Secure communication with the help of flat inputs for chaotic systems

Abstract In this paper, we explain how flatness (in particular, how constructing flat inputs) can be applied to secure communication systems via chaotic models. In order to send confidential messages, we use a transmitter whose dynamics are a flat control system steaming from a dynamical one (with no inputs) originally composed by two independent chaotic subsystems (a Chua and a Rossler circuit, resp.). We explain how from the original dynamical (chaotic) system we can construct a flat control system, the flatness property being achieved by adding control vector fields or, equivalently, inputs. Such inputs are called flat inputs in Waldherr and Zeitz (2008, 2010) since they lead to a flat control system. In our construction, adding inputs is done in a minimal way because they affect only three components of the original dynamical chaotic system. We show numerically that the chaotic behavior of the dynamical system is preserved for the control system (which is crucial for secure communication).