  We propose a concealing-restoring system (CRS) for data on physical layer of
the OSI reference model. CRS conceals those data by disturbing them with some
random noises, and restores the data from the concealed ones to the original
ones by using the noise elimination based on a proper stochastic filtering
theory. Although we introduced the outline of the almost linear version of CRS
in our previous work [Fujii & Hirokawa, Math. Industry, Springer (2020)], we
explain its details, and study its nonlinearization to improve the security of
CRS in this paper.
