揭示去中心化安全聚合的理论极限,给出通信与密钥使用下限。
Information-Theoretic Decentralized Secure Aggregation with Passive Collusion Resilience
- 从信息论出发,分析去中心化安全聚合的最优通信与密钥开销。
- 证明每个用户需传输至少1符号数据,持有至少1符号密钥,共需至少K-1个独立密钥。
- 为无中心节点的联邦学习提供可证明安全且高效协议的设计依据。
在去中心化联邦学习中,多个客户端通过交互交换中间模型更新,协作学习共享机器学习模型,同时保护各自私有数据。为确保数据安全,通常采用密码技术保护聚合过程中的模型更新。尽管安全聚合研究日益增多,现有工作多集中于协议设计与计算保障,对系统的基本信息论极限缺乏理解。尤其在无中心聚合器的去中心化场景中,通信与密钥使用的最优界仍未知。本文从信息论角度研究去中心化安全聚合(DSA)问题。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(抽象为本地训练数据),目标是安全计算所有输入之和。安全约束要求:即使最多T个用户合谋,也无法获得除输入总和外的任何信息。我们刻画了最优速率区域,即实现DSA的最小通信率与密钥率。具体而言,为安全计算一个输入总和符号,每个用户必须(i)向他人传输至少一个符号,(ii)持有至少一个符号的密钥,(iii)所有用户集体持有的独立密钥符号数不少于K−1。结果确立了DSA的根本性能极限,为设计可证明安全且通信高效的去中心化学习协议提供了指导。
原文摘要 · Abstract (English)
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.
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