标题： 信息论的去中心化安全聚合与共谋抵抗 显示英文标题

标题： Information-Theoretic Decentralized Secure Aggregation with Collusion Resilience

摘要： 在去中心化联邦学习（FL）中，多个客户端通过利用分布在网络中的私有数据集，通过中间模型更新的交互式交换，协作学习一个共享的机器学习（ML）模型。 为确保数据安全，通常采用密码技术来保护聚合过程中的模型更新。 尽管对安全聚合的兴趣日益增长，但现有工作主要集中在协议设计和计算保障上，对这类系统的根本信息理论极限理解有限。 此外，在没有中央聚合器的去中心化设置中，通信和密钥使用的最优界限仍未知。 受这些差距的驱动，我们从信息理论的角度研究去中心化安全聚合（DSA）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——局部训练数据的抽象——他们旨在安全地计算所有输入的总和。 安全约束要求，即使与其他最多$T$个用户串通，任何用户也不能了解输入总和之外的任何信息。 我们表征了最优速率区域，该区域指定了DSA的最小可实现通信和秘密密钥速率。 特别是，我们表明，为了安全地计算所需输入总和的一个符号，每个用户必须（i）向其他用户传输至少一个符号，（ii）持有至少一个符号的秘密密钥，并且（iii）所有用户必须共同持有不少于$K - 1$个独立密钥符号。 我们的结果确立了DSA的基本性能极限，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。 显示英文摘要

摘要： 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 distributed learning systems.