[en] It has been established that the security of quantum key distribution protocols can be severely compromised were one to permit an eavesdropper to possess a very limited knowledge of the random sources used between the communicating parties. While such knowledge should always be expected in realistic experimental conditions, the result itself opened a new line of research to fully account for real-world weak randomness threats to quantum cryptography. Here we expand of this novel idea by describing a key distribution scheme that is provably secure against general attacks by a post-quantum adversary. We then discuss possible security consequences for such schemes under the assumption of weak randomness. (paper)