We propose creating for the first time a radiatively-limited single-photon source at telecommunication wavelength based on the Purcell interaction between a single erbium ion and an electromagnetic mode of a nano-tailored silicon nitride photonic-crystal cavity. Building on this achievement, we will furthermore show indistinguishability of photons emitted from two such sources using two-photon (Hong-Ou-Mandel) interference, and pioneer their use in a quantum key distribution protocol that employs a similar measurement. Our research requires merging light-matter interaction with rare-earth-doped crystals, cavity quantum electrodynamic in the solid-state, nano-fabrication, and quantum communication with photons. Being currently emerging and of fundamental nature, it will result in key enabling technology for a future quantum internet, which promises applications in the domains of secure communication, networked computing and distributed metrology that are impossible using conventional technology.