IO-Optimized Design-Time Configurable Negacyclic Seven-Step NTT Architecture for FHE Applications

Abstract

Fully Homomorphic Encryption (FHE) enables computations on encrypted data, proving itself to be an essential building block for privacy-preserving applications. However, it involves computationally demanding operations such as polynomial multiplication, with the Number Theoretic Transform (NTT) being the state-of-the-art solution to perform it. Considering that most FHE schemes operate over the negacyclic ring of polynomials, we introduce a novel formulation of the hierarchical Four-Step NTT approach for the negacyclic ring, eliminating the need for pre- and post-processing steps found in the existing methods. To accelerate NTT operations, the Field-Programmable Gate Array (FPGA) devices offer flexible and powerful computing platforms. We propose an FPGA-based, high-speed, parametric and fully pipelined architecture that implements the improved Seven-Step NTT algorithm, which builds upon the four-step algorithm. Our design supports a wide range of parameters, including ring sizes up to 216 and modulus sizes up to 64-bit. We focus on achieving configurable throughput, as constrained by the bandwidth of High-Bandwidth Memory (HBM), which is an additional in-package memory common in high-end FGPA devices such as Alveo U280. We aim to maximize throughput through an IO parametric design on the Alveo U280 FPGA. The implementation results demonstrate that the average latency of our design for batch NTT operation is 8.32?s for the ring size 216 and 64-bit width; a speed-up of 7.96 × compared to the current state-of-the-art designs. © 2025 Elsevier B.V., All rights reserved.