The present invention provides a computer-implemented method of training an artificial neural network, ANN, on a remote host (110). In order to achieve a high level of accuracy of the ANN training, while at the same time preserving the privacy of the data used to train the ANN, the method comprises computing, by a trusted process (130) deployed in a trusted execution environment, TEE (120), on the remote host (110), a key-pair for a homomorphic encryption scheme and sharing, by the trusted process (130), the public key, PK, of the key-pair with an untrusted process (140) deployed on the remote host (110); and splitting the training procedure of the ANN between the untrusted process (140) and the trusted process (130), wherein the untrusted process (140) computes encrypted inputs to the neurons of the ANN by means of the homomorphic encryption scheme, while the trusted process (130) computes the outputs of the neurons based on the respective encrypted neuron inputs as provided by the untrusted process (140).