摘要： 针对联邦学习中模型聚合时可能会泄露用户的私有数据，以及服务器可能篡改聚合结果以获取某些非法利益的问题，提出一种双服务器架构下基于博弈论的高效可验证的隐私保护联邦学习方案。首先，使用基于种子同态伪随机生成器的单掩码方案来保护数据隐私，同时通过Shamir(t, n)门限秘密共享方案对掩码进行分发与重构，从而使所提方案能够在保证隐私的同时允许部分用户因网络环境不稳定而退出；其次，构造基于Hadamard乘积的轻量级的验证方法，使得用户最后仅需要进行简单的向量乘积运算即可验证聚合结果的正确性，从而减少验证所需的计算开销；最后，引入博弈论中的囚徒契约和背叛契约，通过激励策略促进两个服务器不发起合谋攻击，解决双服务器架构中面临的服务器合谋问题，保障用户隐私的安全性以及全局模型的可信性。实验结果表明，所提方案能够在不影响模型准确率的情况下对用户梯度进行隐私保护，且与现有方案相比，其计算效率和通信效率均有所提升，这种优势在用户退出时更明显。

Abstract: To solve the problems that users' private data may be leaked during model aggregation in federated learning, and that the server may tamper with the aggregation result to obtain certain illegal benefits, an efficient and verifiable privacy-preserving federated learning scheme based on game theory in dual-server architecture was proposed. Firstly, a single mask scheme based on homomorphic pseudorandom generator was used to protect data privacy, and the Shamir (t, n) threshold secret sharing scheme was used to distribute and reconstruct the mask, so that the proposed scheme can ensure privacy while allowing some users to drop out due to instability in the network environment. Secondly, a lightweight verification method based on Hadamard product was constructed, so that users only need to perform simple vector product operations to verify the correctness of the aggregation result, reducing the computational overhead required for verification. Finally, the prisoner contract and betrayal contract in game theory were introduced, and the two servers were promoted not to initiate collusion attacks through incentive strategies, solving the server collusion problem faced in the dual-server architecture, ensuring the security of user privacy and the credibility of the global model. The experimental results show that the proposed scheme can safely aggregate the gradients without affecting the accuracy of the model, and compared with existing schemes, its computational efficiency and communication efficiency have been improved, which is more obvious when users drop out.