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The authors demonstrate that, by using a recently proposed leveled homomorphic encryption scheme, it is possible to delegate the execution of a machine learning algorithm to a computing service while retaining confidentiality of the training and test data. Since the computational complexity of the homomorphic encryption scheme depends primarily on the number of levels of multiplications to be carried out on the encrypted data, they define 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. They propose confidential algorithms for binary classification based on polynomial approximations to least-squares solutions obtained by a small number of gradient descent steps.
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