Bandwidth Efficient Homomorphic Encrypted Discrete Fourier Transform Acceleration on FPGA

Zhihan Xu, Yang Yang, Rajgopal Kannan, Viktor K. Prasanna

Abstract: Fully Homomorphic Encryption (FHE) plays an important role in privacy-preserving computation on the cloud. It allows computations on encrypted data without decryption. Bootstrapping is a fundamental operation in FHE, enabling an unlimited number of homomorphic encrypted computations, but at a significant time cost. A major bootstrapping component, the Homomorphic Encrypted Discrete Fourier Transform (HE DFT), is particularly time-consuming and requires the transfer of a large amount of data from external memory. In this paper, we propose a bandwidth-efficient FPGA implementation of HE DFT. We design a cost model to evaluate the on-chip memory requirement and the off-chip data transfer overhead for HE DFT. Our analysis shows that prior approaches can lead to significant off-chip data transfers, which process the entire ciphertext between subroutines. To address DRAM transfer overhead, we propose LimbFlow, an optimized dataflow approach for HE DFT that enhances fine-grained data reuse by rearranging the processing order of ciphertext and merging several subroutines. Leveraging the LimbFlow, we develop an FPGA-based accelerator tailored for HE DFT. We evaluate the accelerator on AMD U280 FPGA across various sets of security parameters. Our accelerator achieves up to 4.90 × and 1.98 × speedup compared with the State-Of-The-Art (SOTA) GPU and FPGA implementations.