An Efficient Encrypted Floating-Point Representation Using HEAAN and TFHE

Abstract

As a method of privacy-preserving data analysis (PPDA), a fully homomorphic encryption (FHE) has been in the spotlight recently. Unfortunately, because many data analysis methods assume that the type of data is of real type, the FHE-based PPDA methods could not support the enough level of accuracy due to the nature of FHE that fixed-point real-number representation is supported easily. In this paper, we propose a new method to represent encrypted floating-point real numbers on top of FHE. The proposed method is designed to have analogous range and accuracy to 32-bit floating-point number in IEEE 754 representation. We propose a method to perform arithmetic operations and size comparison operations. The proposed method is designed using two different FHEs, HEAAN and TFHE. As a result, HEAAN is proven to be very efficient for arithmetic operations and TFHE is efficient in size comparison. This study is expected to contribute to practical use of FHE-based PPDA.