Secure aggregation of local learning model parameters is crucial for achieving privacy-preserving federated learning. This paper presents a novel and practical aggregation method that effectively combines the advantages of masking-based aggregation with those of homomorphic encryption-based techniques. Each node conceals its local parameters using a randomly selected mask, independently chosen, thereby eliminating the need for additional computations to generate or exchange mask values with other nodes. Instead, each node homomorphically encrypts its random mask using its own encryption key. During each federated learning round, nodes send their masked parameters and the homomorphically encrypted mask to the federated learning server. The server then aggregates these updates in an encrypted state, directly calculating the average of actual local parameters across all nodes without the necessity to decrypt the aggregated result separately. To facilitate this, we introduce a new multi-key homomorphic encryption technique tailored for secure aggregation in federated learning environments. Each node uses a different encryption key to encrypt its mask value. Importantly, the ciphertext of each mask includes a partial decryption component from the node, allowing the collective sum of encrypted masks to be automatically decrypted once all are aggregated. Consequently, the server computes the average of the actual local parameters by simply subtracting the decrypted total sum of mask values from the cumulative sum of the masked local parameters. Our approach effectively eliminates the need for interactions between nodes and the server for mask generation and sharing, while addressing the limitation of a single key homomorphic encryption. Moreover, the proposed aggregation process completes the global model update in just two interactions (in the absence of dropouts), significantly simplifying the aggregation procedure. Utilizing the CKKS (Cheon-Kim-Kim-Song) homomorphic encryption scheme, our method ensures efficient aggregation without compromising security or accuracy. We demonstrate the accuracy and efficiency of the proposed method through varied experiments on MNIST data.
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