Lattice-based cryptography (LBC) is an essential direction in the fields of homomorphic encryption (HE), zero-knowledge proofs (ZK), and post-quantum cryptography (PQC), while number theoretic transformations (NTT) are a performance bottleneck that affects the promotion and deployment of LBC applications. Field-programmable gate arrays (FPGAs) are an ideal platform for accelerating NTT due to their reconfigurability and parallel capabilities. High-level synthesis (HLS) can shorten the FPGA development cycle, but for algorithms such as NTT, the synthesizer struggles to handle the inherent memory dependencies, often resulting in suboptimal synthesis outcomes for direct designs. This paper proposes a systematic HLS co-design to progressively guide the synthesis of NTT accelerators. The approach integrates several key techniques: arithmetic module resource optimization, conflict-free butterfly scheduling, memory partitioning, and template-based automated design fusion. It reveals how to resolve pipeline bottlenecks in HLS-based designs and expand parallel processing, guiding microarchitecture iterations to achieve an efficient design space. Compared to existing HLS-based designs, the area-latency product achieves a performance improvement of 1.93 to 191 times, and compared to existing HDL-based designs, the area-cycle product achieves a performance improvement of 1.7 to 10.6 times.
Hong et al. (2025) studied this question.