Asymmetric dark matter (ADM) is an attractive framework relating the observed baryon asymmetry of the Universe to the DM density. A composite particle in a new strong dynamics is a promising candidate for ADM as the strong dynamics naturally explains the ADM mass in the GeV range. Its large annihilation cross section due to the strong dynamics leaves the asymmetric component to be dominant over the symmetric component. Its large self-scattering cross section may also explain the diversity of galactic rotation curves that is difficult to understand in the conventional collisionless DM. Such scenarios generically require some entropy transfer mechanism below the composite scale; Otherwise, their late-time cosmology is incompatible with observations. We show that a tiny kinetic mixing term between a dark photon and the visible photon is a promising example of the low-energy portal, by introducing a simple dark sector model. We also demonstrate that grand unifications in the dark and the visible sectors explain the origin of the tiny kinetic mixing.