  We develop a new method to investigate color superconductivity (CSC) on the
lattice based on the Thouless criterion, which amounts to solving the
linearized gap equation without imposing any ansatz on the structure of the
Cooper pairs. We perform explicit calculations at the one-loop level with the
staggered fermions on a $8^3 \times 128$ lattice and the Wilson fermions on a
$4^3 \times 128$ lattice, which enables us to obtain the critical
$\beta(=6/g^2)$ as a function of the quark chemical potential $\mu$, below
which the CSC phase is expected to appear. The obtained critical $\beta$ has
sharp peaks at the values of $\mu$ corresponding to the discretized energy
levels of quarks similarly to what was observed in previous studies on
simplified effective models. From the solution to the linearized gap equation,
one can read off the flavor and spatial structures of the Cooper pairs at the
critical $\beta$. In the case of massless staggered fermion, in particular, we
find that the chiral $\mathrm{U}(1)$ symmetry of the staggered fermions is
spontaneously broken by the condensation of the Cooper pairs.
