HF-NTT: Hazard-Free Dataflow Accelerator for Number Theoretic Transform

TL;DR

HF-NTT is a versatile, hazard-free FPGA accelerator for Number Theoretic Transform that improves polynomial multiplication efficiency crucial for applications like fully homomorphic encryption.

Contribution

The paper presents HF-NTT, a novel adaptable NTT accelerator with hazard-free data movement, hardware-friendly modular multiplication, and configurable processing elements for improved performance.

Findings

Significant improvements in Area-Time-Product (ATP) and processing speed.

Outperforms existing designs in multi-modulus polynomial multiplication.

Efficient handling of polynomials with varying degrees and moduli.

Abstract

Polynomial multiplication is one of the fundamental operations in many applications, such as fully homomorphic encryption (FHE). However, the computational inefficiency stemming from polynomials with many large-bit coefficients poses a significant challenge for the practical implementation of FHE. The Number Theoretic Transform (NTT) has proven an effective tool in enhancing polynomial multiplication, but a fast and adaptable method for generating NTT accelerators is lacking. In this paper, we introduce HF-NTT, a novel NTT accelerator. HF-NTT efficiently handles polynomials of varying degrees and moduli, allowing for a balance between performance and hardware resources by adjusting the number of Processing Elements (PEs). Meanwhile, we introduce a data movement strategy that eliminates the need for bit-reversal operations, resolves different hazards, and reduces the clock cycles. Furthermore, Our accelerator includes a hardware-friendly modular multiplication design and a configurable PE capable of adapting its data path, resulting in a universal architecture. We synthesized and implemented prototype using Vivado 2022.2, and evaluated it on the Xilinx Virtex-7 FPGA platform. The results demonstrate significant improvements in Area-Time-Product (ATP) and processing speed for different polynomial degrees. In scenarios involving multi-modulus polynomial multiplication, our prototype consistently outperforms other designs in both ATP and latency metrics.