A None-zero Mean Noise Adding Mechanism in Differential Privacy in Federated Learning of Neural Networks Based on Fully Homomorphic Encryption and Greedy Average Block Kaczmarz

Abstract Scholars propose a noise adding mechanism in local differential privacy to provide a strict privacy guarantee to federated learning. However, there are two problems. On the one hand, the noisy data is close to its original value with high probability due to the zero mean random noise, leading to the information exposure. On the other hand, a large variance of the noise makes the estimated average of the parameters bias. To overcome the difficulties, we propose a framework of none-zero mean noise adding mechanism in differential privacy in federated learning of deep networks based on fully homomorphic encryption and greedy average block Kaczmarz method. In the work, a none-zero mean adding noise to original data is determined locally according to the correlation between the local and global distributions. Using fully homomorphic encryption and greedy average block Kaczmarz method, a de-noising weighting aggregation strategy is derived without decryption of the mean to guarantee the privacy of user by a third party. Moreover, the weight is generated complete randomly so that it is difficult to obtain the mean. As the means are different among the clients and unpredictable for attackers, the variance of the noise can be small. Experiments show that the proposed method provides a higher level of accuracy than the non-privacy-preserving federated learning, while it guarantee privacy for multi-party machine learning tasks.