Verifiable Privacy-Preserving Federated Learning Under Multiple Encrypted Keys

Federated learning is a distributed learning helpful approach for resolving data privacy concerns and eliminating data silos. Homomorphic encryption is a vital technology for preserving user privacy in federated learning, and current studies are mainly concentrated on a single-key environment. However, if one user key is exposed in a single-key environment, it implies that the whole system key has been revealed. To strengthen security, we should allow different participants of federated learning to choose different keys to encrypt their local models. The cloud server should finish model aggregation calculation on ciphertexts under different public keys. Besides, research in this area is insufficient to guarantee mobile users' data integrity verification and authentication in open channels. Therefore, this article proposes a privacy protection federated learning scheme VPFL based on the BCP cryptosystem, which can verify user identity and data integrity in a multikey environment. First, this scheme employs the BCP cryptosystem with double trapdoors for data encryption and transmission, enhancing the user's privacy security. Second, a method for verifying user data integrity and identity was created utilizing bilinear aggregate signatures and verifiable secret sharing. It can effectively eliminate some incorrect data of some users. Third, VPFL tolerates users dropping out during training while still guaranteeing high accuracy. Finally, theoretical analysis and experimental evaluation indicate that the proposed scheme is efficient and secure.