Secure aggregation is concerned with the task of securely uploading the inputs of multiple users to an aggregation server without letting the server know the inputs beyond their summation. It finds broad applications in distributed machine learning paradigms such as federated learning (FL) where multiple clients, each having access to a proprietary dataset, periodically upload their locally trained models (abstracted as inputs) to a parameter server which then generates an aggregate (e.g., averaged) model that is sent back to the clients as an initializing point for a new round of local training. To enhance the data privacy of the clients, secure aggregation protocols are developed using techniques from cryptography to ensure that the server infers no more information of the users' inputs beyond the desired aggregated input, even if the server can collude with some users. Although laying the ground for understanding the fundamental utility-security trade-off in secure aggregation, the simple star client-server architecture cannot capture more complex network architectures used in practical systems. Motivated by hierarchical federated learning, we investigate the secure aggregation problem in a $3$-layer hierarchical network consisting of clustered users connecting to an aggregation server through an intermediate layer of relays. Besides the conventional server security which requires that the server learns nothing beyond the desired sum of inputs, relay security is also imposed so that the relays infer nothing about the users' inputs and remain oblivious. For such a hierarchical secure aggregation (HSA) problem, we characterize the optimal multifaceted trade-off between communication (in terms of user-to-relay and relay-to-server communication rates) and secret key generation efficiency (in terms of individual key and source key rates).

翻译：安全聚合旨在将多个用户的输入安全地上传至聚合服务器，同时确保服务器除输入的总和外无法获知具体输入内容。该技术在分布式机器学习范式中具有广泛应用，例如联邦学习（FL）：多个客户端各自拥有专有数据集，定期将其本地训练的模型（抽象为输入）上传至参数服务器；服务器随后生成聚合模型（如平均模型）并发送回客户端，作为新一轮本地训练的初始化起点。为增强客户端的数据隐私性，安全聚合协议利用密码学技术开发，以确保即使服务器与部分用户共谋，其也无法获取超出所需聚合输入之外的任何用户输入信息。尽管星型客户端-服务器架构为理解安全聚合中基本的效用-安全权衡奠定了基础，但其无法涵盖实际系统中使用的更复杂网络架构。受分层联邦学习的启发，我们研究了一个三层分层网络中的安全聚合问题：该网络由聚类用户组成，用户通过中继层连接到聚合服务器。除要求服务器仅能获知输入总和（服务器安全性）外，我们还施加了中继安全性，即中继器无法推断用户输入信息并保持对其的不可知状态。针对此类分层安全聚合（HSA）问题，我们刻画了通信（用户至中继及中继至服务器的通信速率）与密钥生成效率（个体密钥速率与源密钥速率）之间的多维最优权衡关系。