TP-NTT: Batch NTT Hardware with Application to Relinearization

Abstract

Fully Homomorphic Encryption (FHE) enables arbitrary computation on encrypted data without decryption, providing strong privacy guarantees for secure cloud computing, encrypted analytics, and privacy-preserving machine learning. However, practical deployment of FHE remains limited by the high computational cost of polynomial arithmetic over large modular rings. In particular, Number Theoretic Transform (NTT)–based polynomial multiplication dominates the execution time of modern lattice-based FHE schemes. In this work, we present TP-NTT, a scalable, throughput-optimized NTT architecture supporting a wide range of ring dimensions used in FHE, from 210 to 216. Our design applies optimizations at multiple levels, from modular arithmetic to the NTT algorithm itself, including multi-dimensional decomposition without requiring additional multiplication blocks. The decomposition dimensionality is configurable at design time, supporting 2-D, 3-D, and 4-D decompositions, each advantageous in specific scenarios. Furthermore, TP-NTT provides design-time-configurable throughput. Combined with its scalable architecture, this enables significant advantages for batch NTT operations compared to other works in the literature. At n = 216, it outperforms the best-performing prior design by 1.33x in average latency while achieving 1.24x better area–time-product (ATP). To demonstrate its efficiency, we present a case study on FHE relinearization, focusing on the BFV scheme. We propose a relinearization accelerator that leverages the fast batch NTT capability of TP-NTT, achieving 67.34x speedup over state-of-theart software implementations and highlighting TP-NTT’s effectiveness in real-world FHE applications.