Motivated by the increasing demand for data security in decentralized federated learning (FL) and stochastic optimization, we formulate and investigate the problem of information-theoretic \emph{decentralized secure aggregation} (DSA). Specifically, we consider a network of $K$ interconnected users, each holding a private input, representing, for example, local model updates in FL, who aim to simultaneously compute the sum of all inputs while satisfying the security requirement that no user, even when colluding with up to $T$ others, learns anything beyond the intended sum. 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 bit of the desired input sum, each user must (i) transmit at least one bit to all other users, (ii) hold at least one bit of secret key, and (iii) all users must collectively hold no fewer than $K - 1$ independent key bits. Our result establishes the fundamental performance limits of DSA and offers insights into the design of provably secure and communication-efficient protocols for distributed learning systems.

翻译：受去中心化联邦学习（FL）与随机优化中对数据安全性日益增长的需求所驱动，我们提出并研究了信息论意义上的**去中心化安全聚合**（DSA）问题。具体而言，我们考虑一个由 $K$ 个互连用户构成的网络，每个用户持有一个私有输入（例如代表FL中的本地模型更新），他们的目标是同时计算所有输入的总和，同时满足安全性要求：即使与最多 $T$ 个其他用户共谋，任何用户也无法获知除预期总和之外的任何信息。我们刻画了最优速率区域，该区域指明了DSA可实现的最小通信速率与秘密密钥速率。特别地，我们证明，为了安全地计算所需输入总和中的一比特信息，每个用户必须（i）向所有其他用户至少传输一比特信息，（ii）持有至少一比特的秘密密钥，并且（iii）所有用户共同持有的独立密钥比特数不得少于 $K - 1$。我们的结果确立了DSA的基本性能极限，并为分布式学习系统中可证明安全且通信高效的协议设计提供了见解。