We propose a practical quantum cryptographic scheme which combines high information capacity, such as provided by high-dimensional quantum entanglement, with the simplicity of a two-dimensional Clauser-Horne-Shimony-Holt (CHSH) Bell test for security verification. By applying a state combining entanglement in a two-dimensional degree of freedom, such as photon polarization, with high-dimensional correlations in another degree of freedom, such as photon orbital angular momentum (OAM) or path, the scheme provides a considerably simplified route towards security verification in quantum key distribution (QKD) aimed at exploiting high-dimensional quantum systems for increased secure key rates. It also benefits from security against collective attacks and is feasible using currently available technologies.