<p>As a distributed machine learning framework, federated learning enables users to retain data locally while collaboratively training models by only sharing gradient information. However, the sharing of gradient information still poses risks of privacy breaches. Furthermore, in a distributed setting, privacy-preserving federated learning schemes using cryptographic methods encounter significant challenges in key distribution and management. In addition, cloud servers may return incorrect aggregation results, which can have a negative impact on model performance. To address these challenges, this paper proposes a verifiable privacy-preserving federated learning scheme MVFL. MVFL leverages multi-key homomorphic encryption, allowing each user to independently select a key to encrypt their gradient information, which not only simplifies key distribution and management, but also reduces the risk of key leakage, thereby enhancing user privacy. Moreover, we employ the Chinese Remainder Theorem to reduce the computational cost during the verification phase, enabling users to independently and efficiently verify the correctness of the aggregated results. Furthermore, MVFL enables users to exit the training process at any time. Through security analysis and experiments on real datasets, we demonstrate that MVFL not only protects user privacy, but also exhibits satisfactory practical performance.</p>