  We perform a pilot study of the perturbative renormalization of a
Supersymmetric gauge theory with matter fields on the lattice. As a specific
example, we consider Supersymmetric ${\cal N}{=}1$ QCD (SQCD). We study the
self-energies of all particles which appear in this theory, as well as the
renormalization of the coupling constant. To this end we compute,
perturbatively to one-loop, the relevant two-point and three-point Green's
functions using both dimensional and lattice regularizations. Our lattice
formulation involves the Wilson discretization for the gluino and quark fields;
for gluons we employ the Wilson gauge action; for scalar fields (squarks) we
use na\"ive discretization. The gauge group that we consider is $SU(N_c)$,
while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge
parameter, $\alpha$, are left unspecified.
  We obtain analytic expressions for the renormalization factors of the
coupling constant ($Z_g$) and of the quark ($Z_\psi$), gluon ($Z_u$), gluino
($Z_\lambda$), squark ($Z_{A_\pm}$), and ghost ($Z_c$) fields on the lattice.
We also compute the critical values of the gluino, quark and squark masses.
Finally, we address the mixing which occurs among squark degrees of freedom
beyond tree level: we calculate the corresponding mixing matrix which is
necessary in order to disentangle the components of the squark field via an
additional finite renormalization.
