Fully Homomorphic Privacy-Preserving Naive Bayes Machine Learning and Classification

Despite the revolutionary advancement of homomorphic encryption (HE) technology, no efficient fully homomorphic Naive Bayes (NB) classifier that can perform training with HE-encrypted data has been developed without using a decryption function. In this study, we propose an approximate homomorphic logarithm calculation method with a relative error of less than 0.01% on average. Using the SIMD function of the underlying HE scheme, the logarithm values for thousands of encrypted probability values can be calculated in approximately 2.5s with the help of a GPU. Based on this, we propose an efficient fully homomorphic NB method. The proposed NB classifier could complete the training on the breast cancer dataset considered within approximately 14.3s, and perform inference for a query in 0.84s. This is estimated around 28 times faster compared to the recent privacy-preserving NB classifier supporting an analogous level of security by Liu et al. in 2017 on the same computational environment and the same CKKS HE operations performance.