Abstract
Fully Homomorphic Encryption (FHE) is a technique that enables arbitrary computations on encrypted data directly. Number Theoretic Transform (NTT) is a fundamental component in FHE computations as it allows faster polynomial multiplication. However, it is computationally intensive and requires acceleration for practical deployment of FHE. The latency and throughput of existing NTT hardware designs are limited by the complex data communication pattern between adjacent NTT stages and the modular arithmetic operations. In this paper, we propose a parameterized architecture for NTT on FPGA. The architecture can be configured for a given polynomial degree, modulus and target hardware in order to optimize the latency and/or throughput. We develop a novel low latency fully pipelined modular arithmetic logic to implement the NTT core, the key computational unit of NTT. Streaming permutation network is used to reduce the data communication complexity between NTT stages. We implement the proposed architecture for various polynomial degrees, moduli, and data parallelism on state-of-the-art FPGAs. Experimental results show that our architecture configured to perform 4096 polynomial degree NTT achieves up to \(1.29\times \) and \(4.32\times \) improvement in latency and throughput respectively over state-of-the-art designs on FPGA.
T. Ye and Y. Yang—Equal contribution.
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Notes
- 1.
Given a stride S, a permutation stride is defined as reordering an m-element data vector such that elements with distance of S are shifted into adjacent locations.
- 2.
All logs in this paper are to base 2.
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Acknowledgement
This work has been sponsored by the U.S. National Science Foundation under grant numbers OAC-1911229 and CNS-2009057. Equipment grant by Xilinx is greatly appreciated.
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Ye, T., Yang, Y., Kuppannagari, S.R., Kannan, R., Prasanna, V.K. (2021). FPGA Acceleration of Number Theoretic Transform. In: Chamberlain, B.L., Varbanescu, AL., Ltaief, H., Luszczek, P. (eds) High Performance Computing. ISC High Performance 2021. Lecture Notes in Computer Science(), vol 12728. Springer, Cham. https://doi.org/10.1007/978-3-030-78713-4_6
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