Wearable sensors enable to monitor patients in their everyday environments. However, since they generate highly personal data, their protection from misuse or unauthorized use is crucial. Under certain conditions, it is important to examine whether the data they generate uniquely describe their deployment environment. This can be used to certify the authenticity of the data. In this article, we uniquely identify persons based on the measurements of a wireless electrocardiogram (ECG) and motion sensors. We let 34 subjects perform seven different activities while synchronously sampling a five-lead wireless ECG, two 3-D accelerometers, and a 3-D gyroscope. Using both time- and frequency-domain features, we train a multilayer convolutional neural network (CNN) to achieve a classification accuracy exceeding 98%. Our model is able to uniquely classify 85% of the subjects with 100% accuracy, even though more than 82% of them have similar physical constitution (they are young people between the ages of 21 and 24, with a mean age of 22 years and standard deviation of 1.9 years). The activities we consider place very different demands on the body. To demonstrate this, we perform activity recognition using the same datasets and the model classifies the activities with an average accuracy of 92%.