PrivDNFIS: Privacy-preserving and Efficient Deep Neuro-Fuzzy Inference System

Deep Neuro-Fuzzy Inference Systems (DNFIS) seamlessly fuse neural networks with the fuzzy inference system enabling intricate decision-making and knowledge representation, while upholding a commendable degree of adaptability and interpretability. However, the challenge of privacy-preserving inference (PI) over DNFIS has remained largely uncharted, with no prior research addressing this critical issue. In this paper, we embark on an exploration of this issue. We introduce an efficient and secure PI framework for DNFIS, named PrivDNFIS, which leverages the post-quantum lattice-based homomorphic encryption to implement secure computation protocols for PI over DNFIS. Our work incorporates several non-trivial performance enhancements. Firstly, it consolidates multiple elements of input feature vectors into a single message, reducing encryption/decryption overhead. Secondly, building upon this novel encoding approach, PrivDNFIS can perform ciphertext aggregation and vector-vector inner production without necessitating time-consuming ciphertext rotation operations. Thirdly, we replace the softmax function in the DNFIS layer with a quadratic function to further enhance inference efficiency, without compromising the inference accuracy. Under the given threat model, we provide formal security proof for PrivDNFIS. In comprehensive experimental results, PrivDNFIS demonstrates an approximately 1.9 to 4.4 times reduction in end-to-end time cost compared to the benchmark.