  Kondo insulators have recently aroused great interest because they are
promising materials that host a topological insulator state caused by the
strong electron interactions. Moreover, recent observations of the quantum
oscillations in the insulating state of Kondo insulators have come as a great
surprise. Here, to investigate the surface electronic state of a prototype
Kondo insulator YbB$_{12}$, we measured transport properties of single crystals
and microstructures. In all samples, the temperature dependence of the
electrical resistivity is insulating at high temperatures and the resistivity
exhibits a plateau at low temperatures. The magnitude of the plateau value
decreases with reducing sample thickness, which is quantitatively consistent
with the surface electronic conduction in the bulk insulating YbB$_{12}$.
Moreover, the magnetoresistance of the microstructures exhibits a
weak-antilocalization effect at low field. These results are consistent with
the presence of topologically protected surface state, suggesting that
YbB$_{12}$ is a candidate material of the topological Kondo insulator. The high
field resistivity measurements up to $\mu_0H$ = 50 T of the microstructures
provide supporting evidence that the quantum oscillations of the resistivity in
YbB$_{12}$ occurs in the insulating bulk.
