  We study one-dimensional topological superconductivity in the presence of
time-reversal symmetry. This phase is characterized by having a bulk gap, while
supporting a Kramers' pair of zero-energy Majorana bound states at each of its
ends. We present a general simple model which is driven into this topological
phase in the presence of repulsive electron-electron interactions. We further
propose two experimental setups and show that they realize this model at low
energies. The first setup is a narrow two-dimensional topological insulator
partially covered by a conventional s-wave superconductor, and the second is a
semiconductor wire in proximity to an s-wave superconductor. These systems can
therefore be used to realize and probe the time-reversal invariant topological
superconducting phase. The effect of interactions is studied using both a
mean-field approach and a renormalization group analysis.
