Optimal Communication Rate of Secure Aggregation over Ring Networks with Pairwise Keys

2026-05-03

AI Summary

This work addresses the problem of information-theoretically secure aggregation in a K-user ring network without a central key server, where users share pairwise independent keys. The authors propose a linear masking scheme that relies solely on keys shared between users at distance at most two to enable secure computation of neighborhood sums. Through entropy-based analysis and tight converse bounds, they demonstrate that topological sparsity critically governs communication efficiency: the minimum per-user communication cost is one bit for K = 3,4 and two bits for K ≥ 5. The proposed scheme achieves this fundamental lower bound for all K ≥ 4, thereby establishing the first optimal communication rate for secure aggregation under ring topology.

Abstract

Information-theoretic topological secure aggregation (TSA)\cite{zhang2026information_regular} enables distributed users to compute neighborhood sums over arbitrary networks without revealing individual inputs, while remaining communication-efficient. It has broad applications, including secure model aggregation in decentralized federated learning (FL). Existing TSA formulations rely on arbitrarily correlated keys generated by a trusted key server, which introduces a single point of failure. In this paper, we instead study TSA with \tit{pairwise} secret keys, where each user pair $(i,j)$ shares an independent key $S_{i,j}$. Such keys can be established through inter-user communication, eliminating the need for a key server and improving robustness. Focusing on a ring topology with $K$ users, we characterize the minimum per-user communication rate: \tit{to securely compute one bit of the desired input sum, each user must send at least $1$ bit to its neighbors when $K=3,4$, and at least $2$ bits for all $K\ge 5$}. The higher rate in larger networks arises because each user must simultaneously satisfy two independent key-alignment constraints from its two neighborhoods, which cannot be resolved within a single broadcast symbol under pairwise key independence. We propose a linear pairwise-masking scheme that achieves these rates and prove its optimality via tight entropic converse bounds that exploit the dependency structure of the keys. Notably, for all $K\ge 4$, only a subset of the $\binom{K}{2}$ pairwise keys -- specifically, those between users at ring distance $2$ -- is sufficient to achieve optimality, revealing a nontrivial role of topological sparsity in secure aggregation.

Problem

• secure aggregation
• pairwise keys
• ring network
• communication rate
• information-theoretic security

Innovation

• secure aggregation
• pairwise keys
• ring topology
• communication rate
• information-theoretic security