Chaotic systems, such as Lorenz systems or logistic functions, are known for their rapid divergence property. Even the smallest change in the initial condition will lead to vastly different outputs. This property renders the short-term behavior, i.e., output values, of these systems very hard to predict. Because of this divergence feature, lorenz systems are often used in cryptographic applications, particularly in key agreement protocols and encryptions. Yet, these chaotic systems do exhibit long-term deterministic behaviors-i.e., fit into a known shape over time. In this work, we propose a fast dynamic device authentication scheme that leverages both the divergence and convergence features of the Lorenz systems. In the scheme, a device proves its legitimacy by showing authentication tags belonging to a predetermined trajectory of a given Lorenz chaotic system. The security of the proposed technique resides in the fact that the short-range function output values are hard for an attacker to predict, but easy for a verifier to validate because the function is deterministic. In addition, in a multi-verifier scenario such as a mobile phone switching among base stations, the device does not have to re-initiate a separate authentication procedure each time. Instead, it just needs to prove the consistency of its chaotic behavior in an iterative manner, making the procedure very efficient in terms of execution time and computing resources.