Efficient and Privacy-Preserving Logistic Regression Scheme based on Leveled Fully Homomorphic Encryption

In the era of big data, data are often outsourced at cloud for storage and computation. As data has become a highly valuable resource, data holder needs retain full privacy and control over it. Privacy-preserving machine learning (PPML) aims at extracting data value while preserving its privacy. Homomorphic encryption (HE), as a privacy-preserving technique, is increasingly used in PPML schemes. However, since bootstrapping is required in Fully Homomorphic Encryption (FHE) after a certain number of homomorphic operations to ensure the correctness of decryption, FHE-based PPML may perform a large number of bootstrappings, which greatly reduces the efficiency. Besides, FHE only supports homomorphic addition and multiplication operations. Most of the existing solutions use Taylor theorem to convert nonlinear function into linear polynomial function with sacrifice of model accuracy. To solve the two problems above, we propose to simulate bootstrapping operation in training phase by a pair of decryption and re-encryption operations, which is further transferred to trusted hardware to avoid information leakage after decryption. With this idea, the performance can be enhanced greatly. In addition, all the calculations of activation function (nonlinear) can be executed in plaintext form directly. In this paper, we propose and implement an efficient and privacy-preserving logistic regression scheme based on Leveled FHE, and deploy the bootstrapping simulation and activation function on Raspberry Pi (a simulated trusted hardware). The scheme achieves practical usability demonstrated on standard UCI datasets.