Commutativity of subsystems (SSs) in cascade connected forms to form larger systems gets worthy to improve noise disturbance, stability, robustness and many other properties in system design. There is a huge amount of work on the subject of commutativity of linear time-varying (LTV) systems and the mentioned improvements; these are referenced in the introduction. In this paper, another benefit of commutativity property is investigated in detail and illustrated by examples. This benefit is the gain of a new and original method for hiding the original (possibly secret) signals when sending them from one local area to another. Switching, pseudo-commutativity, and power-spectrum which are important for communication channels are extensively studied. It is shown that switching used for increasing safeness and slight deformations in commutativity conditions hardly spoil to attain the mentioned benefit. Hence, the paper presents an original and alternative method in cryptology. The results are all validated by illustrative examples and Matlab simulation toolbox Simulink.