Federated learning is a promising distributed learning paradigm that enables collaborative model training without exposing local client data, thereby protecting data privacy. However, it also brings new threats and challenges. The advancement of model inversion attacks has rendered the plaintext transmission of local models insecure, while the distributed nature of federated learning makes it particularly vulnerable to attacks raised by malicious clients. To protect data privacy and prevent malicious client attacks, this paper proposes a privacy-preserving Federated Learning framework based on Verifiable Functional Encryption (VFEFL), without a non-colluding dual-server assumption or additional trusted third-party. Specifically, we propose a novel Cross-Ciphertext Decentralized Verifiable Functional Encryption (CC-DVFE) scheme that enables the verification of specific relationships over multi-dimensional ciphertexts. This scheme is formally treated, in terms of definition, security model and security proof. Furthermore, based on the proposed CC-DVFE scheme, we design a privacy-preserving federated learning framework that incorporates a novel robust aggregation rule to detect malicious clients, enabling the effective training of high-accuracy models under adversarial settings. Finally, we provide the formal analysis and empirical evaluation of VFEFL. The results demonstrate that our approach achieves the desired privacy protection, robustness, verifiability and fidelity, while eliminating the reliance on non-colluding dual-server assumption or trusted third parties required by most existing methods.

翻译：联邦学习是一种极具前景的分布式学习范式，能够在无需暴露本地客户端数据的情况下实现协作模型训练，从而保护数据隐私。然而，这一范式也带来了新的威胁与挑战。模型反转攻击的进步使得本地模型的明文传输不再安全，而联邦学习的分布式特性使其特别容易遭受恶意客户端发起的攻击。为保护数据隐私并抵御恶意客户端攻击，本文提出了一种基于可验证功能加密的隐私保护联邦学习框架（VFEFL），该方法无需非共谋双服务器假设或额外可信第三方。具体而言，我们提出了一种新颖的交叉密文可验证功能加密方案（CC-DVFE），该方案能够验证多维密文间的特定关系，并从定义、安全模型和安全证明三个方面对其进行形式化处理。进一步地，基于所提出的CC-DVFE方案，我们设计了一个集成新型鲁棒聚合规则的隐私保护联邦学习框架，用于检测恶意客户端，从而在对抗环境下有效训练高精度模型。最后，我们对VFEFL进行了形式化分析与实验评估。结果表明，该方法在消除大多数现有方法依赖的非共谋双服务器假设或可信第三方需求的同时，实现了理想的隐私保护、鲁棒性、可验证性与保真性。