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与随机优化中对数据安全性日益增长的需求驱动，我们提出并研究了信息论安全的去中心化聚合（DSA）问题。具体而言，我们考虑一个由$K$个互联用户组成的网络，每个用户持有私有输入（例如联邦学习中的局部模型更新），其目标是在满足以下安全要求的同时并行计算所有输入的总和：即任何用户即便与最多$T$个其他用户合谋，也无法获知除预定总和之外的任何信息。我们刻画了DSA的最优速率区域，该区域定义了可实现的最小通信速率与密钥速率。特别地，研究表明：为安全计算一位目标输入总和，每个用户必须（i）向所有其他用户传输至少一位信息，（ii）持有至少一位密钥，且（iii）所有用户必须共同持有不少于$K - 1$个独立密钥位。该结果确立了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理论指导。