  A geometrically thick dusty torus in NGC 1068 has been unambiguously resolved
by an infrared interferometry telescope. This implies clouds composing the
dusty torus are undergoing supersonic collisions with each other. We show that
the collisions form strong non-relativistic shocks, which accelerate
populations of relativistic electrons. Torus reprocesses emission from
accretion disk into infrared band. We show that the energy density of the
infrared photons inside the torus is much higher than that of the magnetic
field in the clouds and the seed photons of inverse Compton scattering are
mainly from the infrared ones. The maximum energy of the relativistic electrons
can reach a Lorentz factor of $10^5$. We calculate the spectrum of the
synchrotron and inverse Compton scattering radiation from the electrons in the
torus. The relativistic electrons in the torus radiate non-thermal emission
from radio to $\gamma$-ray, which isotropically diffuses in the region of the
torus. We find the most prominent character is a peak at $\sim 0.5-1$ GeV. We
apply this model to NGC 1068 and find that the observed radio emission from the
core component $S_1$ can be explained by the synchrotron emission from the
relativistic electrons. We predict that there is a $\gamma$-ray emission with a
luminosity of $10^{40}$ erg/s peaking at $\sim 1$ GeV from the torus, which
could be detected by {\em Gamma-Ray Large-Array Space Telescope} in the future.
This will provide a new clue to understand the physics in the torus. The
non-thermal radiation from dusty torus may explain the radio emission from
Seyfert galaxies. The cosmological implications of the non-thermal emission to
the $\gamma$-ray background radiation have been discussed.
