  A new approach to the generation structure of fermions is proposed. We
consider a brane configuration in which the brane intersection yields a
two-torus in the extra space. It is assumed that the two-torus is discretized
and is given by the torsion points of the elliptic curve over Q . We direct our
attention to the arithmetic structure of the elliptic curve with complex
multiplication (CM). In our approach the flavor symmetry including the R-parity
has its origin in the Galois group of elliptic curves with CM. We study the
possible types of the Galois group. The Galois group is shown to be an
extension of Z_2 by some abelian group. A phenomenologically viable example of
the Galois group is presented, in which the characteristic texture of fermion
masses and mixings is reproduced and the mixed-anomaly conditions are
satisfied.
