Statistical learning based fully homomorphic encryption on encrypted data

Statistical learning has been widely used in many fields, such as science, engineering and finance, to extract important patterns, trends, and understand "what the data say". Privacy of statistical learning, i.e., user and sensitive data, is significant problem of performing computation, especially outsourcing cloud computing. Some fully homomorphic encryption schemes can achieve computation on the encrypted data, but most of them are lack of efficiency. Fully homomorphic encryption based on learning with errors over rings (RLWE) supports a finite number of addition and multiplication on the encrypted data, thus can be viewed as the polynomial computation in cyclotomic fields. Computation on the encrypted data can be converted into computation associated with polynomial. So, fully homomorphic encryption from RLWE is very efficient relative to other schemes. Our contribution includes two aspects. Firstly, we show a scheme to represent the training and testing data for statistical learning. The proposed scheme firstly transforms the data into integer and then encodes them into polynomial so that the encryption, decryption and homomorphic operation can be performed efficiently. We also carefully choose the parameters of fully homomorphic encryption from RLWE to meet the requirement of efficiency. User only needs to upload the encrypted data to cloud server, and then the server trains and tests the encrypted data, returns the analysis and prediction results to user. Secondly, we present a comparison scheme on the encrypted data for statistical learning algorithms, which is security on the known plain-text attack and ciphertext only attack model.