Privacy-Preserving Machine Learning Based On Homomorphic Encryption

Machine learning has been widely used and achieved great success in many fields,such as recommendation systems,medical prediction,and face recognition.Cloud computing allows anyone having access to the Internet to complete complex machine learning tasks.However,since the data must be uploaded to the cloud server before computing,It is becoming an urgent problem how to protect the privacy of the data while making use of machine learning services.In this paper we propose a verifiable neural network framework,which guarantees the privacy and availability of data when computing neural networks on cloud servers.Moreover,since malicious cloud servers are likely to return corrupted results to save costs,proof of learning algorithm is introduced into the neural network to verify the integrity of the training process.The diagonal packing method is used to encode and encrypt the parameter matrix to complete the linear transformation,which improves efficiency in forward propagation.We extend the diagonal packing method to a more general matrix form,so that the method is also applied to forward propagation and backward propagation to reduce the time complexity of the entire algorithm.In this paper we introduce the Proof of Learning algorithm into the privacy-preserving neural network.This allows users to verify the integrity of the entire training process,which is used to prevent malicious servers from returning corrupted results.This proof of learning does not require any changes to the original privacy-preserving neural network algorithm.Only the original training algorithm is needed to generate the proof and verify the proof.The computational cost of generating the proof can be ignored compared with the computational cost of training.In addition,this paper introduces a practical Byzantine fault tolerance mechanism to complete the verification process of distributed machine learning.It is enough for the cloud servers to verify each others’ proof.In this paper we implement another machine learning paradigm,Gaussian process to construct a privacy-preserving machine learning service.The word-wise homomorphic encryption scheme is used to improve the efficiency of matrix-vector operations on the ciphertext,The bitwise homomorphic encryption scheme is used to improve the accuracy of the kernel function.We propose a no-interactive machine learning service through the transformation between the two types of homomorphic encryption,We compare this method with the Gaussian process regression algorithm base on word-wise homomorphic encryption,It is proved that its accuracy is greatly improved and can meet the accuracy required by machine learning tasks.