  We calculate the Andreev conductance of a superconducting ring interrupted by
a flux-biased Josephson junction, searching for electrical signatures of
circulating edge states. Two-dimensional pair potentials of spin-singlet d-wave
and spin-triplet p-wave symmetry support, respectively, (chiral) Dirac modes
and (chiral or helical) Majorana modes. These produce h/e-periodic
magnetoconductance oscillations of amplitude \simeq (e^{2}/h)N^{-1/2}, measured
via an N-mode point contact at the inner or outer perimeter of the grounded
ring. For Dirac modes the oscillations in the two contacts are independent,
while for an unpaired Majorana mode they are phase locked by a topological
phase transition at the Josephson junction.
