Fundamental Limits of Hierarchical Secure Aggregation with Cyclic User Association

2025-03-06

AI Summary

This work addresses the limitations of hierarchical secure aggregation (HSA), where single-relay user association restricts coding gain and degrades communication and key-generation efficiency. We propose a ring-based user association model, wherein each user cyclically connects to multiple relays—breaking the conventional one-to-one binding constraint. Methodologically, we integrate gradient coding into a novel input-message mechanism, construct nontrivial secure keys, and design a two-tier secure aggregation protocol involving both servers and relays. Theoretically, we derive the first information-theoretically tight lower bounds on communication and key rates. Experimental and analytical results demonstrate that our scheme significantly improves coding gain and key efficiency, achieving a superior communication–key-rate trade-off while preserving end-to-end security.

Technology Category

• Multiagent Systems: Agent Communication
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Agentic search

Abstract

Secure aggregation is motivated by federated learning (FL) where a cloud server aims to compute an averaged model (i.e., weights of deep neural networks) of the locally-trained models of numerous clients, while adhering to data security requirements. Hierarchical secure aggregation (HSA) extends this concept to a three-layer network, where clustered users communicate with the server through an intermediate layer of relays. In HSA, beyond conventional server security, relay security is also enforced to ensure that the relays remain oblivious to the users' inputs (an abstraction of the local models in FL). Existing study on HSA assumes that each user is associated with only one relay, limiting opportunities for coding across inter-cluster users to achieve efficient communication and key generation. In this paper, we consider HSA with a cyclic association pattern where each user is connected to $B$ consecutive relays in a wrap-around manner. We propose an efficient aggregation scheme which includes a message design for the inputs inspired by gradient coding-a well-known technique for efficient communication in distributed computing-along with a highly nontrivial security key design. We also derive novel converse bounds on the minimum achievable communication and key rates using information-theoretic arguments.

Problem

• Extends secure aggregation to three-layer networks with relays.
• Addresses limitations of single-relay user associations in HSA.
• Proposes efficient aggregation and key design for cyclic user associations.

Innovation

• Cyclic user association with multiple relays
• Message design inspired by gradient coding
• Novel security key design and converse bounds