The foreseen growing role of outsourced machine learning services is raising concerns about the privacy of user data. Several technical solutions are being proposed to address the issue. Hardware security modules in cloud data centres appear limited to enterprise customers due to their complexity, while general multi-party computation techniques require a large number of message exchanges. This paper proposes a variety of protocols for privacy-preserving regression and classification that (i) only require additively homomorphic encryption algorithms, (ii) limit interactions to a mere request and response, and (iii) that can be used directly for important machine-learning algorithms such as logistic regression and SVM classification. The basic protocols are then extended and applied to feed-forward neural networks.