Paper 2023/402

Discretization Error Reduction for Torus Fully Homomorphic Encryption

Abstract

In recent history of fully homomorphic encryption, bootstrapping has been actively studied throughout many HE schemes. As bootstrapping is an essential process to transform somewhat homomorphic encryption schemes into fully homomorphic, enhancing its performance is one of the key factors of improving the utility of homomorphic encryption. In this paper, we propose an extended bootstrapping for TFHE, which we name it by EBS. One of the main drawback of TFHE bootstrapping was that the precision of bootstrapping is mainly decided by the polynomial dimension $N$. Thus if one wants to bootstrap with high precision, one must enlarge $N$, or take alternative method. Our EBS enables to use small $N$ for parameter selection, but to bootstrap in higher dimension to keep high precision. Moreover, it can be easily parallelized for faster computation. Also, the EBS can be easily adapted to other known variants of TFHE bootstrappings based on the original bootstrapping algorithm. We implement our EBS along with the full domain bootstrapping methods known ($\mathsf{FDFB}$, $\mathsf{TOTA}$, $\mathsf{Comp}$), and show how much our EBS can improve the precision for those bootstrapping methods. We provide experimental results and thorough analysis with our EBS, and show that EBS is capable of bootstrapping with high precision even with small $N$, thus small key size, and small complexity than selecting large $N$ by birth.