Accelerating homomorphic ReLU via segmented lookup table and dynamic CG-NTT reuse

Liao Yinglong; Luo Yuqiao; Li Danjie; Li Lingwu; Yao Lei; Jiang Lin; Fang Junbin

doi:10.11959/j.issn.2096-109x.AQ25232

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Accelerating homomorphic ReLU via segmented lookup table and dynamic CG-NTT reuse

Papers | 更新时间：2026-07-15

- Accelerating homomorphic ReLU via segmented lookup table and dynamic CG-NTT reuse
- Chinese Journal of Network and Information Security Vol. 12, Issue 3, Pages: 135-153(2026)
- 作者机构：
  
  1.暨南大学物理与光电工程学院，广东广州 510632
  2.暨南大学智能科学与工程学院，广东珠海 519070
  3.深圳云安宝科技有限公司，广东深圳 518055
  4.哈尔滨工业大学（深圳）计算机科学与技术学院，广东深圳 518055
  5.教育部“光电混合集成电路”国际合作联合实验室，广东广州 510632
- 作者简介：
- 基金信息：
  
  Shenzhen Major Science and Technology Project(KJZD20240903104301003)
- DOI：10.11959/j.issn.2096-109x.AQ25232
  CLC： TP309.2
- Received：05 December 2025，
  
  Revised：2026-05-03，
  
  Published：25 June 2026
- 稿件说明：
移动端阅览
廖颖龙, 罗羽乔, 李丹婕, 等. 基于分段查找表与动态CG-NTT复用的同态ReLU加速[J]. 网络与信息安全学报, 2026, 12(3): 135-153.

Liao Yinglong, Luo Yuqiao, Li Danjie, et al. Accelerating homomorphic ReLU via segmented lookup table and dynamic CG-NTT reuse[J]. Chinese Journal of Network and Information Security, 2026, 12(3): 135-153.
廖颖龙, 罗羽乔, 李丹婕, 等. 基于分段查找表与动态CG-NTT复用的同态ReLU加速[J]. 网络与信息安全学报, 2026, 12(3): 135-153. DOI： 10.11959/j.issn.2096-109x.AQ25232.

Liao Yinglong, Luo Yuqiao, Li Danjie, et al. Accelerating homomorphic ReLU via segmented lookup table and dynamic CG-NTT reuse[J]. Chinese Journal of Network and Information Security, 2026, 12(3): 135-153. DOI： 10.11959/j.issn.2096-109x.AQ25232.

摘要

全同态加密不支持非线性同态计算，导致隐私保护机器学习中的同态ReLU评估难以直接实现。现有采用高阶多项式近似ReLU激活函数的方案设计大位宽模乘与高阶多项式乘法运算，使得系统吞吐量受限、资源利用率低。对此，提出了一种CPU-FPGA异构协同的同态ReLU评估方案：由CPU端执行ReLU的高阶多项式近似，FPGA端执行同态多项式评估加速。具体而言，首先设计了分段查找表模运算方法，借助双级分解映射机制将大位宽模乘转化为并行高低位查表与线性组合，模乘时延较现有最优方案降低97%。其次，提出动态资源复用CG-NTT架构优化多项式乘法效率，依托固定访存模式实现动态表复用策略，相较于传统NTT架构，减少15%~37%计算单元，降低45%~50.8%运算时延。最后，构建CPU-FPGA异构加速框架，通过相位调优接口与资源协调机制，使同态ReLU评估获得21.4倍加速比。实验验证了该方案在加速密文推理中的可行性，但最耗时的自举操作仍需在CPU端执行。因此，未来研究将聚焦自举操作的硬件加速，以进一步提升密文推理系统的实用性能。

Abstract

Fully homomorphic encryption does not support nonlinear homomorphic computation

making it difficult to directly implement homomorphic ReLU evaluation in privacy-preserving machine learning. Existing schemes that employ high-degree polynomials to approximate the ReLU activation function involve large-bitwidth modular multiplication and high-degree polynomial multiplication operations

resulting in limited system throughput and low resource utilization.To address this

a CPU-FPGA heterogeneous collaborative architecture was proposed for homomorphic ReLU evaluation

with the CPU executing high-degree polynomial approximation and the FPGA accelerating homomorphic polynomial evaluation. Specifically

a segmented lookup table modular reduction algorithm was first designed. By means of a two-level decomposition mapping mechanism

large-bitwidth modular multiplication was converted into parallel high/low-bit lookup table operations and linear combinations. As a result

the modular multiplication delay was reduced by 97% compared to the existing state-of-the-art scheme. Secondly

a dynamic resource-reusing CG-NTT architecture was proposed to optimize polynomial multiplication efficiency. Relying on a fixed memory access pattern

a dynamic table reuse strategy was implemented. Compared with traditional NTT architectures

15%～37% of the computation units were reduced

and 45%～50.8% of the operation latency was decreased. Finally

a CPU-FPGA heterogeneous acceleration framework was constructed. Through a phase-tuning interface and a resource coordination mechanism

a speedup of 21.4 times was achieved for homomorphic ReLU evaluation. The feasibility of the proposed scheme in accelerating ciphertext inference was verified by experiments

although the most time-consuming bootstrapping operation still had to be executed on the CPU side. Therefore

future research will be focused on the hardware acceleration of the bootstrapping operation

in order to further improve the practical performance of the ciphertext inference system.

关键词

Keywords

references

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