This paper proposes "Zero-stop Authentication" system, which requires no intentional interactions between users and authentication applications. Our Zero-stop Authentication model simplifies the current complicated authentication process by automating detection of users and objects. Our challenge is to eliminate the necessity for users to wait for a moment to be authenticated without reducing security level of authentication. To accomplish such real time user authentication in a physical environment, user mobility needs to be modelled. This paper models and formulates the user mobility and time constraints as "1/N × 1/M model", considering user speed, sensor coverage areas, communication time between the sensors and the server, and processing time consumed by an authentication process. We also prototyped a library application based on 1/N × I/M model, and installed it into Smart Furniture  which is an experimental platform to examine feasibility of our model.