This paper deals with an hybrid architecture involving LPV dynamical systems for encryption purpose, having in mind the context of cybersecurity. Such an hybrid architecture is motivated by the fact that it is a natural model, recast in a control-theoretic framework, of a so-called statistical self-synchronizing stream cipher. It is shown that flatness is central to guarantee the necessary synchronization between the cipher and the decipher. In this context, beyond synchronization, security must be a constraint to be taken into account as well. We especially focus on diffusion as a security criterion. The hybrid architecture is motivated to take advantage of both properties simultaneously. An illustrative example presents a numerical application and must be considered as a proof-of-concept before further investigation.