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We demonstrate that by using a recently proposed somewhat homomorphic encryption (SHE) scheme it is possible to delegate the execution of a machine learning (ML) algorithm to a compute service while retaining confidentiality of the training and test data. Since the computational complexity of the SHE scheme depends primarily on the number of multiplications to be carried out on the encrypted data, we devise a new class of machine learning algorithms in which the algorithm's predictions viewed as functions of the input data can be expressed as polynomials of bounded degree. We propose confidential ML algorithms for binary classification based on polynomial approximations to least-squares solutions obtained by a small number of gradient descent steps. We present experimental validation of the confidential ML pipeline and discuss the trade-offs regarding computational complexity, prediction accuracy and cryptographic security.