An Efficient Polynomial Multiplier Architecture for the Bootstrapping Algorithm in a Fully Homomorphic Encryption Scheme

Weihang Tan, Aengran Au, Benjamin Aase, Shuhong Aao, Yingjie Lao

Abstract: Bootstrapping algorithm, which is the intermediate refreshing procedure of a processed ciphertext, has been the performance bottleneck among various existing Fully Homomorphic Encryption (FHE) schemes. Specifically, the external product of polynomials is the most computationally expensive step of bootstrapping algorithms that are based on the Ring Learning With Error (RLWE) problem. In this paper, we design a novel and scalable polynomial multiplier architecture for a bootstrapping algorithm along with a conflict-free memory management scheme to reduce the latency, while achieving a full utilization of the processing elements (PEs). Each PE is a modified radix-2 butterfly unit from fast Fourier transform (FFT), which can be reconfigured to use in both the number theoretic transform (NTT) and the basic modular multiplication of polynomial multiplication in the external product step. The experimental results show that our design yields 33% less area-time product than prior designs.