Electronic archives are now widely used in many different industries and serve as the primary method of information management and storage because of the rapid growth of information technology and mobile networks. To enhance the security of electronic archives in mobile networks, the research utilizes the federated learning mechanism to design a federated learning model based on homomorphic aggregation cryptographic signature scheme combined with mobile network management. The use of homomorphic encryption technology in the signing process of electronic archives enables the aggregation of multiple electronic file signatures into a single signature without exposing the data of the electronic archives. This reduces the computational and storage requirements for signature verification. At the same time, a secure aggregation signature scheme is used to ensure the integrity and security of the data in the aggregation process. A novel approach is presented in this study, whereby trusted federated learning models are innovatively combined with homomorphic aggregate signature technology. This integration ensures data integrity through aggregate signature schemes. The results showed that, under mobile network management, the longest encryption time of the trusted federated learning model was 52 ms, and the longest decryption time was 44 ms. The accuracy of the optimized learning model reached 97.49%, and the loss value was significantly reduced to 0.09. To summarize, the electronic archive security protection method based on homomorphic aggregation signature scheme effectively improves the archive data protection efficiency and security.