Keyword Spotting in the Homomorphic Encrypted Domain Using Deep Complex-Valued CNN

In this paper, we propose a non-interactive scheme to achieve end-to-end keyword spotting in the homomorphic encrypted domain using deep learning techniques. We carefully designed a complex-valued convolutional neural network (CNN) structure for the encrypted domain keyword spotting to take full advantage of the limited multiplicative depth. At the same depth, the proposed complex-valued CNN can learn more speech representations than the real-valued CNN, thus achieving higher accuracy in keyword spotting. The complex activation function of the complex-valued CNN is non-arithmetic and cannot be supported by homomorphic encryption. To implement the complex activation function in the encrypted domain without interaction, we design methods to approximate complex activation functions with low-degree polynomials while preserving the keyword spotting performance. Our scheme supports single-instruction multiple-data (SIMD), which reduces the total size of ciphertexts and improves computational efficiency. We conducted extensive experiments to investigate our performance with various metrics, such as accuracy, robustness, and F1-score. The experimental results show that our approach significantly outperforms the state-of-the-art solutions on every metric.