This paper deals with hybrid dynamical systems in the context of cybersecurity and Cyber–Physical Systems. It is shown how the design of a cipher, called self-synchronizing stream cipher, can be recast as control-theoretic issues, in particular left inversion, flatness and structural analysis. From an automatic control point of view, the main contribution lies in a methodology to construct generic flat LPV systems. Beyond pure control theoretic matters, the design also addresses computational complexity and security concerns. Those considerations motivate a hybrid architecture involving switched automata. A Proof-Of-Concept example illustrates the design of a statistical self-synchronizing stream cipher and the way how it operates to encrypt data flows.