Secure aggregation is motivated by federated learning (FL) where a cloud server aims to compute an {aggregated} model (i.e., weights of deep neural networks) of the locally-trained models of numerous clients {through an iterative communication process}, while adhering to data security requirements. Hierarchical secure aggregation (HSA) extends this concept to a three-layer hierarchical network, where clustered users communicate with the server through an intermediate layer of relays. In HSA, beyond conventional server security, relay security is also enforced to ensure that the relays remain oblivious to the users' inputs (an abstraction of the local models in FL). {Existing studies on HSA that jointly consider communication and secret key generation efficiency typically assume that each user is associated with only one relay, limiting opportunities for coding across inter-cluster users to achieve efficient communication and key generation.} In this paper, we consider HSA with a cyclic association pattern where each user is connected to $B$ consecutive relays in a wrap-around manner. We propose an efficient aggregation scheme which includes a message design for the inputs inspired by gradient coding-a well-known technique for efficient communication in distributed computing-along with a highly non-trivial security key design.

翻译：安全聚合技术源于联邦学习（FL）的应用场景，其中云服务器需要通过迭代通信过程，在满足数据安全要求的前提下，计算众多客户端本地训练模型（即深度神经网络权重）的聚合模型。分层安全聚合（HSA）将这一概念扩展到三层分层网络架构，其中分簇用户通过中继层与服务器进行通信。在HSA框架下，除传统的服务器安全要求外，还需强制执行中继安全机制，以确保中继节点无法获取用户输入数据（即FL中本地模型的抽象表示）。现有关于HSA的研究在联合考虑通信与密钥生成效率时，通常假设每个用户仅关联单个中继节点，这限制了跨簇用户通过编码实现高效通信与密钥生成的可能性。本文研究具有循环关联模式的HSA系统，其中每个用户以循环回绕方式连接至B个连续中继节点。我们提出一种高效聚合方案，其设计包含：受梯度编码（分布式计算中高效通信的经典技术）启发的输入消息设计，以及具有高度非平凡特性的安全密钥设计。