  We study the surface critical behavior of semi-infinite quenched random
Ising-like systems at the special transition using three dimensional massive
field theory up to the two-loop approximation. Besides, we extend up to the
next-to leading order, the previous first-order results of the
$\sqrt{\epsilon}$ expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917
(1992)]. The numerical estimates for surface critical exponents in both cases
are computed by means of the Pade analysis. Moreover, in the case of the
massive field theory we perform Pade-Borel resummation of the resulting
two-loop series expansions for surface critical exponents. The obtained results
confirm that in a system with quenched bulk randomness the plane boundary is
characterized by a new set of surface critical exponents.
