HEaaN-NB: Non-Interactive Privacy-Preserving Naive Bayes Using CKKS for Secure Outsourced Cloud Computing

Although there has been significant progress in homomorphic encryption (HE) technology, a fully homomorphic Naive Bayes (NB) classifier capable of training on HE-encrypted data without decryption has not yet been efficiently developed. This research introduces a new method for approximating homomorphic logarithm calculations with an average relative error under 0.01%. Leveraging the SIMD functionality of the HE framework and a GPU, this technique can compute logarithm values for thousands of encrypted probabilities in about 2.5 seconds. Building upon this, we present a more efficient fully homomorphic NB classifier. Our method can train on a breast cancer dataset in roughly 14.3 seconds and perform query inferences in 0.84 seconds. Compared to the recent privacy-protecting NB classifier from Liu et al. in 2017, which offers a similar security level, our method is estimated to be about 28 times faster.