A Bitwise Logistic Regression Using Binary Approximation and Real Number Division in Homomorphic Encryption Scheme

Homomorphic Encryption (HE) is considered to be one of the most promising solutions to maintain secure data outsourcing because the user’s query is processed under encrypted state. Accordingly, many of existing literature related to HE utilizes additive and multiplicative property of HE to facilitate logistic regression which requires high precision for prediction. In consequence, they inevitably transform or approximate nonlinear function of the logistic regression to adjust to their scheme using simple polynomial approximation algorithms such as Taylor expansion. However, such an approximation can be used only in limited applications because they cause unwanted error in results if the function is highly nonlinear. In response, we propose a different approximation approach to constructing the highly accurate logistic regression for HE using binary approximation. Our novel approach originates from bitwise operations on encrypted bits to designing (1) real number representation, (2) division and (3) exponential function. The result of our experiment shows that our approach can be more generally applied and accuracy-guaranteed than the current literature.