Optimal Communication Rate of Secure Aggregation over Ring Networks with Pairwise Keys
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917462010757120 |
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| author | Zhang, Xiang Yu, Han Li, Zhou Zhao, Yizhou Caire, Giuseppe |
| author_facet | Zhang, Xiang Yu, Han Li, Zhou Zhao, Yizhou Caire, Giuseppe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Communication Rate of Secure Aggregation over Ring Networks with Pairwise Keys Zhang, Xiang Yu, Han Li, Zhou Zhao, Yizhou Caire, Giuseppe Information Theory 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. |
| title | Optimal Communication Rate of Secure Aggregation over Ring Networks with Pairwise Keys |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.01849 |