A Federated Learning Framework Using a Secure, Controllable and Efficient Multi-Key Homomorphic Encryption Scheme

Federated learning (FL) allows clients to cooperatively train a global model without sharing their sensitive training data. However, it is well known that the gradients uploaded by clients in the training processes of FL still will reveal the privacy of clients. Homomorphic Encryption (HE) has theoretical advantages to solve this problem, but its computational costs are considerably high for both the server and clients. Recently, the IND-CPA \(^{D}\) security definition for approximate HE and the corresponding solution have been proposed. However, the inserted Differential Privacy (DP) noise will affect the accuracy of the training model. Moreover, all messages are encrypted by HE with the same pair of public and secret keys by default cannot resist collusion attacks. To solve the above problems, we propose a novel FL framework for privacy-preserving, which uses our proposed CMK-CKKS (Controllable Multi-key CKKS) algorithm to protect messages during training, and combines the shuffle model to improve the model accuracy and reduce the communication costs. Furthermore, our framework improves controllability by dynamically adjusting the errors added. Experimental results show that the CMK-CKKS is not only efficient but also has very little effect on the model’s accuracy. It is worth noting that, our algorithm can effectively resist most attacks such as Chosen Plaintext Attack (CPA), Chosen Ciphertext Attack (CCA), and collusion attacks.