3: The security analysis of the Step 2.
• Figure 4: The security analysis of the Step 3.
• Figure 5: Comparison of HECC and the actual number of concepts.