  In order to theoretically understand dust properties in the circum-galactic
medium (CGM), we construct a dust evolution model that incorporates the
evolution of grain size distribution. We treat each of the galaxy and the CGM
as a one-zone object, and consider the mass exchange between them. We take into
account dust production and interstellar dust processing for the galaxy based
on our previous models, and newly incorporate sputtering in the hot phase and
shattering in the cool phase for the CGM. We find that shattering increases the
dust destruction (sputtering) efficiency in the CGM. The functional shape of
the grain size distribution in the CGM evolves following that in the galaxy,
but it is sensitive to the balance between sputtering and shattering in the
CGM. For an observational test, we discuss the wavelength dependence of the
reddening in the CGM traced by background quasar colors, arguing that, in order
to explain the observed reddening level, a rapid inflow from the CGM to the
galaxy is favored because of quick dust/metal enrichment. Small grain
production by shattering in the CGM also helps to explain the rise of dust
extinction toward short wavelengths.
