Abstract: With the development of big data and cloud computing,the demand for cloud computing services is growing dramatically.When users apply for cloud computing services,their privacy data needs to be stored and computed on cloud platforms,which may cause leakage of private data.Homomorphic encryption allows direct computation on ciphertexts,and the decryption of the resulting ciphertext is the same as computing on plaintexts,so homomorphic encryption can protect users' private data.Here a framework for two parties in the semi-honest model is considered.The client encrypts the privacy data into ciphertext according to a homomorphic encryption scheme and sends it to the server,and the server uses the plain machine learning model to classify the encrypted data from the client.Finally,the server sends the encrypted classification result back to the client,and the client decrypts the classification result by itself.With the framework above,three machine learning classifiers,the hyperplane,decision tree,and k-nearest neighbor classifier,based on the Brakerski-Gentry-Vaikuntanathan(BGV) homomorphic encryption scheme are investigated.According to the characteristics of each classifier,different ciphertext data packaging strategies and calculation processes are designed with single-instruction-multiple-data (SIMD) technology,which significantly reduces the communication overhead between the client and the server.In the prediction phase,the hyperplane and decision tree classifiers achieve interaction-free,and the KNN classifier only needs one interaction.Moreover,the three classifiers are implemented with a homomorphic encryption library HElib.For several UCI public datasets,the hyperplane classifier can complete the privacy-preserving classification within tens of milliseconds to hundreds of milliseconds for a single sample,and the decision tree can complete it within tens of milliseconds.The prediction accuracy of the first two classifiers for ciphertext data exceeds 90%,and the two parties only need the communication cost of the client sending the encrypted private data to the server,and the server returns the encrypted classification label to the client.The k-nearest-neighbor classifier completes one sample's classification in about 4 seconds on average,and the prediction accuracy of ciphertext data is also more than 90%.In addition to the communication overhead of privacy data and classification labels,the two parties also need an additional round of intermediate calculation results between the server and the client to complete the classification.Compared with similar protocols based on homomorphic encryption,the proposed protocols have advantages in the number of communication rounds,prediction accuracy,and computational efficiency.

Key words: Homomorphic encryption, Secure multi-party computation, Privacy protection, Machine learning, HElib