In decentralized federated learning (FL), multiple clients collaboratively learn a shared machine learning (ML) model by leveraging their privately held datasets distributed across the network, through interactive exchange of the intermediate model updates. To ensure data security, cryptographic techniques are commonly employed to protect model updates during aggregation. Despite growing interest in secure aggregation, existing works predominantly focus on protocol design and computational guarantees, with limited understanding of the fundamental information-theoretic limits of such systems. Moreover, optimal bounds on communication and key usage remain unknown in decentralized settings, where no central aggregator is available. Motivated by these gaps, we study the problem of decentralized secure aggregation (DSA) from an information-theoretic perspective. Specifically, we consider a network of $K$ fully-connected users, each holding a private input -- an abstraction of local training data -- who aim to securely compute the sum of all inputs. The security constraint requires that no user learns anything beyond the input sum, even when colluding with up to $T$ other users. We characterize the optimal rate region, which specifies the minimum achievable communication and secret key rates for DSA. In particular, we show that to securely compute one symbol of the desired input sum, each user must (i) transmit at least one symbol to others, (ii) hold at least one symbol of secret key, and (iii) all users must collectively hold no fewer than $K - 1$ independent key symbols. Our results establish the fundamental performance limits of DSA, providing insights for the design of provably secure and communication-efficient protocols in decentralized learning.

翻译：在去中心化联邦学习中，多个客户端通过交互式交换中间模型更新，利用分布在整个网络中的私有数据集协作学习共享的机器学习模型。为确保数据安全，通常采用加密技术来保护聚合过程中的模型更新。尽管人们对安全聚合的兴趣日益增长，现有工作主要集中在协议设计和计算保证上，对此类系统基本的信息论极限理解有限。此外，在无中央聚合器的去中心化环境中，通信和密钥使用的最优界限仍属未知。受这些空白启发，我们从信息论角度研究去中心化安全聚合问题。具体而言，我们考虑一个由 $K$ 个全连接用户组成的网络，每个用户持有一个私有输入（作为本地训练数据的抽象），旨在安全计算所有输入之和。安全约束要求，即使与最多 $T$ 个其他用户共谋，任何用户也不能获取超出输入和的任何信息。我们刻画了最优速率区域，该区域给出了 DSA 的最小可达到通信速率和密钥速率。特别地，我们表明，为安全计算目标输入和的一个符号，每个用户必须 (i) 向其他用户传输至少一个符号，(ii) 持有至少一个密钥符号，且 (iii) 所有用户必须共同持有不少于 $K - 1$ 个独立密钥符号。我们的研究结果确立了 DSA 的基本性能极限，为设计去中心化学习中可证明安全且通信高效的协议提供了洞见。