分层安全分布式线性可分计算：任意异构数据分配
Hierarchical Secure Distributed Linearly Separable Computation with Arbitrary Heterogeneous Data Assignment
- Technical University of Berlin（柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对三层分层网络中的安全分布式线性可分计算，提出一种容忍用户掉线与串通的方案，在Kc=1时实现最优或阶最优通信速率，并扩展至Kc>1的多维任务。
AI中文摘要：
本文研究三层分层网络中的安全分布式线性可分计算，其中分簇用户通过中继与中央服务器通信。服务器旨在恢复Kc个中间结果的线性组合，每个中间结果是单个数据集的可分函数。我们考虑更一般的设置，即用户间任意异构数据分配，其中“任意”指数据分配预先给定（可为任何形式），“异构”指用户可能持有不同数量的数据集。在此分配下，每个用户计算其分配数据集的中间结果，并向关联中继发送掩码消息。中继随后处理并转发接收到的消息给服务器。我们施加两个安全约束：（i）针对服务器的安全性，要求服务器仅学习所需任务函数，不获取用户输入的任何额外信息；（ii）针对中继的安全性，确保每个中继对用户输入一无所知。此外，服务器或任何中继可能与部分用户串通。对于Kc=1，底层计算退化为分布式梯度编码。我们提出一种容忍用户掉线和用户串通的安全方案，在一种情形下实现最优两层通信速率，在另一种情形下实现因子2内的阶最优通信速率。对于Kc>1，我们在无掉线设置下将所提构造扩展至多维线性可分任务。
英文摘要：
This paper studies secure distributed linearly separable computation over a three-layer hierarchical network, where clustered users communicate with a central server through relays. The server aims to recover Kc linear combinations of K intermediate outcomes, where each intermediate outcome is a separable function of one dataset. We consider a more general setting with arbitrary heterogeneous data assignment across users, where ''arbitrary'' means that the data assignment is given in advance (which can be in any form) and ''heterogeneous'' means that the users may hold different numbers of datasets. Under this assignment, each user computes the intermediate outcomes of its assigned datasets and sends masked messages to its associated relay. The relays subsequently process and forward the received messages to the server. We impose two security constraints: (i) security against server, requiring the server to learn only the desired task function without gaining any additional information about users' inputs; and (ii) security against relays, ensuring each relay learns nothing about users' inputs. Moreover, the server or any relay may collude with a subset of users. For Kc=1, the underlying computation reduces to distributed gradient coding. We propose a secure scheme tolerating user dropouts and user collusion, achieving the optimal two-layer communication rates in one regime and order-optimal communication rates within a factor of 2 in the other regime. For Kc>1, we extend the proposed construction to multi-dimensional linearly separable tasks under the no-dropout setting.
