The observed dark matter phenomenon is attributed to the presence of a gas of wormholes. We show that due to topological polarization effects, the background density of baryons generates non-vanishing values for wormhole rest masses. We infer basic formulae for the scattering cross-section between baryons and wormholes and equations of motion. Such equations are then used for the kinetic and hydrodynamic description of the gas of wormholes. In the Newtonian approximation, we consider the behaviour of density perturbations and show that at very large distances wormholes behave exactly like heavy non-baryonic particles, thus reproducing all features of cold dark matter models. At smaller galactic scales, wormholes strongly interact with baryons and cure the problem of cusps. We also show that collisions of wormholes and baryons lead to some additional damping of the Jeans instability in baryons.