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

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.