Gait analysis is important for evaluating neurological disorders such as stroke and Parkinson's disease. Traditionally, healthcare professionals had to rely on subjective assessments (i.e., human-based) of gait which were time consuming and not very reproducible. However, with the advent of IoT and indeed more objective (e.g., measurement-based) assessment methods, gait analysis can now be performed more accurately and effectively. It is worth noting, however, that there are still limitations to these objective methods, especially the lack of privacy-preserving continuous data collection. To overcome this limitation, we present in this paper a privacy-by-design monitoring application for post-stroke patients to evaluate their gait before, during, and after a rehabilitation program. Gait measurements are collected by a mobile application that continuously captures spatiotemporal parameters in the background using the built-in smartphone accelerometer. Statistical techniques are then applied to extract general indicators about the performed activity, as well as some more specific gait metrics in real-time such as regularity, symmetry and walking speed. These metrics are calculated based on the detected steps while patients are performing an activity. Additionally, a deep learning approach based on an auto-encoder is implemented to detect abnormal activities in the gait of patients. These analyses provides both valuable insights and statistical information about the activities performed by the patient, and a useful tool for practitioners to monitor the progression of neurological disorders and detect anomalies. We conducted experiments using this application in real conditions to monitor post-stroke patients in collaboration with a hospital, demonstrating its ability to compute valuable metrics and detect abnormal events patient's gait.