Federated Learning (FL) has emerged as a promising paradigm in distributed machine learning, enabling collaborative model training while preserving data privacy. However, despite its many advantages, FL still contends with significant challenges -- most notably regarding security and trust. Zero-Knowledge Proofs (ZKPs) offer a potential solution by establishing trust and enhancing system integrity throughout the FL process. Although several studies have explored ZKP-based FL (ZK-FL), a systematic framework and comprehensive analysis are still lacking. This article makes two key contributions. First, we propose a structured ZK-FL framework that categorizes and analyzes the technical roles of ZKPs across various FL stages and tasks. Second, we introduce a novel algorithm, Verifiable Client Selection FL (Veri-CS-FL), which employs ZKPs to refine the client selection process. In Veri-CS-FL, participating clients generate verifiable proofs for the performance metrics of their local models and submit these concise proofs to the server for efficient verification. The server then selects clients with high-quality local models for uploading, subsequently aggregating the contributions from these selected clients. By integrating ZKPs, Veri-CS-FL not only ensures the accuracy of performance metrics but also fortifies trust among participants while enhancing the overall efficiency and security of FL systems.

翻译：联邦学习（FL）已成为分布式机器学习中一种前景广阔的范式，它能够在保护数据隐私的同时实现协作式模型训练。然而，尽管具有诸多优势，联邦学习仍面临重大挑战——尤其是在安全性与信任方面。零知识证明（ZKPs）通过在整个联邦学习过程中建立信任并增强系统完整性，提供了一种潜在的解决方案。尽管已有若干研究探索了基于零知识证明的联邦学习（ZK-FL），但目前仍缺乏系统性的框架与综合分析。本文作出两项关键贡献。首先，我们提出了一种结构化的ZK-FL框架，对零知识证明在联邦学习各阶段及任务中的技术作用进行了分类与分析。其次，我们提出了一种新颖算法——可验证客户端选择联邦学习（Veri-CS-FL），该算法利用零知识证明来优化客户端选择过程。在Veri-CS-FL中，参与客户端为其本地模型的性能指标生成可验证证明，并将这些简洁证明提交至服务器进行高效验证。服务器随后选择具有高质量本地模型的客户端进行上传，并聚合这些选定客户端的贡献。通过集成零知识证明，Veri-CS-FL不仅确保了性能指标的准确性，还强化了参与者间的信任，同时提升了联邦学习系统的整体效率与安全性。