提出轻量级安全聚合框架，让签名联邦学习更隐私、更高效。
Hi-SAFE: Hierarchical Secure Aggregation for Lightweight Federated Learning
- 用数论构造投票多项式，实现签名梯度的安全聚合。
- 支持任意用户数下恒定计算开销，通信效率提升显著。
- 适合物联网等资源受限场景，兼顾隐私与性能。
联邦学习（FL）在资源受限的物联网和边缘网络中面临隐私与通信效率的双重挑战。尽管基于符号的方法（如带多数投票的符号随机梯度下降，SIGNSGD-MV）能大幅节省带宽，但其暴露的梯度符号仍易受推断攻击。现有安全聚合方法或不兼容符号方法，或带来过高开销。为此，我们提出 Hi-SAFE，一种轻量级且密码学安全的符号联邦学习聚合框架。核心贡献是基于费马小定理构建高效的多数投票多项式，将多数投票表示为有限域上的低次多项式，从而实现中间值隐藏、仅公开最终结果的安全计算。此外，引入分层子组策略，确保乘法深度恒定且每个用户的计算复杂度有界，与用户总数 n 无关。
原文摘要 · Abstract (English)
Federated learning (FL) faces challenges in ensuring both privacy and communication efficiency, particularly in resource-constrained environments such as Internet of Things (IoT) and edge networks. While sign-based methods, such as sign stochastic gradient descent with majority voting (SIGNSGD-MV), offer substantial bandwidth savings, they remain vulnerable to inference attacks due to exposure of gradient signs. Existing secure aggregation techniques are either incompatible with sign-based methods or incur prohibitive overhead. To address these limitations, we propose Hi-SAFE, a lightweight and cryptographically secure aggregation framework for sign-based FL. Our core contribution is the construction of efficient majority vote polynomials for SIGNSGD-MV, derived from Fermat's Little Theorem. This formulation represents the majority vote as a low-degree polynomial over a finite field, enabling secure evaluation that hides intermediate values and reveals only the final result. We further introduce a hierarchical subgrouping strategy that ensures constant multiplicative depth and bounded per-user complexity, independent of the number of users n.
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