Title: Hi-SAFE: Hierarchical Secure Aggregation for Lightweight Federated Learning
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Hierarchical secure aggregation, federated learning, majority vote polynomial, subgrouping

Abstract: 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 $n$. Hi-SAFE reduces per-user communication by over 94\% when $n \geq 24$, and total cost by up to 52\% at $n = 24$, while preserving model accuracy. Experiments on benchmark datasets confirm the scalability, robustness, and practicality of Hi-SAFE in bandwidth-constrained FL deployments.

TL;DR: Hi-SAFE introduces a new Majority Vote Polynomial for sign-based federated learning, enabling hierarchical secure aggregation with provable privacy and over 94% communication reduction.