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Mobile behavioral biometrics have become a popular topic of research, reaching promising results in terms of authentication, exploiting a multimodal combination of touchscreen and background sensor data. However, there is no way of knowing whether state-of-the-art classifiers in the literature can distinguish between the notion of user and device. In this article, we present a new database, BehavePassDB, structured into separate acquisition sessions and tasks to mimic the most common aspects of mobile Human-Computer Interaction (HCI). BehavePassDB is acquired through a dedicated mobile app installed on the subjects' devices, also including the case of different users on the same device for evaluation. We propose a standard experimental protocol and benchmark for the research community to perform a fair comparison of novel approaches with the state of the art. We propose and evaluate a system based on Long-Short Term Memory (LSTM) architecture with triplet loss and modality fusion at score level.